Do halos that form early, have high concentration, are part of a pair, or contain a central galaxy potential host more pronounced planes of satellite galaxies?

The Milky Way, the Andromeda galaxy, and Centaurus A host flattened distributions of satellite galaxies which exhibits coherent velocity trends indicative of rotation. Comparably extreme satellite structures are very rare in cosmological LCDM simulations, giving rise to the `satellite plane problem'. As a possible explanation it has been suggested that earlier-forming, higher concentration host halos contain more flattened and kinematically coherent satellite planes. We have tested for such a proposed correlation between the satellite plane and host halo properties in the ELVIS suite of simulations. We find evidence neither for a correlation of plane flattening with halo concentration or formation time, nor for a correlation of kinematic coherence with concentration. The height of the thinnest sub-halo planes does correlate with the host virial radius and with the radial extent of the sub-halo system. This can be understood as an effect of not accounting for differences in the radial distribution of sub-halos, and selecting them from different volumes than covered by the actual observations. Being part of a halo pair like the Local Group does not result in more narrow or more correlated satellite planes either. Additionally, using the PhatELVIS simulations we show that the presence of a central galaxy potential does not favor more narrow or more correlated satellite planes, it rather leads to slightly wider planes. Such a central potential is a good approximation of the dominant effect baryonic physics in cosmological simulations has on a sub-halo population. This suggests that, in contrast to other small-scale problems, the planes of satellite galaxies issue is made worse by accounting for baryonic effects.