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