Characteristically simple and NSCFN implies monolith

Statement
A NSCFN-subgroup of a group that is characteristically simple as a group, must be a monolith: it is a minimal normal subgroup and is contained in every nontrivial normal subgroup.

Facts used

 * 1) Characteristically simple and normal fully normalized implies minimal normal
 * 2) Self-centralizing and minimal normal implies monolith

Proof
The proof follows by combining facts (1) and (2).