We provide a complete answer to the following question: what are the flavour
groups and representations providing, in the symmetric limit, an approximate description
of lepton masses and mixings? We assume that neutrino masses are described by the Wein-
berg operator. We show that the pattern of lepton masses and mixings only depends on the
dimension, type (real, pseudoreal, complex), and equivalence of the irreducible components
of the flavour representation, and we find only six viable cases. In all cases the neutrinos
are either anarchical or have an inverted hierarchical spectrum. In the context of SU(5)
unification, only the anarchical option is allowed. Therefore, if the hint of a normal hier-
archical spectrum were confirmed, we would conclude (under the above assumption) that
symmetry breaking effects must play a leading order role in the understanding of neutrino
flavour observables. In order to obtain the above results, we develop a simple algorithm
to determine the form of the lepton masses and mixings directly from the structure of the
decomposition of the flavour representation in irreducible components, without the need
to specify the form of the lepton mass matrices.
