Good way to organize group of constants in enum-like fashion

I'm trying to find a good way to orginize a group of constant values that are used simply for immutable data.

Here is what I'm currently attempting:

public class FishType {

    //PredatorFishType extends FishType
    public static final PredatorFishType SHARK = new PredatorFishType(5, 20, "Shark");
    public static final FishType CAT_FISH = new FishType("Cat Fish");

    private String name;

    private FishType(String name) {
        this.name = name;
    }

    public String getName() {
        return name;
    }

}

I use reflection to gather the final values into a collection aswell. I used to utilize enum but was forced to think of a new way to do this when different types of fish came into play such as the predator which contains other data such as food and so on. These constants are only used for data displaying purposes and have no reason to be mutated.

If there is some way to have multiple enum types within the same enum (If that makes any sense at all), that'd be great.

Thanks for reading.