Logitechs are a different animal.
That "sub" is not really a sub at all.
A true powered subwoofer contains only the amplifier for the subwoofer, and perhaps an adjustable crossover as well.
Your Logitech "sub", I believe, contains all the amplifiers for all the other speakers in the system as well along with a preset crossover, which may be set at an unusually high number. Many times, these "systems" also limit the low end going to the satellite speakers to preserve them.
This creates two possible situations:
1) Integrating the sub only into a "real" HT receiver may be a challenge.
2) If you use the satellite speakers on an "real" HT receiver without their low end limited, there may be problems.