Totally permuting subgroups

Symbol-free definition
Two subgroups of a group are said to be totally permuting if every subgroup of either permutes with every subgroup of the other.

Definition with symbols
Two subgroups $$H$$ and $$K$$ of a group $$G$$ are said to be totally permuting if for every subgroup $$M$$ of $$H$$ and every subgroup $$N$$ of $$K$$, $$MN = NM$$.

Weaker relations

 * Mutually permuting subgroups
 * Permuting subgroups