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Suppose that $G$ is an Abelian group of order $16$ with an element of order $8$ and (at least) two elements of order $2$.

Determine $G$ up to isomorphism.

$\mathbb{Z}_2\times \mathbb{Z}_2\times \mathbb{Z}_4$

$\mathbb{Z}_8\times \mathbb{Z}_2$

$\mathbb{Z}_{16}$

$\mathbb{Z}_4\times \mathbb{Z}_4$