Definition:Conjugacy Action/Subgroups

Definition
Let $X$ be the set of all subgroups of $G$.

The (left) conjugacy action on subgroups is the group action $* : G \times X \to X$:
 * $g * H = g \circ H \circ g^{-1}$

The right conjugacy action on subgroups is the group action $* : X \times G \to X$:
 * $H * g = g^{-1} \circ H \circ g$

Also see

 * Conjugacy Action is Group Action