To me, the most obvious one of these is the conflict between Mrs. Dubose and Jem and the way that that plays out.
Mrs. Dubose is always picking on Jem and Scout, saying bad things about them and about their father. Finally, Jem has had enough of it and he destroys her flower beds. After he does this, Atticus forces him to go to Mrs. Dubose's home and read to her for an hour a day. This is where we find out that she is dying and is trying to get off her morphine addiction so she can die on her own terms.
Another subplot that comes to my mind is Scout's conflicts with the education system and her own gender. Scout does a lot of growing over the summer and through the school year. One of the challenges that she faces is the fact that Atticus has already taught her how to read, and this gets her in trouble at school because her teacher does not think that Atticus is teaching her the correct way. This says a great deal about the history of our educational system and the fact that it values conformity.
Along the same lines, society valued (and, to an extent still values) gender conformity. Scout is at odds with her gender for she plays with the boys and is a tomboy. She prefers pants to dresses, much to the chagrin of her aunt, and solves her problems at school with her fists.
The idea of being a free thinker, individuality, is a theme in the novel as much so as the concept of groweing up is a theme. It is played out through scout in both of these subplots, giving ther reader a character with whom many of us can identify.
While Boo Radley is an important character who figures into the entire narrative of To Kill a Mockingbird, the subplot that involves the superstitions of the children and their attempts to overcome them figures in as a minor episodes.
As Scout and Walter walk home for dinner after school, she tells him "this is where a haint lives." Later, Dill dares Jem to do such things as run up to the Radley house and look in the window and they are involved in play-acting in which they recreate the defining scissor scene.
This subplot focuses on the games and tricks that Dill, Jem and Scout engage in as they toy with the fear and excitement of a "haint."
One minor conflict that helps support the major racial conflict is that of Mr. Dolphus Raymond, who has chosen to live with the blacks. In order to help the whites reconcile their feelings about this situation, Mr. Raymond feigns alcoholism by carrying around a bottle of Coca-Cola wrapped in a brown paper bag as one would wrap a bottle of beer or liquor.
The story of Jem and Scout's summer neighbor, Dill, immediately comes to mind. Dill is not a particularly important character, but the various subplots concerning his unusual family life reoccur throughout the novel. Dill mostly serves as a pal of the Finch children--indeed, he seems to be their closest friend even though he only lives in Maycomb for about 10 weeks per year. Specifically, one of the subplots concerns Dill's escape from his home in Meridian, Mississippi. After running away, he turns up--tired, dirty and hungry--under Scout's bed.
Main plot- Boo Radley--> from the beginning the children had started to make up games, to the very end where Boo Radley saves Jem's and Scout's lives.\
Subplot- Tom Robinson trial
Subplot- Tim Johnson
Subplot- Education(in the beginning of the novel)