This paper provides a comparative study of the geometrical structures of the magnetic fields of Earth, Jupiter, Saturn, and Uranus, starting from the traditional multipolar representations of these fields. For Earth, Jupiter, and Saturn the centered dipole, quadrupole, and octupole contributions are included, while at Uranus, only the dipole and quadrupole contributions are considered. The magnetic fields are analyzed by decomposing them into those parts which have simple symmetry properties with respect to the rotation axis and the equatorial plane. It is found that there are a number of common features of the magnetic fields of Earth and Jupiter. Compared to Earth and Jupiter, the Saturnian field exhibits not only a high degree of symmetry about the rotation axis, by now rather well known, but also a high degree of anitsymmetry about the equatorial plane. The Uranian field shows strong deviations from both such symmetries. Nevertheless, there remain features common to all four planets. The implications of these results for dynamo models are discussed. With a view to Cowling's theorem the symmetry of the fields is investigated with respect to not only the rotation axis but also to other axes intersecting the planetary center. Surprisingly, the high degree of asymmetry of the Uranian field that is observed with respect to the rotation axis reduces considerably to being comparable to that for Earth or Jupiter when the appropriate axis is employed. ¿ American Geophysical Union 1990