Exceptional points of order appear in non-Hermitian systems as points where the eigenvalues and eigenvectors coalesce. They emerge if real constraints are imposed, such that EP2s generically appear in two dimensions (2D). Local symmetries have been shown to reduce this number of constraints. In this work, we provide a complete characterization of the appearance of symmetry-induced higher-order EPs in 2D parameter space. We find that besides EP2s only EP3s, EP4s, and EP5s can be stabilized in 2D.
