Complex sentence: The Party found that its peak of influence had passed after the 1940s, e.g., in 1954, in a case managed by the NAACP, the US Supreme Court ruled in "Brown v. Board of Education" that segregation of public schools was unconstitutional.
Split into simpler sentences: The Party found that its peak of influence had passed after the 1940s. In 1954, in a case managed by the NAACP, the US Supreme Court ruled in "Brown v. Board of Education" that segregation of public schools was unconstitutional.