Random suggested stuff:
Symmetric group:S3: The symmetric group of degree three (order six). Also, the dihedral group of degree three (order six). See also subgroups of S3, representations of S3, and elements of S3.
Thompson's critical subgroup theorem (FACT): Every group of prime power order has a critical subgroup: a characteristic subgroup that is commutator-in-center, Frattini-in-center, and self-centralizing.
Category:Group property implications: A listing of pages giving the statement and proof of group property implications: one group property implying another. For instance, abelian implies nilpotent.
Category:Facts about odd-order groups that break down for even-order groups: A list of facts that are true for the finite odd-order groups but break down (in general) for groups of even order.