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The effective Higgs theories at the TeV scale in supersymmetric $SU(5)$ grandunification models are systematically derived. Restricted to extensions on$\mathbf{5}_{H}$ containing the Higgs sector we show that only two types ofreal (vector-like) models and one type of chiral model are found to beconsistent with perturbative grand unification. While the chiral model has beenexcluded by the LHC data, the fate of perturbative unification will be uniquelydetermined by the two classes of vector-like models.

Effective Higgs Theories in Supersymmetric Grand Unification