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Symmetry and non-Hermiticity play pivotal roles in photonic lattices. Whilesymmetries such as parity-time ($\mathcal{PT}$) symmetry have attracted ampleattention, more intricate crystalline symmetries have been neglected incomparison.  Here, we investigate the impact of the 17 wallpaper space groups oftwo-dimensional crystals on non-Hermitian band structures. We show that thenon-trivial space group representations enforce degeneracies at high symmetrypoints and dictate their dispersion away from these points. In combination witheither $\mathcal{T}$ or $\mathcal{PT}$, the symmorphic p4mm symmetry, as wellas the non-symmorphic p2mg, p2gg, and p4gm symmetries, protect novelexceptional chains intersecting at the pertinent high symmetry points.

Nodal phases in non-Hermitian wallpaper crystals