Statistical analyses of the magnetopause (MP) motion observed by THEMIS suggested that the MP oscillates preferably at some prominent (sometimes called "magic") frequencies, which were found to stand out also in ground-based and ionospheric measurements of geomagnetic ultra-low frequency pulsations. In this paper we present an extension to these statistical analyses of the observed MP oscillations examining their dependence on the prevalent interplanetary magnetic field (IMF), solar wind (SW) flow speed and cone angle conditions as well as their local time of occurrence. Our results show enhanced oscillation activity at these frequencies in the noon local time sector during periods of northward IMF, slow or moderate SW speed and low SW cone angle. This combination of conditions supports an interpretation in terms of standing Alfvénic Kruskal-Schwarzschild surface modes on the MP.