A full amplitude analysis of Λ0b→J/ψpπ− decays is performed with a data sample acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3  fb−1. A significantly better description of the data is achieved when, in addition to the previously observed nucleon excitations N→pπ−, either the Pc(4380)+ and Pc(4450)+→J/ψp states, previously observed in Λ0b→J/ψpK− decays, or the Zc(4200)−→J/ψπ− state, previously reported in B0→J/ψK+π− decays, or all three, are included in the amplitude models. The data support a model containing all three exotic states, with a significance of more than three standard deviations. Within uncertainties, the data are consistent with the Pc(4380)+ and Pc(4450)+ production rates expected from their previous observation taking account of Cabibbo suppression.