No answer to this question is complete without including Jude 1:7:
Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire.
Clearly the "example" the Lord intended to set by their destruction included warning against their sins of fornication and "going after strange flesh", which is logically corroborated by the fact that their men tried to rape holy men in Genesis 19.
The fact that they were determined to do so by force and violence is another grievous sin; the Earth being filled with violence is given by the Lord as a reason why He brought the waters of the Flood upon mankind to drown all flesh except for Noah and those who were safe aboard the Ark (Genesis 6:11).
There is yet another reference that correlates haughtiness, lust, and warranting destruction:
Because the daughters of Zion are haughty, and walk with stretched forth necks and wanton eyes, walking and mincing as they go, and making a tinkling with their feet: Therefore the Lord will smite ... (Isaiah 3:16-17)
In the same chapter, the Lord says:
The shew of their countenance doth witness against them; and they declare their sin as Sodom, they hide it not. Woe unto their soul! for they have rewarded evil unto themselves.
(Interestingly, as an aside, this says that the evidence of the sin of Sodom is visible in one's countenance.)
This answer could go on and on but I believe these examples are sufficient to demonstrate the point.
Truly, detestable things come in hordes, and it might be difficult to enumerate them
all, but in each of these verses we have a sampling.