This section really isn't that bad, the trickiest part is probably just keeping straight when certain things hold for normal subgroups and thus remembering that sometimes they don't hold (multiplying congruence classes). I think it's cool when nonabelian subgroups end up being normal because you can't tell that they will be right off the bat. Also, the equivalence statements are pretty easy to use, and are not even THAT difficult to prove.
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