The energy shifts due to interactions violating time-reversal invariance and parity symmetry, g factors, and energies for the hyperfine levels of the ground rotational level of the Δ13 electronic state of the Hf177F+19 ion are calculated as functions of the external electric and magnetic fields. The calculations can be used to plan an experiment to measure the magnetic quadrupole moment of the Hf177 nucleus and to interpret the obtained data.