# Definition(s)
> [!NOTE] Definition 1 ()
> Let $G$ a be a [[Groups|group]] and $H$ a [[Subgroup|subgroup]] of $G.$ $H$ is normal, denoted $H \unlhd G,$ iff all its [[Conjugate of Subgroup|conjugates]] equal $H,$ that is, for all $g \in G,$ $gHg^{-1}=H.$
**Remark**: $\unlhd$ is the symbol for 'under left-hand division'.
> [!Example] Example
> Contents
# Properties(s)
By [[Subgroup is Normal iff Every Conjugate is Contained in Subgroup]], $H \unlhd G$ iff $gHg^{-1}\subset H.$
# Application(s)
**More examples**:
# Bibliography