  A linear \'etale representation of a complex algebraic group $G$ is given by
a complex algebraic $G$-module $V$ such that $G$ has a Zariski-open orbit on
$V$ and $\dim G=\dim V$. A current line of research investigates which \'etale
representations can occur for reductive algebraic groups. Since a complete
classification seems out of reach, it is of interest to find new examples of
\'etale representations for such groups. The aim of this note is to describe
two classical constructions of Vinberg and of Bala & Carter for nilpotent orbit
classifications in semisimple Lie algebras, and to determine which reductive
groups and \'etale representations arise in these constructions. We also
explain in detail the relation between these two~constructions.
