The spatial and time-reversal symmetries of excitons in quantum wires are discussed, including possible use in numerical computation. Particular attention is paid to the important case of a single symmetry plane (group C-s). Even in such a low symmetry case group theory proves very useful. For instance we can explain the appearance of new transitions recently observed and find interesting excitonic optical selection rules describing in a new way the polarization anisotropy coming from valence band-mixing.