Complex sentence: Dynasties throughout the world have traditionally been reckoned patrilineally, most famously under the Frankish Salic law, with succession through a daughter (when permitted) considered to establish a new dynasty in her husband's ruling house.
Split into simpler sentences: Dynasties throughout the world have traditionally been reckoned patrilineally such as under the Frankish Salic law. Succession through a daughter when permitted was considered to establish a new dynasty in her husband's ruling house.