  We extend the definition of generalized parity $P$, charge-conjugation $C$
and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian
Hamiltonians, and we use these generalized operators to describe the full set
of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold
classification. In particular we show that $TP$ and $CTP$ are the generators of
the antiunitary symmetries; moreover, a necessary and sufficient condition is
provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting
symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary
symmetries. Finally, a physical example is considered and some hints on the
$P$-unitary evolution of a physical system are also given.
