Sylow implies isomorph-conjugate

Statement
Any Sylow subgroup of a finite group is an isomorph-conjugate subgroup: it is conjugate to any isomorphic subgroup.

Applications

 * Sylow implies intermediately isomorph-conjugate
 * Sylow implies automorph-conjugate
 * Sylow implies intermediately automorph-conjugate
 * Sylow implies procharacteristic
 * Sylow implies pronormal
 * Sylow of normal implies pronormal

Facts used

 * 1) uses::Sylow implies order-conjugate: This is the conjugacy part of Sylow's theorem.
 * 2) uses::Order-conjugate implies isomorph-conjugate

Proof
The proof follows directly from facts (1) and (2).