Complex sentence: The Republic of Cuba, under president (and later nationalist dictator) Fulgencio Batista, was an authoritarian police state during his rule and continued following his overthrow during the Cuban Revolution in 1959, with the rise to power of Fidel Castro and his communist regime.
Split into simpler sentences: The Republic of Cuba under president (and later nationalist dictator) Fulgencio Batista was an authoritarian police state during his rule. Police influence continued following his overthrow during the Cuban Revolution in 1959 with the rise to power of Fidel Castro and his communist regime.