  Cardy-Frobenius algebra is the algebraic structure on the space of states in
open-closed topological field theory. We prove that every semisimple super
Cardy-Frobenius algebras is the direct sum of the super Cardy-Frobenius
algebras of three simple types. We also apply our results to singularity theory
via Landau-Ginzburg models and matrix factorizations.
