Conjugacy-closed subgroup of ambivalent group is ambivalent

Verbal statement
Any fact about::conjugacy-closed subgroup of an fact about::ambivalent group is an ambivalent group.

In particular, any fact about::conjugacy-closed normal subgroup, fact about::central factor, fact about::retract, or fact about::direct factor of an ambivalent group is ambivalent.

Related facts

 * Ambivalence is direct product-closed
 * Normal subgroup of ambivalent group implies every element is automorphic to its inverse
 * Every element is automorphic to its inverse is characteristic subgroup-closed