The Quran mentions the following 26 messengers by name.
In addition, the Quran also addresses the Patriarchs (al-asbāṭi / ٱلْأَسْبَاطِ) four times.
If we organize the messengers named in the Quran in the order understood by history according to the Bible, we can deduce the following order and rough timeline from Adam to Jesus.
Two individuals whose timelines are unclear are Idris and Job. Some speculate that Idris is Enoch, which would mean he predated Noah.
Additionally, we have the following messengers who were not of the Children of Israel, and from the analysis of the Quran, we can deduce that Hud and Saleh came before Abraham, but Shu’aib came after Abraham.
Clues to this come from the following verse. Firstly, we see that according to the specified order it appears that Ad who received Hud and Thamud who received Saleh were pre-Abraham, while Midyan was post Abraham.
9:70 Have they not learned anything from the previous generations; the people of Noah, ‘Ãd, Thamûd, the people of Abraham, the dwellers of Midyan, and the evildoers (of Sodom and Gomorrah)? Their messengers went to them with clear proofs. GOD never wronged them; they are the ones who wronged their own souls.
Also, in Suras 7, 11, and 26 when speaking about the communities that were annihiliated it all three occurences it speaks of them in the following order: Noah, Hud, Saleh, Lot (& Abraham), Shu’aib.
7:65 To ‘Ãd we sent their brother Hûd. He said, “O my people, worship GOD; you have no other god beside Him. Would you then observe righteousness?”
7:66 The leaders who disbelieved among his people said, “We see that you are behaving foolishly, and we think that you are a liar.”
7:67 He said, “O my people, there is no foolishness in me; I am a messenger from the Lord of the universe.
7:68 “I deliver to you my Lord’s messages, and I am honestly advising you.
7:69 “Is it too much of a wonder that a message should come to you from your Lord, through a man like you, to warn you? Recall that He made you inheritors after the people of Noah, and multiplied your number. Remember GOD’s blessings, that you may succeed.”
7:73 To Thamûd we sent their brother Sãleh. He said, “O my people, worship GOD; you have no other god beside Him. Proof has been provided for you from your Lord: here is GOD’s camel, to serve as a sign for you. Let her eat from GOD’s land, and do not touch her with any harm, lest you incur a painful retribution.
7:74 “ Recall that He made you inheritors after ‘Ãd, and established you on earth, building mansions in its valleys, and carving homes from its mountains. You shall remember GOD’s blessings, and do not roam the earth corruptingly.”
We also see the following statement from Shuaib to his people indicating that he came after Noah, Hud, Saleh, and Lot.
11:89 “And, O my people, do not be provoked by your opposition to me into incurring the same disasters as the people of Noah, or the people of Hûd, or the people of Sãleh; and the people of Lot are not too far from you.
Additionally, we see that God taught Abraham how to perform the Salat and give the Zakat (21:73), yet the Quran never specifies that Hud or Saleh observed either of these rites, yet we see that Shuaib did.
11:87 They said, “O Shu’aib, does your religion (salat) dictate upon you that we must abandon our parents’ religion, or running our businesses in any manner we choose? Surely, you are known for being clement, wise.”
Now, let’s see how we can order messengers according to the Quran.
Adam
All human beings (insan) are descendants of Adam
7:27 O children of Adam, do not let the devil dupe you as he did when he caused the eviction of your parents from Paradise, and the removal of their garments to expose their bodies. He and his tribe see you, while you do not see them. We appoint the devils as companions of those who do not believe.
The following verse informs us that Noah came before Abraham.
6:83 Such was our argument, with which we supported Abraham against his people. We exalt whomever we will to higher ranks. Your Lord is Most Wise, Omniscient.
6:84 And we granted him Isaac and Jacob, and we guided both of them. Similarly, we guided Noah before that, and from his descendants (we guided) David, Solomon, Job, Joseph, Moses, and Aaron. We thus reward the righteous.
