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The class-S theories of type $E_8$ were analyzed in\cite{Chacaltana:2018vhp}. The basic building blocks consisted of 49,836isolated SCFTs (three-punctured spheres). In 244 cases, there were undeterminedlevels for the flavour symmetry current algebra. Here, we rectify thatomission. Using S-duality and nilpotent Higgsing we compute the levels of 235of the 244. There remain 9 three-punctured spheres with unknown levels. Alongthe way, we provide a detailed discussion of the Drinfeld-Sokolov reduction ofthe VOA, which captures various features of the Higgs branch RG flows arisingfrom giving a VEV to a nilpotent moment map.

Current Algebra Levels in the $E_8$ Theory