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The major plot is the betrayal of King Lear by his two elder daughters Goneril and Regan, and his banishment of the daughter who loves him. The subplot is found in the similarity of the the Earl of Gloucester's story and his illegitimate son Edmund's betrayal.
The subplot supports the main plot. It reiterates the theme that fathers should be wary of children who flatter them too much...... and should not base this misinterpretation on their reaction to the children who truly love them. The second part of the subplot's relation comes in the way the play is resolved. King lear's story is a complete tragedy; the Earl's story has a positive although sad ending.