The most difficult part of this material was understanding the concept of the index of H in G and also Lagrange's Theorem. The concept of congruence with subgroups doesn't quite make sense to me which is why the rest of these concepts aren't quite clicking. Also it talks about right cosets but not left cosets...are there left cosets and if there are do they have the same properties.
The most interesting part of this section for me was relating all of the similar properties to rings and integers. I also found it interesting that you can even define congruence when you mod out by a subgroup. This idea was really interesting to me, however it still doesn't quite make sense.
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