  Degeneracy points in non-Hermitian systems are of great interest. While a
homotopic framework exists for understanding their behavior in the absence of
symmetry, it does not apply to symmetry-protected degeneracy points with
reduced codimension. In this work, utilizing algebraic topology, we provide a
systematic classification of these symmetry-protected degenerate points and
investigate the braid conservation rule followed by them. Using a model
Hamiltonian and circuit simulation, we discover that, contrary to simple
annihilation, pairwise-created symmetry-protected degeneracy points merge into
a higher-order degeneracy point, which goes beyond the abelian picture. Our
findings empower researchers across diverse fields to uncover new phenomena and
applications harnessing symmetry-protected non-Hermitian degeneracy points.
