The effect of a quantizing magnetic field on the filling of energy subbands of a degenerate nonrelativistic electron gas, whose magnetic moments are parallel and antiparallel to the direction of the field, is studied. Calculations are made under the assumption that the Fermi kinetic energy of the electron system increases as a result of Pauli's paramagnetism as compared to the kinetic energy calculated without taking this effect into account. Numerical values of the electron concentration are calculated as a function of the magnetic moment direction for magnetic fields under which the electrons are in states with given numbers of the Landau quantum level.