According to the Bible, Lot was Abraham’s nephew. The Quran doesn’t confirm this but shows that they were contemporaries. When the angels went to Abraham to tell him that his wife was going to bear a son, they also informed him that they were going to annihilate Sodom.
29:31 When our messengers went to Abraham with good news (about Isaac’s birth), they also said, “We are on our way to annihilate the people of that town (Sodom). For its people have been wicked.”
29:32 He said, “But Lot is living there.” They said, “We are fully aware of everyone who lives in it. We will of course save him and his family, except his wife; she is doomed.”
14:35 Recall that Abraham said, “My Lord, make this a peaceful land, and protect me and my children from worshiping idols.
14:36 “My Lord, they have misled so many people. As for those who follow me, they belong with me. As for those who disobey me, You are Forgiver, Most Merciful.
14:37 “Our Lord, I have settled part of my family in this plantless valley, at Your Sacred House. Our Lord, they are to observe the Contact Prayers (Salat), so let throngs of people converge upon them, and provide for them all kinds of fruits, that they may be appreciative.
14:38 “Our Lord, You know whatever we conceal and whatever we declare— nothing is hidden from GOD on earth, nor in the heavens.
14:39 “ Praise be to GOD for granting me, despite my old age, Ismail and Isaac. My Lord answers the prayers.
In the following verses, we see that Abraham was granted Isaac and Jacob and that before him was Noah.
6:83 Such was our argument, with which we supported Abraham against his people. We exalt whomever we will to higher ranks. Your Lord is Most Wise, Omniscient.
6:84 And we granted him Isaac and Jacob, and we guided both of them. Similarly, we guided Noah before that, and from his descendants (we guided) David, Solomon, Job, Joseph, Moses, and Aaron. We thus reward the righteous.
29:27 We granted him (Abraham) Isaac and Jacob, we assigned to his descendants prophethood and the scriptures, we endowed him with his due recompense in this life, and in the Hereafter he will surely be with the righteous.
2:133 Had you witnessed Jacob on his death bed; he said to his children, “What will you worship after I die?” They said, “We will worship your god; the god of your fathers Abraham, Ismail, and Isaac; the one god. To Him we are submitters.”
19:58 These are some of the prophets whom GOD blessed. They were chosen from among the descendants of Adam, and the descendants of those whom we carried with Noah, and the descendants of Abraham and Israel, and from among those whom we guided and selected. When the revelations of the Most Gracious are recited to them, they fall prostrate, weeping.
In the following verse Joseph states that his ancestors.
12:38 “And I followed instead the religion of my ancestors, Abraham, Isaac, and Jacob. We never set up any idols beside GOD. Such is the blessing from GOD upon us and upon the people, but most people are unappreciative.
After Joseph was given kingship (12:101) of Egypt he had his father and all this brothers come to Egypt. This marks the start of the Children of Israel in Egypt.
12:93 “Take this shirt of mine; when you throw it on my father’s face, his vision will be restored. Bring your whole family and come back to me.”
12:94 Even before the caravan arrived, their father said, “I can sense the smell of Joseph. Will someone enlighten me?”
12:95 They said, “By GOD, you are still in your old confusion.”
12:96 When the bearer of good news arrived, he threw (the shirt) on his face, whereupon his vision was restored. He said, “Did I not tell you that I knew from GOD what you did not know?”
12:97 They said, “Our father, pray for our forgiveness; we were wrong indeed.”
12:98 He said, “I will implore my Lord to forgive you; He is the Forgiver, Most Merciful.”
12:99 When they entered Joseph’s quarters, he embraced his parents, saying, “Welcome to Egypt. GOD willing, you will be safe here.”
12:100 He raised his parents upon the throne. They fell prostrate before him. He said, “O my father, this is the fulfillment of my old dream. My Lord has made it come true. He has blessed me, delivered me from the prison, and brought you from the desert, after the devil had driven a wedge between me and my brothers. My Lord is Most Kind towards whomever He wills. He is the Knower, the Most Wise.”
