We report a measurement of the branching fractions of B-->D**(l) nu(l), decays based on 417 fb(-1) of data collected at the Y(4S) resonance with the BABAR detector at the PEP-II e+e- storage rings. Events are selected by full reconstructing one of the B mesons in a hadronic decay mode. A fit to the invariant mass differences m(D(*) pi)- m(D(*)) is performed to extract the signal yields of the different D** states. We observe the B-->D**l(-1)nu(l) decay modes corresponding to the four D states predicted by heavy quark symmetry with a significance greater than 5 standard deviations including systematic uncertainties.