Semipermutable subgroup

Symbol-free definition
A subgroup of a finite group is termed semipermutable if it permutes with every subgroup whose order is relatively prime to it.

Definition with symbols
A subgroup $$H$$ of a finite group $$G$$ is termed semipermutable if for any group $$K$$ such that the orders of $$H$$ and $$K$$ are relatively prime, $$HK = KH$$.

Stronger properties

 * Normal subgroup
 * Permutable subgroup
 * R-normal subgroup