  We construct a canonical irreducible representation for the orthofermion
algebra of arbitrary order, and show that every representation decomposes into
irreducible representations that are isomorphic to either the canonical
representation or the trivial representation. We use these results to show that
every orthosupersymmetric system of order $p$ has a parasupersymmetry of order
$p$ and a fractional supersymmetry of order $p+1$.
