# gr.group theory – Structures of subgroups of a finite abelian p-group


Let $$H$$ be a subgroup of $$G$$. Then $$H$$ is of the same form with less or equal number of factors.

Does there exist a choice of generators $${x_1,ldots,x_r}$$ of $$G$$ as above such that $$H$$ is a product of subgroups of $$la x_jra$$?

If it is not true, is there an easy counterexample?