Observations by the Viking and Cluster satellites at altitudes up to 35000km show that Lower Hybrid Cavities (LHCs) are common in the inner magnetosphere. LHCs are density depletions filled with waves in the lower hybrid frequency range. The LHCs have, until recently, only been found at altitudes up to 2000km. Statistics of the locations and general shape of the LHCs is performed to obtain an overview of some of their properties. In total, we have observed 166 LHCs on Viking during 27h of data, and 535 LHCs on Cluster during 87h of data. These LHCs are found at invariant latitudes from the auroral region to the plasmapause. A comparison with lower altitude observations shows that the LHC occurrence frequency does not scale with the flux tube radius, so that the LHCs are moderately rarer at high altitudes. This indicates that the individual LHCs do not reach from the ionosphere to 35000km altitude, which gives an upper bound for their length. The width of the LHCs perpendicular to the geomagnetic field at high altitudes is a few times the ion gyroradius, consistent with observations at low altitudes. The estimated depth of the density depletions vary with altitude, being larger at altitudes of 20000-35000km (Cluster, 10-20%), smaller around 1500-13000km (Viking and previous Freja results, a few percent) and again larger around 1000km (previous sounding rocket observations, 10-20%). The LHCs in the inner magnetosphere are situated in regions with background electrostatic hiss in the lower hybrid frequency range, consistent with investigations at low altitudes. Individual LHCs observed at high altitudes are stable at least on time scales of 0.2s (about the ion gyro period), which is consistent with previous results at lower altitudes, and observations by the four Cluster satellites show that the occurrence of LHCs in a region in space is a stable phenomenon, at least on time scales of an hour.