We present a method to identify symmetry groups of the Yukawa sector of the three-Higgs-doublet model and to determine the implication that the symmetry has on the lepton masses and mixing. The method can accommodate different hypotheses about the group representation assignments, and thus support the exploration of candidate symmetry groups. For one particular representation selection scheme we apply the computer-implemented method to scan all discrete groups of order less than 1035. It can be proven that none of these groups defines a flavor symmetry that implies masses and neutrino mixing angles consistent with the experimental lepton data, although several cases are found that are partially or approximately consistent.

When the Higgs doublets in the three-Higgs-doublet model (3HDM) transform as a flavor triplet under the \(A_4\) group, the resulting lepton mass matrices reproduce the experimentally observed neutrino mixing angles with arbitrary precision, while simultaneously maintaining the correct mass ordering of both charged and neutral leptons, where the latter are Dirac neutrinos with a normal mass hierarchy. Imposing the \(A_4\) symmetry also allows for agreement between the calculated and observed lepton masses for Higgs vacuum configurations that differ from those required to fit \(U_{\mathrm {PMNS}}\). Among all discrete groups of order less than or equal to 600, no contraction other than the one associated with \(A_4\) leads to a better agreement with experimental data, and the solution structure presented here is unique within the set of groups investigated. Published by the Jagiellonian University 2026 authors