  The confirmation of the discrepancy with the Standard Model predictions in
the anomalous magnetic moment by the Muon g-2 experiment at Fermilab points to
a low scale of new physics. Flavour symmetries broken at low energies can
account for this discrepancy but these models are much more restricted, as they
would also generate off-diagonal entries in the dipole moment matrix.
Therefore, if we assume that the observed discrepancy in the muon $g-2$ is
explained by the contributions of a low-energy flavor symmetry, lepton flavour
violating processes can constrain the structure of the lepton mass matrices and
therefore the flavour symmetries themselves predicting these structures. We
apply these ideas to several discrete flavour symmetries popular in the
leptonic sector, such as $\Delta (27)$, $A_4$, and $A_5 \ltimes {\rm CP}$.
