How many (non-isomorphic) abelian groups of order $200$ are there?

Question

I used the fundamental theorem of finite abelian groups.

$\mathbb{Z}_{2} \times \mathbb{Z}_{2} \times \mathbb{Z}_{2} \times \mathbb{Z}_{5} \times \mathbb{Z}_{5}$

$\mathbb{Z}_{2} \times \mathbb{Z}_{2} \times \mathbb{Z}_{2} \times \mathbb{Z}_{25}$

$\mathbb{Z}_{2} \times \mathbb{Z}_{4} \times \mathbb{Z}_{5} \times \mathbb{Z}_{5}$

$\mathbb{Z}_{2} \times \mathbb{Z}_{4} \times \mathbb{Z}_{25}$

$\mathbb{Z}_{8} \times \mathbb{Z}_{5} \times \mathbb{Z}_{5}$

$\mathbb{Z}_{8} \times \mathbb{Z}_{25}$

My question is:

Isn't $\mathbb{Z}_{2} \times \mathbb{Z}_{2} \times \mathbb{Z}_{2} \times \mathbb{Z}_{5} \times \mathbb{Z}_{5}$ isomorphic to the group of order $200$ by the theorem? Should such a product be included in the list?