On finite groups factorised by submodular subgroups

A subgroup $H$ of a finite group $G$ is submodular in $G$ if there is a subgroup chain $H=H_0\le \dots \le H_i\le H_{i+1}\le \dots \le H_n=G$ such that $H_i$ is a modular subgroup of $H_{i+1}$ for every $i$. We investigate finite factorised groups with submodular primary (cyclic primary) subgroups in factors. We indicate a general approach to the description of finite groups factorised by supersolvable submodular subgroups.