Moses Sent to Pharoah to Free the Children of Isreal
17:101 We supported Moses with nine profound miracles—ask the Children of Israel. When he went to them, Pharaoh said to him, “I think that you, Moses, are bewitched.”
20:47 “Go to him and say, ‘We are two messengers from your Lord. Let the Children of Israel go. You must refrain from persecuting them. We bring a sign from your Lord, and peace is the lot of those who heed the guidance.
7:142 We summoned Moses for thirty nights, and completed them by adding ten.* Thus, the audience with his Lord lasted forty nights. Moses said to his brother Aaron, “Stay here with my people, maintain righteousness, and do not follow the ways of the corruptors.”
2:246 Have you noted the leaders of Israel after Moses? They said to their prophet, “If you appoint a king to lead us, we will fight in the cause of GOD.” He said, “Is it your intention that, if fighting is decreed for you, you will not fight?” They said, “Why should we not fight in the cause of GOD, when we have been deprived of our homes, and our children?” Yet, when fighting was decreed for them, they turned away, except a few. GOD is aware of the transgressors.
2:247 Their prophet said to them, “GOD has appointed Taloot (Saul) to be your king.” They said, “How can he have kingship over us when we are more worthy of kingship than he; he is not even rich?” He said, “GOD has chosen him over you, and has blessed him with an abundance in knowledge and in body.” GOD grants His kingship to whomever He wills. GOD is Bounteous, Omniscient.
2:248 Their prophet said to them, “ The sign of his kingship is that the Ark of the Covenant will be restored to you, bringing assurances from your Lord, and relics left by the people of Moses and the people of Aaron. It will be carried by the angels. This should be a convincing sign for you, if you are really believers.”
2:249 When Saul took command of the troops, he said, “GOD is putting you to the test by means of a stream. Anyone who drinks from it does not belong with me—only those who do not taste it belong with me—unless it is just a single sip.” They drank from it, except a few of them. When he crossed it with those who believed, they said, “ Now we lack the strength to face Goliath and his troops.” Those who were conscious of meeting GOD said, “Many a small army defeated a large army by GOD’s leave. GOD is with those who steadfastly persevere.”
2:250 When they faced Goliath and his troops, they prayed, “Our Lord, grant us steadfastness, strengthen our foothold, and support us against the disbelieving people.”
2:251 They defeated them by GOD’s leave, and David killed Goliath. GOD gave him kingship and wisdom, and taught him as He willed. If it were not for GOD’s support of some people against others, there would be chaos on earth. But GOD showers His grace upon the people.
David → Solomon
27:15 We endowed David and Solomon with knowledge, and they said, “Praise GOD for blessing us more than many of His believing servants.”
27:16 Solomon was David’s heir. He said, “O people, we have been endowed with understanding the language of the birds, and all kinds of things have been bestowed upon us. This is indeed a real blessing.”
3:35 The wife of Amram said, “My Lord, I have dedicated (the baby) in my belly to You, totally, so accept from me. You are Hearer, Omniscient.”
3:36 When she gave birth to her, she said, “My Lord, I have given birth to a girl”—GOD was fully aware of what she bore—”The male is not the same as the female. I have named her Mary and I invoke Your protection for her and her descendants from the rejected devil.”
3:37 Her Lord accepted her a gracious acceptance, and brought her up a gracious upbringing, under the guardianship of Zachariah. Whenever Zachariah entered her sanctuary he found provisions with her. He would ask, “Mary, where did you get this from?” She would say, “It is from GOD. GOD provides for whomever He chooses, without limits.”
3:38 That is when Zachariah implored his Lord: “My Lord, grant me such a good child; You are the Hearer of the prayers.”
3:39 The angels called him when he was praying in the sanctuary: “GOD gives you good news of John; a believer in the word of GOD, honorable, moral, and a righteous prophet.”
3:45 The angels said, “O Mary, GOD gives you good news: a Word from Him whose name is ‘The Messiah, Jesus the son of Mary.’ He will be prominent in this life and in the Hereafter, and one of those closest to Me.