Questions around the number of subgroups of a $p$-group

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 $G$ ?)

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