  We aim to identify and quantify the effects of the satellite distribution
around a sample of galaxies in the Catalogue of Isolated Galaxies (CIG), as
well as the effects of the Large Scale Structure (LSS) using the SDSS-DR9. To
recover the physically bound galaxies we focus on the satellites which are
within the escape speed of each CIG galaxy. We also propose a more conservative
method using the stacked Gaussian distribution of the velocity difference of
the neighbours. The tidal strengths affecting the primary galaxy are estimated
to quantify the effects of the local and LSS environments. We also define the
projected number density parameter at the 5$^{\rm th}$ nearest neighbour to
characterise the LSS around the CIG galaxies. Out of the 386 CIG galaxies
considered in this study, at least 340 (88\% of the sample) have no physically
linked satellite. Out of the 386 CIG galaxies, 327 (85\% of the sample) have no
physical companion within a projected distance of 0.3 Mpc. The CIG galaxies are
distributed following the LSS of the local Universe, although presenting a
large heterogeneity in their degree of connection with it. A clear segregation
appears between early-type CIG galaxies with companions and isolated late-type
CIG galaxies. Isolated galaxies are in general bluer, with likely younger
stellar populations and rather high star formation with respect to older,
redder CIG galaxies with companions. Reciprocally, the satellites are redder
and with an older stellar populations around massive early-type CIG galaxies,
while they have a younger stellar content around massive late-type CIG
galaxies. This suggests that the CIG is composed of a heterogeneous population
of galaxies, sampling from old to more recent, dynamical systems of galaxies.
