Hi, my problem-problem goes like this:

Prove that if H is a normal subgroup of G with prime index p, then for all subgroups K of G

i)K is a subgroup of G, or

ii)G=HK

I have a feeling that an isomorphism theorem is in order, but every arrangement I've tried fails...or else I'm just not seeing it. Any suggestions would be warmly appreciated. Also, in the event that I ever come back with another question, how should I get started with Latex?