Two elements $g$ and $g'$ of a group $G$ are said to be conjugate if there exists $h \in G$ such that $g' = hgh^{-1}$ Conjugacy of elements is an equivalence relation, and the equivalence classes of $G$ are called conjugacy classes.

Two subsets $S$ and $T$ of $G$ are said to be conjugate if there exists $g \in G$ such that $$ T = \{gsg^{-1} \mid s \in S\} \subset G. $$ In this situation, it is common to write $gSg^{-1}$ for $T$ to denote the fact that everything in $T$ has the form $gsg^{-1}$ for some $s \in S$ We say that two subgroups of $G$ are conjugate if they are conjugate as subsets.