Below the Gojo Clan 's main family, there are currently six other branch families that exist within the clan. The lowest-ranked among them is the Tobiume branch family, and the highest-ranked is the Oimatsu.

Gojo Hajime is not the Oimatsu branch head, but he

is

one of the aging Oimatsu head 's most trusted advisors. Someone who is entrusted with a great number of important responsibilities within his branch family. The

most

trusted, arguably, if certain rumors are anything to go by.

It's a respectable position that Gojo Hajime holds, although there is little respect that Shiki holds for the man as a person.

He had, after all, essentially abandoned Yuzuki, because Yuzuki was a sickly son who was of little value to him.