We classify the hulls of different limit-periodic potentials and show that the hull of alimit-periodic potential is a procyclic group. We describe how limit-periodic potentialscan be generated from a procyclic group and answer arising questions. As an expositorypaper, we discuss the connection between limit-periodic potentials and profinite groups ascompletely as possible and review some recent results on Schrödinger operators obtained inthis context.