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