For the 580 (NA with Hemi), that may be a '68 only thing. I don't have any Chrysler literature with that on it, I'm referencing a pdf I have of 62-68 option codes that says:

580 Road Wheels (n/a with Hemi)
581 15 inch deluxe wheel cover
582 Sport wheel covers
583 Bolt/on design wheel cover
584 Deep Dish Wheel Covers (n/a with Hemi)
586 Simulated Mag Wheel Covers (n/a with Hemi)
587 Simulated Mag Wheel Covers (1968 Dart)

We know in 1966 the Hemi Charger would have had 584 as standard equipment, so it doesn't fit 1966. And the Hemi Chargers in 1967 would have had 14" wheels as well.

I also have an Option code list from a Paul Herd book for 1968 that aligns with the above list, basically saying the 1968 Hemi cars got 15" wheel covers.

580 Road Wheels (n/a with Hemi)
581 15 inch deluxe wheel cover
584 Deep Dish Wheel Covers (n/a with Hemi)
586 Simulated Mag Wheel Covers (n/a with Hemi)

Looks like I need to update my list to reflect 1966-67 cars more accurately. Thanks!