At least for the major US airlines (Delta, United, AA):
- Group 0/pre-boarding is active military, disabled, and infants
- Group 1 is first class & mileage club people
- Group 2 is business class
- Group 3/4 is usually economy
- Group 5 is usually the cheapest basic economy people
You can usually get bumped up to Group 2 by getting the airline's credit card or having a bunch of miles