Are there offices? Really?

Magyars had 3 kind of (known) offices.

Kende - sybolic leader
Gyula - military leader
Horka - judge

The exact use of the word gyula by the Magyars is unclear but, based on contemporary sources, many Hungarian historians believe that under the system of dual kingship which the Magyars used in the 9th century, the two kings of the tribal confederation were the kende (or kündü) and the gyula. While the former was the nominal leader, the latter was the chief warlord or military commander.

Horka or harka was a title used by the Magyar tribes in the 9th and centuries. According to Emperor Constantine Porphyrogennetos in De administrando imperio, the horka had judicial authority. However, in other sources the term horka was applied to a military leader (such as Bulcsú who led the Magyar forces at the Battle of Lechfeld). Certainly at some point in the 10th century the roles of horka and gyula (the chief warlord) had became similar, with the horka having authority in Western Transdanubia and the gyula in Transylvania in the east. In later sources the word appears only as a personal name.

The Faction leader can be the kende with many but only influence bonus. The Gyula can play the role of the faction heir as a commanding leader. I suggest to choose the Gyula by the command rank of the characters instead of the influence (?).
The Horka can be a trait, too but the other two cannot get this office. He may get law bonus - what else?