am wondering what is the largest language class that is known for which set inclusion is decidable, ie a class such that if $A, B$ are in that class then $A \subset B$ is decidable.
am also interested in the same question for what were once called "GSMs", generalized sequential machines, or maybe more modernly, FSM "transducers", where if $f(x)$ is the transducer, $C \subset f(C)$, $C$ in the class.
(of course, the problem is also equivalent to determining whether the intersection of a complement is empty.)
[simply asking for the "largest known" language is a literature related question. however some kind of proof that there exists a "largest class" I believe is an open question. although, there might be a straightfwd argument of nonexistence via diagonalization...?]
unfortunately wikipedia does not have some of this basic info for major language classes. wonder if there is any table, paper, or reference esp online.
there is a nice table of decidability & undecidability of basic language questions in  but its quite dated at this point.