Ganymede is the only known moon with an active dynamo. No mission has discovered intrinsic magnetism at the other Galilean satellites: Io, Europa, and Callisto. A dynamo requires a large magnetic Reynolds number, which in turn demands, for these moons, a large metallic core that is cooling fast enough for convection. Here we quantify these requirements to construct a regime diagram for the Galilean satellites. We compute the internal heat fluxes that would sustain a dynamo over the wide ranges of plausible radii for their metallic cores. Below a critical radius, no plausible heat flux will sustain a dynamo. Europa likely sits on the opposite side of this limit than Ganymede and Io. We predict that future missions may confirm a small (or absent) core, meaning that Europa could not sustain a dynamo even if its interior were cooling as quickly as Ganymede's core.