The decay continues to oligarchy, by 550, and then to democracy, at 555b. The explanation for democracy comes at 557. At 559 the discussion shifts to the characters of individuals. They appear in the Odyssey bk. The argument proceeds from there, at 562, to tyranny.
Undisciplined desire is folly.
He claims at 572c-573b that democracy and tyranny are like undisciplined desire. The life of the tyrannical man is described at 574e-575. Note that the discussion jumps back from individuals to their corresponding cities, at 576-7. For the next couple of pages, the level of analysis switches back and forth. Refer to your conclusions about the sections on women noted above.