  Based on the concepts of $\mathbb{R}$-factorizable topological groups and
$\mathcal{M}$-factorizable topological groups, we introduce four classes of
factorizabilities on topological groups, named
$P\mathcal{M}$-factorizabilities, $Pm$-factorizabilities,
$S\mathcal{M}$-factorizabilities and $PS\mathcal{M}$-factorizabilities,
respectively. Some properties of the four classes of spaces are investigated.
