Complex sentence: Following the Nazi takeover, the National Socialists moved quickly to outlaw other political parties, and, following a campaign of intimidation, the Catholic Centre Party and the Bavarian People's Party (a regional Catholic party) had ceased to exist by July 1933.
Split into simpler sentences: Following the Nazi takeover, the National Socialists moved quickly to outlaw other political parties. And following a campaign of intimidation, the Catholic Centre Party and the Bavarian People's Party (a regional Catholic party) ceased to exist by July 1933.