  For certain non-magnetic solids with low symmetry the occurrence of
spin-polarized longitudinal currents is predicted. These arise due to an
interplay of spin-orbit interaction and the particular crystal symmetry. This
result is derived using a group-theoretical scheme that allows investigating
the symmetry properties of any linear response tensor relevant to the field of
spintronics. For the spin conductivity tensor it is shown that only the
magnetic Laue group has to be considered in this context. Within the introduced
general scheme also the spin Hall- and additional related transverse effects
emerge without making reference to the two-current model. Numerical studies
confirm these findings and demonstrate for (Au$_{1-x}$Pt$_{\rm x}$)$_4$Sc that
the longitudinal spin conductivity may be in the same order of magnitude as the
conventional transverse one. The presented formalism only relies on the
magnetic space group and therefore is universally applicable to any type of
magnetic order.
