There are 3 ways of including a budget into a group:
While reordering the budgets, put them under the budget group name.
Modify the budget and use the "Put in Group" field.
Modify the budget group and use the list to put new accounts into the group.
Remember that budgets do not have to belong to a group - it's optional. If you have budget groups, budgets that are not part of any group will always be listed at the top of the list.