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We employ a bottom-up and model-independent technique to search fornon-Abelian discrete flavour symmetries capable of predicting viable CKM andPMNS matrices alongside of special patterns of leptoquark couplings. Inparticular, we analyze patterns derived when an ultra-violet flavour theory isassumed to break to global Abelian symmetries in Standard Model fermion massesand new Yukawa-like terms sourced by the leptoquark representation. Thephenomenology of different classes of these `simplified models' can be exploredwithout reference to explicit model-building assumptions, e.g. the nature offlavour symmetry breaking or any additional field content associated to it, andare also capable of explaining hints of lepton non-universality in$\mathcal{R}_{K^{(\star)}}$. Assuming experimentally interesting CKM and PMNSmatrix elements, our algorithm finds an abundance of predictive non-Abelianflavour groups and therefore provides promising directions for future modelbuilding in the flavoured leptoquark space, regardless of whether the anomalous$\mathcal{R}_{K^{(\star)}}$ measurements withstand further experimentalscrutiny.

Finite Family Groups for Fermionic and Leptoquark Mixing Patterns