Comparable with all normal subgroups implies characteristic in finite nilpotent group

Statement
If a subgroup of a finite nilpotent group is comparable with all normal subgroups, then it is a characteristic subgroup.

Facts used

 * 1) Comparable with all normal subgroups implies normal in nilpotent
 * 2) Normal subgroup comparable with all normal subgroups implies characteristic in finite

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