For ten points, name this clan that won the Gempei war, in which they defeated the rival Taira clan.
A general from this clan was defeated at the Battle of Sunomatagawa. One leader of this clan was assisted by the monk Benkei, whom he had earlier defeated in a duel. One leader of this clan committed suicide after his destruction of a bridge failed to prevent the enemy from seizing a temple at Uji. This clan claimed descent from Emperor Seiwa, leading them also being called the Genji. This clan was eventually forced to grant the title of shikken, or regent, to members of the Hojo clan. Earlier, this clan was supported by Emperor Go-Shirakawa and had established the first bakufu by winning the Battle of Dan-no-ura. For ten points, name this clan that won the Gempei war, in which they defeated the rival Taira clan.
A general from this clan was defeated at the Battle of Sunomatagawa.
{Minamoto} Clan [accept {Seiwa Genji} before mention]