Nilpotent orbits in $\mathfrak{sl}_{n}$ are in one to one correspondence with the set of partitions.
Nilpotent orbits in $\mathfrak{so}_{2n+1}$ are in one to one correspondence with the set of partitions of 2n+1 in which even parts occur with even multiplicity.
Nilpotent orbits in $\mathfrak{sp}_{2n}$ are in one to one correspondence with the set of partitions of 2n in which odd parts occur with even multiplicity.
I wonder if these statements can be generalized to the most general case.