Complex sentence: Later, during the Soviet era, it was a part of the Armed Forces sports society, which in turn was associated with the Soviet Army; bcause of this, it was popularly referred to in the West as "the Red Army team".
Split into simpler sentences: Later, during the Soviet era, it was a part of the Armed Forces sports society, which in turn was associated with the Soviet Army. So it is popularly referred to in the West as "Red Army" or "the Red Army team".