Magnetic quivers and their Coulomb branches provide a framework for studying the Higgs branch of theories with eight supercharges, including those without a known Lagrangian description. In particular, they capture the foliation structure of the Higgs branch, which encodes the sequence of spontaneous symmetry-breaking phenomena in the theory. Each elementary step in this process corresponds to an isolated symplectic singularity. We employ the fission–decay algorithm to classify all magnetic quivers whose Coulomb branches exhibit such isolated singularities.