Direct factor of complemented normal subgroup

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a direct factor of complemented normal subgroup if there exists an intermediate subgroup $$K$$ of $$G$$ containing $$H$$ such that $$H$$ is a direct factor of $$K$$ and $$K$$ is a complemented normal subgroup of $$G$$.

Stronger properties

 * Weaker than::Base of a wreath product
 * Weaker than::Base of a wreath product with diagonal action

Weaker properties

 * Stronger than::Complemented normal subgroup of complemented normal subgroup
 * Stronger than::Direct factor of normal subgroup
 * Stronger than::Normal subgroup of complemented normal subgroup
 * Stronger than::Complemented normal subgroup of normal subgroup
 * Stronger than::2-subnormal subgroup