There are plenty of conflicts in The Great Gatsby by F. Scott Fitzgerald, which is undoubtedly one of the reasons the novel has remained so popular over time. All conflicts can be classified as either internal (those conflicts which a character experiences within his own mind, heart, or conscience) or external (those conflicts which a character has with elements which are outside of himself), and both kinds are evident on this novel.
The primary conflict in this story centers around Jay Gatsby. He was born Jay Gatz in North Dakota and lived his early years in significant poverty. Gatz always felt he was destined for something more (as evidenced by the lists he made about how to improve himself), which puts him in a kind of conflict with both himself and society. In his experiences with Dan Cody, Gatz is in conflict with the women who take advantage of his friend; when he changes his name and his life he leaves that conflict behind.
Gatsby loves Daisy but is too poor and lacks the pedigree to marry her, which is another kind of conflict with society and with Daisy. This time Gatsby does not change his name, but he does begin a course of action which makes him rich but also puts him in conflict with society because his actions are illegal. His primary internal conflict is the love he has for Daisy. When he does finally win her, being with her is not what he had envisioned for so long. She could not live up to his unrealistic expectations and ideals. His primary external conflict, obviously, is with Daisy's husband Tom.
Daisy has two significant conflicts. The first is external, and that conflict is with her philandering (cheating) husband. Of course his infidelity bothers her (thus the conflict), but it is not as much of a conflict as many other women would have had in her situation. She has the ability to leave, yet she stays. Her internal conflict is with Gatsby. Though she loved him, she was unwilling to marry him because he did not meet the standards set by her parents and, evidently, by herself. She could have run away with him, and even on the night before her wedding to Tom she seems to love Gatsby, drunkenly claiming she has "chang' her mine!"
Despite this internal conflict, she marries the "brute," Tom, despite knowing what kind of man he is. When she and Gatsby renew their relationship, she feels no conflict--until she is forced to choose. Then what a conflict she has.
Jordan should feel an internal conflict about cheating at her sport, but she does not.
Tom is in conflict with everyone because he is arrogant and aggressive. He treats everyone badly, even Myrtle. His ugliest conflict is perhaps with Gatsby. Even though it is short-lived, it is his aggressive feelings for Gatsby that compel Tom to tell Wilson where to find Gatsby, knowing that Wilson wants to kill Gatsby.
Myrtle is in constant conflict with her circumstances and certainly her husband. From the moment she discovered that he borrowed the suit she was so impressed by, Myrtle's life was in turmoil in nearly every way.
Wilson is not conflicted until he discovers his wife has been having an affair and then again when Myrtle is killed. Then all Wilson wants is to get revenge on the man he assumes wronged him.
Nick's conflicts are interesting. While he hates everything Gatsby represents, he also says:
“You're worth the whole damn bunch put together!"
In the end, his conflicts are all focused on what he calls "careless people," such as Tom and Daisy.