dave black wrote:

I've always been puzzled that even 'planet-sized' moons such as Titan
don't have any satellites going round them.

Is there a particular reason?

If there are several moons in the system then it will be virtually
impossible to find any stable orbits that do not suffer from resonance
coupling with the other moons leading to instability.

However, for the case of the Earth-Moon system mass ratio 82.3:1 there
are huge families of periodic orbits available for a small test
particle. They were investigated extensively during the race to put a
man on the moon. Low energy ones that get close to both Earth and Moon
being of particular interest. These orbits are mostly very strange
shaped - the more exotic they are the more marginal their stability.

ISTR there are potentially stable orbits around the L4 L5 points for the
Earth Moon system - much complicated by the influence of the Sun.

Regards,
Martin Brown