Group in which any two characteristic subgroups are comparable

Definition
A group is termed a group in which any two characteristic subgroups are comparable if given any two characteristic subgroups of it, one is contained inside the other. In other words, the lattice of characteristic subgroups of the group is a totally ordered set.

Stronger properties

 * Weaker than::Simple group
 * Weaker than::Characteristically simple group
 * Weaker than::Group in which any two normal subgroups are comparable