Originally , Brown referred to Corythosaurus as a member of the family Trachodontidae ( now Hadrosauridae ) . Inside Trachodontidae was the subfamilies Trachodontinae and Saurolophinae . Brown classified Hadrosaurus , Trachodon , Claosaurus , and Kritosaurus in Trachodontinae , and Corythosaurus , Stephanosaurus , and Saurolophus in Saurolophinae .