group G = Z_4 x Z_4
Let H be a subgroup of G of order 4. Explain why H is normal in G and why the quotient group of G by H is Abelian and of order 4.
Of course this is true since the quotient group will be the image of the canonical homomorphism and the image of an abelian group under a homomorphism is always abelian.
The OP will have to decide which he likes better I guess.