Lepton mass textures from non-invertible multiplication rules

We study the lepton mass textures, which are derived by ${\mathbb{Z}}_2$ gauging of ${\mathbb{Z}}_M$ symmetries. We can obtain various textures for the Yukawa couplings in the charged lepton sector, but the patterns of neutrino mass matrices are limited. All the obtained textures can not be realized by group-theoretical symmetries, and certain textures can lead to realistic results.