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We present the group-thoretical classification of gap functions insuperconductors coexisting with some magnetic order in non-symmorphic magneticspace groups. Based on the weak-coupling BCS theory, we show that UCoGe-typeferromagnetic superconductors must have horizontal line nodes on either $k_z=0$or $\pm\pi/c$ plane. Moreover, it is likely that additional Weyl point nodesexist at the axial point. On the other hand, in UPd$_2$Al$_3$-typeantiferromagnetic superconductors, gap functions with $A_g$ symmetry possesshorizontal line nodes in antiferromagnetic Brillouin zone boundaryperpendicular to $c$-axis. In other words, the conventional fully-gapped$s$-wave superconductivity is forbidden in this type of antiferromagneticsuperconductors, irrelevant to the pairing mechanism, as long as the Fermisurface crosses a zone boundary. UCoGe and UPd$_2$Al$_3$ are candidates forunconventional superconductors possessing hidden symmetry-protected line nodes,peculiar to non-symmorphic magnetic space groups.

Symmetry protected line nodes in non-symmorphic magnetic space groups: Applications to UCoGe and UPd$_2$Al$_3$