  We present the spatial analysis of five Compton thick (CT) active galactic
nuclei (AGNs), including MKN 573, NGC 1386, NGC 3393, NGC 5643, and NGC 7212,
for which high resolution Chandra observations are available. For each source,
we find hard X-ray emission (>3 keV) extending to ~kpc scales along the
ionization cone, and for some sources, in the cross-cone region. This
collection represents the first, high-signal sample of CT AGN with extended
hard X-ray emission for which we can begin to build a more complete picture of
this new population of AGN. We investigate the energy dependence of the
extended X-ray emission, including possible dependencies on host galaxy and AGN
properties, and find a correlation between the excess emission and obscuration,
suggesting a connection between the nuclear obscuring material and the galactic
molecular clouds. Furthermore, we find that the soft X-ray emission extends
farther than the hard X-rays along the ionization cone, which may be explained
by a galactocentric radial dependence on the density of molecular clouds due to
the orientation of the ionization cone with respect to the galactic disk. These
results are consistent with other CT AGN with observed extended hard X-ray
emission (e.g., ESO 428-G014 and the Ma et al. 2020 CT AGN sample), further
demonstrating the ubiquity of extended hard X-ray emission in CT AGN.
