Board Thread:Naruto: The Last Discussion/@comment-732150-20150205151208/@comment-26112212-20150210154716

The main and Branch family divided on the moon, on earth there was no main family except Hagoromo's direct descendants. There was a war on the moon between Main family and Branch family after Hamura's death it was the branch family who misinterpreted Hamura's celestial decree, Hamura is main family member if you have seen the movie he was also with main family Ōtsutsuki Clan Patriarch. Toneri Otsutsuki is a branch family member, who misinterprets Hamura's will.

I think as majority states Hamura might have left a Hyuga member with Byakugan before leaving earth, also I think it is possible that some clan members from the moon who had Byakugan could have travelled to earth via portal