The transverse momentum (pT) dependence of the nuclear modification factor RAA and the centrality dependence of the average transverse momentum hpTi for inclusive J/ψ have been measured with ALICE for Pb-Pb collisions at √sNN = 2.76 TeV in the e +e − decay channel at mid-rapidity (|y| < 0.8). The hpTi is significantly smaller than the one observed for pp collisions at the same centre-of-mass energy. Consistently, an increase of RAA is observed towards low pT. These observations might be indicative of a sizable contribution of charm quark coalescence to the J/ψ production. Additionally, the fraction of non-prompt J/ψ from beauty hadron decays, fB, has been determined in the region 1.5 < pT < 10 GeV/c in three centrality intervals. No significant centrality dependence of fB is observed. Finally, the RAA of non-prompt J/ψ is discussed and compared with model predictions. The nuclear modification in the region 4.5 < pT < 10 GeV/c is found to be stronger than predicted by most models.