The ABCDEFGJK of maximally strongly coupled N=2 SCFTs

We classify all possible charge lattices and 1-form symmetry groups for N=2 SCFTs with characteristic dimension \1, 2\. For rank-r SCFTs that are not stacks of lower rank theories the order of the 1-form symmetry group can be 1, 2, 3, 4 and r+1. As an application of the classification we show that N=2 S-folds and Minahan-Nemeschansky SCFTs have trivial 1-form symmetry. We find two sporadic lattices compatible with the Coulomb branch geometries C⁵/G₃₃ and C⁶/G₃₄ that are not realized by any known SCFT. The former, if realized, would have a Z₂ 1-form symmetry and a non-invertible topological defect.