I don't know how to go about this. So the group has $\displaystyle p^{n}$ elements and I have to somehow use cosets or Langrage's theorem, but I really don't understand much of this. And I can't use Cauchy's Theorem, it uses concepts I haven't covered yet. Any help would be appreciated.

Edit: So I know by Lagrange's theorem that the order of a subgroup of $\displaystyle G$ must divide the order of $\displaystyle G$, so given $\displaystyle g\in G$, the cyclic subgroup $\displaystyle <g>$ has order that divides $\displaystyle p^{n}$. At this part, I'm stuck.