Template:Group properties because p-group

Satisfies property::group of prime power order || Yes || ||
 * Satisfies property::nilpotent group || Yes || prime power order implies nilpotent ||
 * Satisfies property::supersolvable group || Yes || via nilpotent: finite nilpotent implies supersolvable ||
 * Satisfies property::solvable group || Yes || via nilpotent: nilpotent implies solvable ||
 * Satisfies property::supersolvable group || Yes || via nilpotent: finite nilpotent implies supersolvable ||
 * Satisfies property::solvable group || Yes || via nilpotent: nilpotent implies solvable ||
 * Satisfies property::solvable group || Yes || via nilpotent: nilpotent implies solvable ||