For the design of advanced microwave and antenna components, efficient and accurate electromagnetic methods are required. In this work, we present a technique to fast simulate mirror- and glide-symmetric periodic structures. More concretely, a novel Green's function is proposed which allows to reduce the computational domain to one half of the unit cell. Full dispersion diagrams are computed for metallic glide- and mirror-symmetric structures with three stages of mesh refinement. The results converge with the meshing and agree well with conventional eigenmode analyses.