An exotic feature of the fractional quantum Hall effect is the emergence of anyons, which are quasiparticle excitations with fractional statistics. In the presence of a symmetry, such as U(1) charge conservation, it is well known that anyons can carry fractional symmetry quantum numbers. In this work we reveal a different class of symmetry realizations: i.e. anyons can "breed" in multiples under symmetry operation. We focus on the global Ising (Z_2) symmetry and show examples of these

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... onal symmetry realizations in Laughlin-type fractional quantum Hall states. One remarkable consequence of such an Ising symmetry is the emergence of anyons on the Ising symmetry domain walls. We also provide a mathematical framework which generalizes this phenomenon to any Abelian topological orders.