  This paper is about nilpotent orbits of reductive groups over local
non-Archimedean fields. In this paper we will try to identify for which groups
there are only finitely many nilpotent orbits, for which groups the nilpotent
orbits are separable and for which groups Howe's conjecture holds. For general
reductive groups we get some partial results. For split reductive groups we get
a classification in terms of the root data and the characteristic of the
underlying local field.
