  We study the symmetric properties of waveguide modes in presence of
gain/losses, anisotropy/bianisotropy, or continuous/discrete rotational
symmetry. We provide a comprehensive approach to identity the modal symmetry by
constructing a $4\times4$ waveguide Hamiltonian and searching the symmetric
operation in association with the corresponding waveguides. We classify the
chiral/time reversal/parity/parity time/rotational symmetry for different
waveguides, and provide the criterion for the aforementioned symmetry
operations. Lastly, we provide examples to illustrate how the symmetry
operations can be used to classify the modal properties from the symmetric
relation between modal profiles of several different waveguides.
