  Rich topological phenomena, edge states and two types of corner states, are
unveiled in a two-dimensional square-lattice dielectric photonic crystal
without both $C_4$ and $M_{x(y)}$ symmetries. Specifically, non-trivial type-I
corner states, which do not exist in systems with $C_4$ and $M_{x(y)}$ since
the degeneracy, are protected by non-zero quadrupole moment, no longer
quantized to but less than $0.5$. Excellent properties, e.g. sub-wavelength
localization and air-concentrated field distribution, are presented. Type-II
corner states, induced by long-range interactions, are easier realized due to
asymmetry. This work broadens the topological physics for the symmetries-broken
systems and provides potential applications.
