Spin line groups describe the symmetries of spin arrangements in quasi-one-dimensional systems. These groups are derived for the first family of line groups. Among them, magnetic groups are singled out as a special case. Spin arrangements generated by the derived groups are first discussed for single-orbit systems and then the conclusions are extended to multi-orbit cases. The results are illustrated by the examples of a CuO₂zigzag chain, a¹³C nanotube and the hexaferrite Ba₂Mg₂Fe₁₂O₂₂. Applications to neutron diffraction and classical ground-state determination are indicated.