This is a great question. The longest speech that Haemon offers to Creon is found in the lines 765-810. The content and form of this speech is masterful.
It is filled with tact and wisdom. Here are some of the rhetorical points.
It starts off with a logical point. It praises man for his ability to reason and come to rational conclusions. I suspect Haemon starts this way to show that his father's decisions are not rational at this point. In addition, he offers a perspective on what the people of the town are saying. In other words, he is giving the collective wisdom of the town. In short, Antigone does not deserve death; rather she deserve a crown for her piety and faithfulness to her dead brother.
The speech is also filled with pathos as he paints a picture of Antigone's deceased brother dead in the streets, left for the dogs. No one deserves this horrible end. An honorable burial is what is proper.
Finally, he appeals to his father to change and embrace a course of wisdom. He also confesses his loyalty to his father.