There are two main political parties in the United States, as the political system we have today, the Republican and Democratic Parties, which began around 1800’s.
Many political parties emerged as Anti-Masonic Party or Whig Party during The Antebellum Era between 1828-1864, but the correct answer for the ones that split from the two major political parties are Dixiecrats (1948 from Democrats), Roosevelt Progressive (around 1908 from Republicans) and the Liberal Republicans (around 1870 from Republicans).