Complex sentence: In some schools corporal punishment was administered solely by the headmaster, but in English and Commonwealth private schools authority to punish was often also given to selected staff and sometimes even to certain senior students (often called prefects).
Split into simpler sentences: In some schools corporal punishment was administered solely by the headmaster, while in others the task was delegated to other teachers. In many English and Commonwealth private schools, authority to punish was also traditionally given to certain senior students (often called prefects).