In short: you might have a shot !
I'm not an astrophotography expert, but here are some facts (I hope I interpreted them correctly):
- Jupiter is in average about 780 millions of kilometers from the Sun. Compared to Saturn and its 1400 millions, it will receive about 4 times less light per unit of surface from the sun. The same is true for their moons.
- Currently (info from The Sky Live), Jupiter if about 5 AU from Earth and Saturn is about 10 AU from the Earth. The light coming from Saturn will be reduced by another factor 4 before reaching Earth.
If the exact same moons were orbiting Jupiter and Saturn, the intensity of light coming from the one orbiting Saturn will be diminished by a factor 16 compared to the one coming from Jupiter's. If you want to receive the same amount of light, you will need to increase your shutter time by 16.
Now considering the real moons, Io (Jupiter) has a diameter of about 3600 km with an albedo of 0.6 and Titan (Saturn) is about 2500 km wide with an albedo of 0.2. All thing being equals, Io will reflect about 6 times more light than Titan. Titan is about 100 times less luminous than Io !
As a side note, Jupiter and Saturn have about the same diameter (143 vs 120 thousand kilometers) and about the same Bond albedo.
Considering distance, using the same lens, your camera's sensor will perceive Saturn as being about 2 times less "big" than it did with Jupiter, so you will have 4 times fewer pixels to resolve it. Considering the moons, it should be about the same.
Given those informations, you should be able to judge if you can get a good image of Saturn and its moons, given the image you got from Jupiter.
Comparaison to telescope
For information, this website indicates that you need a 90-millimeter telescope to see the brightest moons of Saturn (90 millimeters being the telescope aperture). This kind of telescope is usually associated with a focal length of about 600 or 700mm (so about a f/7 600mm lens). As your Canon PowerShot SX410 IS is equivalent to a 960mm focal length with a f/5.6 aperture, you might have a shot :)