  We use group theory to classify the superconducting states of systems with
two orbitals on a tetragonal lattice. The orbital part of the superconducting
gap function can be either symmetric or anti-symmetric. For the orbital
symmetric state, the parity is even for spin singlet and odd for spin triplet;
for the orbital anti-symmetric state, the parity is odd for spin singlet and
even for spin triplet. The gap basis functions are obtained with the use of the
group chain scheme by taking into account the spin-orbit coupling. In the weak
pairing limit, the orbital anti-symmetric state is only stable for the
degenerate orbitals. Possible application to iron-based superconductivity is
discussed.
