  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.
