The onset of intruder ground states in Na isotopes is investigated by comparing experimental data and shell-model calculations. This onset is one of the consequences of the disappearance of the N = 20 magic structure, and the Na isotopes are shown to play a special role in clarifying the change of this magic structure. Both the electromagnetic moments and the energy levels clearly indicate an onset of ground state intruder configurations at neutron number N = 19 already, which arises only with a narrow N = 20 shell gap in Na isotopes resulting from the spin-isospin dependence of the nucleon-nucleon interaction (as compared to a wider gap in stable nuclei like 40 Ca). It is shown why the previous report based on the mass led to a wrong conclusion.