We classify all possible charge lattices and 1-form symmetry groups for $\mathcal{ N}=2$ SCFTs with characteristic dimension $\varkappa \neq \{ 1,2\}$. 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 $\mathcal{ N}=2$ $S$-folds and Minahan-Nemeschansky SCFTs have trivial 1-form symmetry. We find two sporadic lattices compatible with the Coulomb branch geometries $\mathbb{ C}^5/G_{ 33}$ and $\mathbb{ C}^6/G_{ 34}$ that are not realized by any known SCFT. The former, if realized, would have a $\mathbb{ Z}_2$ 1-form symmetry and a non-invertible topological defect.
Categories: hep-th