Prove that every group of order 9 has an element of order 3.
So my attempt at this proof was:
Pf. Let $G$ be a group of order 9. Then $\exists H$ such that $H$ is a subgroup of $G$ and $|H|$ $\vert$ $|G|$. Thus $|H|= $ 1,3, or 9 by Lagrange's Theorem.
I know this proof is not complete, but I am unsure on how to proceed from here.