I am looking for a mechanism to find a decomposition of symmetric groups. For finitely generated abelian group G, there is a mechanism to decompose G such that G is isomorphic to a direct sum of cyclic groups.

For symmetric groups, it seems a bit complex for me to find it.

For example,

(1) is it possible for $\displaystyle S_{3}, S_{4}, S_{5}$ to be decomposed as a direct product of groups?

In more general cases, is there any mechanism to decompose $\displaystyle S_{n}$ as a direct product of groups?

(2) is there any mechanism to find an isomorphic group of a direct product of symmetric groups? Let's say,

$\displaystyle G = S_{3} \times S_{4} \times S_{5}$

Any isomorphic group of above G?