I need help with the following problem:
Let G be a finite group, H and N are subgroups of G such that N is normal, and |N| and [G:N] are relatively prime. Show that if H is contained in N, then |H| divides |N|.
I would really help anyone's help on this. Thank you in advance
Thank you for your response. In regards to your comment, I was thinking about using the Lagrange's theorem too. So if we assume that H is contained in N, we would have to show that H is a subgroup of N. If this is true, then we can conclude that |H| divides |N|, right? But, I already tried to prove that H is a subgroup of N, and I am kinda stuck now.