A subfactor $N \subset M $ is maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.

Question: are there only finitely many maximal subfactors of a fixed finite index (up to isomorphism)?

(Need to add "finite depth" and "irreducible" ?)

Bonus question: let $\alpha$ the index of a finite depth irreducible subfactor.
Does there exist a maximal finite depth irreducible subfactor of index $\alpha$ ?

A subfactor $N \subset M $ is maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.

Question: Are there only finitely many maximal irreducible amenable subfactors at fixed finite index (up to isomorphism)?

Bonus question: let $\alpha$ the index of a irreducible amenable subfactor.
Is there a maximal irreducible amenable subfactor of index $\alpha$ ?

A subfactor $N \subset M $ is maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.

Question: are they only finitely many maximal subfactors of a fixed finite index (up to isomorphism)?

(Need to add "finite depth" and "irreducible" ?)

Bonus question: let $\alpha$ the index of a finite depth irreducible subfactor.
Does there exist a maximal finite depth irreducible subfactor of index $\alpha$ ?

A subfactor $N \subset M $ is maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.

Question: are there only finitely many maximal subfactors of a fixed finite index (up to isomorphism)?

(Need to add "finite depth" and "irreducible" ?)

Bonus question: let $\alpha$ the index of a finite depth irreducible subfactor.
Does there exist a maximal finite depth irreducible subfactor of index $\alpha$ ?

A subfactor $N \subset M $ is maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.

Are they only finitely many maximal subfactors of a fixed finite index (up to isomorphism)?
(need to add finite depth and irreducible ?)

A subfactor $N \subset M $ is maximal if it admits no non-trivial intermediate subfactors $N \subset P \subset M $.

Question: are they only finitely many maximal subfactors of a fixed finite index (up to isomorphism)?

(Need to add "finite depth" and "irreducible" ?)

Bonus question: let $\alpha$ the index of a finite depth irreducible subfactor.
Does there exist a maximal finite depth irreducible subfactor of index $\alpha$ ?