We investigate a quantum system possessing a parasupersymmetry of order 2, an
orthosupersymmetry of order p, a fractional supersymmetry of order p+1, and
topological symmetries of type (1,p) and (1,1,...,1). We obtain the
corresponding symmetry generators, explore their relationship, and show that
they may be expressed in terms of the creation and annihilation operators for
an ordinary boson and orthofermions of order p. We give a realization of
parafermions of order~2 using orthofermions of arbitrary order p, discuss a
p=2 parasupersymmetry between p=2 parafermions and parabosons of arbitrary
order, and show that every orthosupersymmetric system possesses topological
symmetries. We also reveal a correspondence between the orthosupersymmetry of
order p and the fractional supersymmetry of order p+1.Comment: 12 page