  Order-$p$ parasupersymmetric and orthosupersymmetric quantum mechanics are
shown to be fully reducible when they are realized in terms of the generators
of a generalized deformed oscillator algebra and a ${\rm Z}_{p+1}$-grading
structure is imposed on the Fock space. The irreducible components provide
$p+1$ sets of bosonized operators corresponding to both unbroken and broken
cases. Such a bosonization is minimal.
