Group in which every normal subgroup is characteristic

Symbol-free definition
A group in which every normal subgroup is characteristic is a group such that every normal subgroup of the group is characteristic in the group.

Formalisms
The property can be viewed as the following subgroup property collapse: normal subgroup = characteristic subgroup

The property can be viewed as the following collapse: $$G$$ satisfies the property if and only if whenever $$G$$ is embedded as a normal subgroup of some group $$K$$, then $$G$$ is a transitively normal subgroup of $$K$$.

Stronger properties

 * Weaker than::Group in which every normal subgroup is fully characteristic
 * Weaker than::Simple group
 * Weaker than::Cyclic group
 * Weaker than::Complete group
 * Weaker than::Group in which every automorphism is inner

Weaker properties

 * Stronger than::Group in which every normal subgroup is potentially characteristic: Here, every normal subgroup is potentially characteristic