Short problem on group theory q.1

[betty2301]

short problem on group theory q.1[urgent due in 13 hrs]

due now

 

[jbunniii]

Homework Statement

Let G be a finite group, N is a normal subgroup in G and H$\leq$ G. Prove that if |H| and
(G : N) are coprimes, then H$\leq$ N

Let $\phi : G \rightarrow G/N$ be the canonical map $g \mapsto gN$, and consider $\phi(H)$.