The study of symmetry: groups, subgroups, homomorphisms, group actions.

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Whether two quotients of $\mathbb{Z}^2$ are isomorphic.

Let $H_1$ be the subgroup of $\mathbb{Z}^2$ generated by $\{(1,2),(4,1)\}$, let $H_2$ be the subgroup of $\mathbb{Z}^2$ generated by $\{(3,2),(1,3)\}$. Is it true that $\mathbb{Z}^2/H_1\cong ...