Which closure properties are always valid between regular, context-free and non context-free languages?

I am making a scheme that respresents some closure properties (union, intersection, complement and concatenation) for regular languages, context-free languages, decidable languages and RE languages. Below you can see my scheme. Feel free to let me know if there are any errors.


I am trying to find all possible internal closure properties of these different languages that will always be valid. E.g., I know that $$text{Regular language } cup text{ CFL } = text{ CFL } $$

$$text{Regular language } cap text{ CFL } = text{ CFL } $$
$$text{Regular language } ^* text{ CFL } = text{ CFL } $$

What other internal properties are there between these languages?