The arrival of the railroad in Groesbeck enabled it to become the county seat.The city of Groesbeck is served by the Groesbeck Independent School District, which includes five different schools: Preschool, H.O.Whitehurst, Enge Washington, Groesbeck Middle School, and Groesbeck High School. Cynthia Ann Parker, mother of Quannah Parker was captured by the Comanche north of Groesbeck. Groesbeck is a city in and the county seat of Limestone County, Texas, United States. The population was 4,291 at the 2000 census. The community is named after a railroad employee.