Yep. And that was something Joseph Stalin knew quite well. That's why the Soviets always referred to the nazis as "fascists", never as "nazis".
Mussolini was a communist before declaring himself “fascist”. Only difference between him and the commies was the state’s corporatization of business (predecessor of today’s “crony capitalism”, still leftist insofar that it is syndicalist) and pandering to religion; the state was still all-powerful.
Not to mention Stalin was in part a panderer to nationalist feelings, what with his “socialism in one country”.