One and two-neutron removal-reactions from 19 C and 20 C have been studied using a liquid-hydrogen target at 40 A MeV. A small cross section has been observed in the one-neutron removal reaction from 20 C. The observed inclusive removal cross sections are compared with theoretical removal cross sections calculated by using shell model spectroscopic factors and Glauber-model single-particle cross-sections. The observed momentum distributions are also compared with those calculated by using continuum-discretized coupled-channel methods. Good consistency between theory and experiment is shown in the one-neutron removal reaction from 19 C. However, our theoretical calculation fails to reproduce the neutron removal reactions from 20 C, which suggests that further improvements of the theoretical descriptions are necessary.