The Multimodal Transfer Matrix Method (MMTMM) is a hybrid approach that efficiently computes the dispersion relation of a periodic structure. It is able to retrieve both the phase shift and attenuation constant of any arbitrary structure susceptible to be analyzed by means of commercial simulators. Here, we propose the use of this method in order to get a physical insight of periodic structures possessing higher symmetries. The MMTMM is here explained and corroborated with two different structures: a glide-symmetric dielectric-filled corrugated rectangular waveguide and a three-fold twist-symmetric bricks embedded in a dielectric waveguide. The first structure allows for the propagation of backward modes below the hollow waveguide cut-off frequency, whereas the second one has handedness selection.