The long standing problem of proton-neutron pairing and, in particular, the limitations imposed on the solutions by the available symmetries, is revisited. We look for solutions with nonvanishing expectation values of the proton Δp, the neutron Δn, and the isoscalar Δ0 gaps. For an equal number of protons and neutrons we find two solutions with Δp = ± Δn, respectively. The behavior and structure of these solutions differ for spin saturated (single l shell) and spin unsaturared systems (single j shell). In the former case the BCS results are checked against an exact calculation.