I know that a group H has exactly one 3-Sylow subgroup L. Also, |H|=30. And |M|=15 is normal.

Now I should consider the quotient group H/M and prove that $\displaystyle \forall a \in H$ $\displaystyle a^2 \in M$. And then that each element of odd order in H is in M.

Can someone help me please?