Let $G$ pe a $p$ group. I have to show that
- the number of nonnormal subgroups is divisible by $p$
- the number of subgroups differs from the number of normal subgroups by a power of $p$.
Are there any theorem that can help me to prove this ? We have discussed the Sylow theorems but I don't know how to apply them - if those are the theorems I need. (Does this theorem also hold for infinite groups $G$ ?)