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parliamenterians and royalists
It depends on which civil war you're talking about. In 1455-1485, the House of Lancaster and the House of York fought in the Wars of the Roses. The victor was Henry Tudor (of Lancaster), who married Elizabeth of York, thus uniting the warring houses into one House of Tudor (which ruled for 117 years).
In 1642-1651, it was the Parliamentarians (nicknamed "Roundheads") and the Royalists (nicknamed "Cavaliers") who fought. Oliver Cromwell led the New Model Army to victory. In the end, Charles I was executed, and a Puritan society was formed under Cromwell. Cromwell established a commonwealth (or a republic), which was later abolished when the English people called for Charles II to return to England and rule, in an event known as the "Restoration".