We report theoretical, algorithmic, and computational aspects of exploiting space-group symmetry in self-consistent field (SCF) calculations, primarily Kohn-Sham density functional theory (DFT), with periodic boundary conditions (PBC) and Gaussian-type orbitals. Incorporating exact exchange leads to generally better performance for a broad class of systems, but leads to a significant increase of computation time, especially for 3D solids, due to a large number of explicitly evaluated two-electron integrals. We exploit reduction of the list thereof based on the space-group symmetry of a crystal. As distinct from previous achievements, based on the use of symmorphic groups only, we extend our technique to non-symmorphic groups, thus enabling application of any of 230 3D space groups. Algorithms facilitating efficient reduction of the list of two-electron integrals and restoring the full Fock-type matrix have been proposed and implemented in the development version of Gaussian program. These schemes are applied not only to the HFx, but also to explicit evaluation of the near-field Coulomb contribution. In 3D solids with smallest unit cells speedup factors range from 2X to 9X for the near field Coulomb part and from 3X to 8X for the exact exchange, thus leading to a substantial reduction of the overall computational cost. Factors noticeably lower than the number of the operations are due to the highly symmetric atomic positions in crystals, as well as to the choice of primitive cells. In systems with atoms on general positions or in special positions of low multiplicity, the speedup factors readily exceed one order of magnitude being almost 70X (near-field Coulomb) and 57X (HFx) for the largest tested (16,7) single-walled nanotube with 278 symmetry operations.