It is suggested that it is not necessary to solve the full non-perturbative problem of two-dimensional charge transport in order to obtain global information about the phase and flow diagrams for the quantum Hall system and its relatives. It is argued that the effective quantum field theories encoding the macroscopic properties of these systems are invariant under a symmetry contained in the modular group. New phase and flow diagrams are obtained which exhibit a hierarchy of only odd or only even phases (Hall plateaus). The Kramers-Wannier-like symmetry determines the exact location of all renormalization group fixed points, which appear to be in agreement with available scaling experiments on the quantum Hall system. It also explains the observed 'super-universality', of the delocalization exponent.