Yet another confusing chapter that I couldn't spend enough time in. Overall, the Sylow Theorems just relate to subgroups of prime, and prime-power, order. Very generally, you can use the Sylow Theorems themselves to determine isomorphism and whether or not a group is a direct product of other cyclic groups.
That was the last of group theory! I'm about to submit my group theory assignment, and I can tell I'll have a lot to write about once that is returned. Next up, is the third book of the set, "Numbers and Rings".