  Second-order topological insulators and superconductors have a gapped
excitation spectrum in bulk and along boundaries, but protected zero modes at
corners of a two-dimensional crystal or protected gapless modes at hinges of a
three-dimensional crystal. A second-order topological phase can be induced by
the presence of a bulk crystalline symmetry. Building on Shiozaki and Sato's
complete classification of bulk crystalline phases with an order-two
crystalline symmetry [Phys.\ Rev.\ B {\bf 90}, 165114 (2014)], such as mirror
reflection, twofold rotation, or inversion symmetry, we classify all
corresponding second-order topological insulators and superconductors. The
classification also includes antiunitary symmetries and antisymmetries.
