you cannot be that beginner if you're in normalizers of subgroups...at least 3-4 hours of class?

Anyway, what's the definition of subgroup? And how do we check whether a given set is a subgroup of a given group? Begin with this and try to prove (1), and now apply the definition of normal subgroup of a group to prove (2) and (3).

(4) is, perhaps, the "hardest", as it actually asks from you to prove maximality of something, but let's first see if you can handle the above.

Tonio