Question: Suppose G is a group with |G| = 30 and N is a normal subgroup of G. WHat are the possible orders for the group G/N

I know by Lagrange's theorem that |N| divides |G| so |N| = {1,2,3,5,10,15,30}.

I also know that |G/N| / |N| = |G| / |N| so I believe |G/N| = |N| = {1,2,3,5,10,15,30}

Am I off base or is there a better way to approach this?

Thanks