The study of the physical properties of the topside ionosphere is fundamental to investigating the energy balance of the ionosphere and developing accurate models to predict relevant phenomena, which are often at the root of Space Weather effects in the near-Earth environment. One of the most important physical parameters characterising the ionospheric medium is electrical conductivity, which is crucial for the onset and amplification of ionospheric currents and for calculating the power density dissipated by such currents. We characterise, for the first time, electrical conductivity in the direction perpendicular to the geomagnetic field, namely Pedersen and Hall conductivities, in the topside ionosphere at an altitude of about 450 km. For this purpose, we use eight years of in situ simultaneous measurements of electron density, electron temperature and geomagnetic field strength acquired by the Swarm A satellite. We present global statistical maps of perpendicular electrical conductivity and study their variations depending on magnetic latitude and local time, seasons, and solar activity. Our findings indicate that the most prominent features of perpendicular electrical conductivity are located at low latitudes and are probably driven by the complex dynamics of the Equatorial Ionisation Anomaly. At higher latitudes, perpendicular conductivity is a few orders of magnitude lower than that at low latitudes. Nevertheless, conductivity features are modulated by solar activity and seasonal variations at all latitudes.