A Subgroup H ⊆ G 𝐻 𝐺 H\subseteq G is normal if it is invariant under Conjugation, EG: for all h ∈ H ℎ 𝐻 h\in H and g ∈ G 𝑔 𝐺 g\in G , g h g − 1 ∈ H 𝑔 ℎ superscript 𝑔 1 𝐻 ghg^{-1}\in H .