This paper is part of a eries in which we study a hard-X-rav-selected
sample of AGN, mainly optically classified as Seyfert 1 nuclei. In thi
s paper, we use our optical and infrared imaging data of the sample to
study the properties of the host galaxies. We separate the non-stella
r and stellar components of the nuclear light, on the basis of the res
ults from Papers I and III. The stellar colours in the nucleus are gen
erally much redder in B - V and V - K indices than normal spiral galax
y bulges, and can be reproduced using stellar evolution models modifie
d by approximately 1 mag of reddening in A(V) and/or reradiation from
hot dust. The J - H colour is normal, but H - K is usually very red, i
ndicating that the near-infrared (NIR) colours are affected by dust re
radiation within the K band, either heated by the active nucleus or by
young stars in H II regions associated with enhanced star formation a
round the nucleus. The NIR colours are similar to those observed in a
sample of starburst/LINER galaxies. The B - V, V - K and J - K colours
have red gradients towards the nucleus, although there is considerabl
e scatter. The B - V and J - K colour gradients are not correlated, an
d are therefore likely to be caused by different mechanisms. The colou
r gradients are in good agreement with those seen in normal spiral gal
axies. We present luminosity distributions of the host galaxies in B,
V, J and K. There is a strong correlation between the AGN and the host
galaxy luminosity, in the sense that the more powerful AGN reside in
more luminous host galaxies. The luminosities of the host galaxies for
our sample fall between those of normal spiral galaxies and the hosts
of quasars. The central surface brightnesses and the length scales of
the discs are not well determined from the decomposition fits, but on
average they are consistent with values found in previous studies.