Extensible implies subgroup-conjugating

This article gives the statement and possibly, proof, of an implication relation between two automorphism properties. That is, it states that every automorphism satisfying the first automorphism property (i.e., extensible automorphism) must also satisfy the second automorphism property (i.e., subgroup-conjugating automorphism)
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Statement

Every extensible automorphism of a group must be a subgroup-conjugating automorphism: it must sned every subgroup to a conjugate subgroup.

Related facts

Corollaries

• Extensible implies normal
• Extensible automorphism-invariant equals normal

Facts used

1. Extensible implies permutation-extensible
2. Permutation-extensible implies subgroup-conjugating

Proof

The proof follows by piecing together facts (1) and (2).