Characteristic subgroup of direct factor

Symbol-free definition
A subgroup of a group is said to be a characteristic subgroup of direct factor if it occurs as a characteristic subgroup of a direct factor of the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is said to be a characteristic subgroup of direct factor if there are subgroups $$K,L$$ such that $$H$$ is characteristic in $$K$$, and $$K \times L = G$$.

Stronger properties

 * Weaker than::Characteristic subgroup
 * Weaker than::Direct factor

Weaker properties

 * Stronger than::Normal subgroup