Identify all finitely generated Abelian groups of order 500 that have exactly 3 elements of order 2 and identify those elements.

I think that finitely generated Abelian groups of order 500 are:

$\displaystyle \mathbb{Z}_2\oplus \mathbb{Z}_2\oplus\mathbb{Z}_5\oplus\mathbb{Z}_5\o plus\mathbb{Z}_5\$

$\displaystyle \mathbb{Z}_4\oplus\mathbb{Z}_5\oplus\mathbb{Z}_5\o plus\mathbb{Z}_5\$

$\displaystyle \mathbb{Z}_2\oplus \mathbb{Z}_2\oplus\mathbb{Z}_5\oplus\mathbb{Z}_{25 }\$

$\displaystyle \mathbb{Z}_2\oplus \mathbb{Z}_2\oplus\mathbb{Z}_{125}$

$\displaystyle \mathbb{Z}_4\oplus\mathbb{Z}_5\oplus\mathbb{Z}_{12 5}$

$\displaystyle \mathbb{Z}_4\oplus \mathbb{Z}_{125}$

Is this correct?

And if it is, which ones have exactly 3 elements of order 2?

Any help or hint is appreciated.