Let $G$ be any algebraic subgroup of $\mathrm{GL}_n$ over an algebraically closed field of any characteristic.
If $s$ is a semisimple element of $G$, can the $G$conjugacy class of $s$ fail to be closed in $G$?
Let $G$ be any algebraic subgroup of $\mathrm{GL}_n$ over an algebraically closed field of any characteristic. If $s$ is a semisimple element of $G$, can the $G$conjugacy class of $s$ fail to be closed in $G$? 


Noit's always closed. See 18.2 in Humphreys, Linear Algebraic Groups. 

