  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.
