Shakespeare's King Lear, like anything by Shakespeare, has very complex character relationships. This diagram is intended to help readers visualize the play.
What follows is a short explanation of how the various characters betray eachother.
Lear's excessive pride leads him to banish his daughter Cordelia for not expressing her love for him. His trusty servant Kent attempts to defend her, only to be banished himself.
Both Goneril and Regan betray the trust their father bestowed upon them when he entrusted them with his kingdom. They both disrespect him and seek his death.
Albany & Goneril
Goneril loves the evil Edmund, and so plots against the life of her husband Albany. She writes to Edmund via Oswald with these instructions to kill Albany:
Let our reciprocal vows be remembered. You have
many opportunities to cut him off: if your will
want not, time and place will be fruitfully offered.
There is nothing done, if he return the conqueror:
then am I the prisoner, and his bed my goal; from
the loathed warmth whereof deliver me, and supply
the place for your labour.
'Your--wife, so I would say--
Albany, however, intercepts the letter and so foils her plans.
Edmund & Edgar
Edmund convinces his father that Edgar was implicated on a plot on his life. He fakes a letter by Edgar saying
This policy and reverence of age makes
the world bitter to the best of our times; keeps
our fortunes from us till our oldness cannot relish
them. I begin to find an idle and fond bondage
in the oppression of aged tyranny; who sways, not
as it hath power, but as it is suffered. Come to
me, that of this I may speak more. If our father
would sleep till I waked him, you should half his
revenue for ever, and live the beloved of your
Gloucester is fooled by the deception, and banishes innocent Edgar.
Edmund & Gloucester
Gloucester dilvuges in his son Edmund that the army of France is preparing an invatsion. Edmund betrays this confidence by telling all to the Duke. He explains that by creating the downfall of his father, he will move up in power.
This courtesy, forbid thee, shall the duke
Instantly know; and of that letter too:
This seems a fair deserving, and must draw me
That which my father loses; no less than all:
The younger rises when the old doth fall.