Thorfinn had five sons: Arnfinn, Havard, Hlodvir, Ljot, and Skuli. Their mother was Grelad, a daughter of "Earl Dungad of Caithness" and Groa, herself a daughter of Thorstein the Red. Grelad's Norse credentials were thus impressive, but it has been suggested that her connection to this "earl" of Caithness may have been more important for the Orkney earldom. It is likely that Dungad was a member of a pre-Norse era ruling family and that the marriage brought Groa's descendants within the Celtic "derbfine" and helped to legitimise their ambitions on the north mainland of Scotland. Thorfinn and Grelod also had two daughters whose names are not known, each of whom had a son called Einar - Einar "kliningr" ("Buttered-bread") and Einar "harðkjotr" ("Hard-mouth").