Definition:Normal Subgroup/Notation

Definition
The statement that $N$ is a normal subgroup of $G$ is represented symbolically as $N \lhd G$.

A normal subgroup is often represented by the letter $N$, as opposed to $H$ (which is used for a general subgroup which may or may not be normal).

To use the notation introduced in the definition of the congugate:
 * $N \lhd G \iff \forall g \in G: N^g \in N$