G/h

[linzedun]

Let G =Z4 external direct product Z4, H= {(0,0),(2,0),(0,2),(2,2)} and K=<(1,2)>. Is G/H isomorphic to Z4 or Z2 external direct product Z2? Is G/K isomorphic to either?

[matt grime]

What are the elements of G/H and what are their orders is anything of order 4? What is the order of K? hence the order of G/K (there are only two abelian groups of order 4).