Let $|G| = pq^n$ for $p primes and $n$ is in the natural numbers
a) Show there is $H$ a normal subgroup of $G$ with $|H|=q^n$
b) If $P$ is a normal subgroup of $G$ with $|P| = p$, show that for any $m$ with $m$ divides $|G|$, there is $H_m$ (a subgroup of $G$) with $|H_m| =m$.
I am completely lost on how to start this, so any help would be appreciated, thanks!