  We investigated the formation and evolution of satellite systems in a cold,
extended circumplanetary disc around a 10 $M_{\rm{Jupiter}}$ gas giant which
was formed by gravitational instability at 50\,AU from its star. The disc
parameters were from a 3D global SPH simulation. We used a population synthesis
approach, where we placed satellite embryos in this disc, and let them accrete
mass, migrate, collide until the gaseous disc is dissipated. In each run we
changed the initial dust-to-gas ratio, dispersion- and refilling time-scales
within reasonable limits, as well as the number of embryos and their starting
locations. We found that most satellites have mass similar to the Galilean
ones, but very few can reach a maximum of 3 $M_{\rm{Earth}}$ due to the massive
circumplanetary disc. Large moons are often form as far as 0.5 $R_{\rm{disc}}$.
The migration rate of satellites are fast, hence during the disc lifetime, an
average of 10 $M_{\rm{Earth}}$ worth of moons will be engulfed by the planet,
increasing greatly its metallicity. We also investigated the effect of the
planet's semi-major axis on the resulting satellite systems by re-scaling our
model. This test revealed that for the discs closer to the star, the formed
moons are lighter, and a larger amount of satellites are lost into the planet
due to the even faster migration. Finally, we checked the probability of
detecting satellites like our population, which resulted in a low number of
$\leq$ 3\% even with upcoming powerful telescopes like E-ELT.
