Normal Subgroup, also called an invariant subgroup:
* Given a group G, a subgroup H is called normal
* <=> the left cosets and the right cosets are the same.
* <=> H contains the complete conjugacy classes of G.
* <=> forall a ~ b, a in H or a notin H.
* <=> H=g^Hg
{e},G are trivially normal
if G has no nontrivial normal subgroups => G is simple
N normal subset of G => G/N (group division) is a group of order n/m