Odd-frequency superconductivity describes a class of superconducting states where the superconducting gap is an odd function in relative time and Matsubara frequency. We present a group theoretical analysis based on the linearized gap equation in terms of Shubnikov groups of the second kind. By discussing systems with spin-orbit coupling and an interaction kernel which is symmetric under the reversal of relative time, we show that both even-and odd-frequency gaps are allowed to occur. Specific examples are discussed for the square lattice, the octahedral lattice, and the tetragonal lattice. For irreducible representations that are even under reversal of relative time the common combinations of s-and d-wave spin singlet and p-wave spin triplet gaps are revealed, irreducible representations that are odd under reversal of relative time give rise to s-and d-wave spin triplet and p-wave spin singlet gaps. Furthermore, we discuss the construction of a generalized GinzburgLandau theory in terms of the associated irreducible representations. The result complements the established classification of superconducting states of matter. [7]; and the organic superconductors like the BEDT-TTF-based charge transfer salts [8][9][10][11][12] exhibit symmetries of the superconducting gap beyond the conventional BCS s-wave [13]. In this connection, a group theory analysis based on the underlying symmetry of the pairing potential is crucial in establishing an unified classification of the arising superconducting states of matter [14][15][16][17][18][19]. In general, the pairing wave function of two electrons has to be anti-symmetric under particle interchange leading to the Pauli-principle. At equal times, and by neglecting orbital degrees of freedom two cases can occur: first, a gap odd in spin and even in parity, such as spin singlet s-and d-wave gaps, and, second, a gap even in spin and odd in parity, such as spin triplet p-and f -wave gaps.However, as pointed out by Berezinskii [20] and Balatsky and Abrahams [21] a pairing of particles beyond the conventional ones is possible, if the particle-particle correlator is zero at equal times but non-zero otherwise. This is achieved when the superconducting gap is an odd function in relative time, leading to the notion of odd-time or odd-frequency superconductivity, respectively (odd-frequency also refers to gap functions odd in Matsubara frequency). Among others, odd-frequency contributions were reported to occur in connection to diffusive ferromagnet/superconductor junctions [22,23] [28,29]. Also, odd-frequency states were discussed in connection to time-reversal topological superconductivity in double Rashba wires, where it was found that odd-frequency pairing is strongly enhanced in the topological state [30]. For some of the above mentioned systems, the respective signatures of odd-frequency correlations could also be verified experimentally [31][32][33][34]. An extensive discussion of edge-states and topology in superconductors including odd-frequency gap functions was communicat...