8.3, due April 11

I feel like these theorems (once i understand/use them more) will help me to  figure out how many subgroups a group has. This would be awesome because right now I have no idea how to tell if I have found them all or not. I'm not really sure how the second sylow theorem is particularly useful (even after reading the examples). Even though I feel pretty unsure about this section, things usually come together by the time I do the homework, so i think it'll be okay.