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Using an isospin- and momentum-dependent hadronic transport model, we investigate effects of the symmetry energy on several collective flows in heavy-ion collisions induced by radioactive beams at intermediate energies.It is found that the neutron-proton differential directed flow and the neutron-proton differential elliptic flow are strongly correlated with the symmetry energy, while the position averaged radial flow is weakly correlated with the symmetry energy.