Conjugacy-closed characteristic subgroup

Definition
A subgroup of a group is termed a conjugacy-closed characteristic subgroup if it is both a conjugacy-closed subgroup (i.e., any two elements of the subgroup that are conjugate in the whole group are conjugate in the subgroup) and a characteristic subgroup.

Stronger properties

 * Weaker than::Characteristic direct factor
 * Weaker than::Characteristic central factor

Weaker properties

 * Stronger than::Conjugacy-closed normal subgroup
 * Stronger than::Transitively normal subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Characteristic transitively normal subgroup