I would define "Major" as being founded by one of O sensei's students, and run successfully. Like Tomiki, Iwama, or Yoshinkan.
According to that criteria, you might consider the following as "major":
- Manseikan Aikido established by Kanshu Sunadomari
- Tendo Ryu Aikido established by Kenji Shimizu
- Shinshin Aiki Shurenkai established by Hitohiro Saito