Right-transitively complemented normal subgroup

Symbol-free definition
A subgroup of a group is termed a right-transitively complemented normal subgroup if every complemented normal subgroup of the subgroup is also a complemented normal subgroup of the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a right-transitively complemented normal subgroup if whenever $$K$$ is a complemented normal subgroup of $$H$$, $$K$$ is also a complemented normal subgroup of $$G$$.

Stronger properties

 * Weaker than::Direct factor

Weaker properties

 * Stronger than::Complemented normal subgroup

Related properties

 * Left-transitively complemented normal subgroup