While the main plot concern of a cozy is to solve the mystery and unmask the murderer, subplots are necessary. They add depth, character development, and color. Subplots reveal character and relationships. They can increase tension or slow down pacing. Since cozies are usually written in series, subplots often continue from one book to another. Close friendships, enmities and romance are all examples of subplots.
Subplots can also develop into future main plots. In my Haunted Library mystery series, Carrie's best friend Angela gets engaged. Her wedding will take place in book five of the series, where someone will be murdered.
Another subplot revolves around Carrie's nemesis, Dorothy Hawkins, the nasty reference librarian. Dorothy resents Carrie because she believes erroneously that she should have become the head of programs and events, not Carrie. In Buried In The Stacks, Dorothy is murdered and solving the murder becomes part of the major plot.
Carrie's relationship with her father is a subplot in Read and Gone. Jim Singleton leaps back into her life after an absence of many years and asks Carrie to help him retrieve money from one of his partners in crime. Horrified, Carrie refuses. She thinks that's the end of the matter until her father becomes a suspect in the man's murder. Knowing her father is no killer, she sets out to prove his innocence. Their relationship goes through various changes as Carrie investigates the murder.
Subplots often involve activities and events that take place in the town where the sleuth lives and works. In Buried in the Stacks, the library becomes a refuge for many homeless people who need a warm place to stay during the day. Wanting to do something positive about the problem, Carrie gets involved in the creation of Haven House, a day center for the homeless.
The number of possible subplots is endless and as varied as a writer's imagination will allow.