How do I move a Category to a different Group?

If you have a Category out of place, simply go to Settings > Manage Categories, click the edit tool for that category (at the right of the row) and change the Group to which it is assigned. If you need to reorder the group now that it contains an additional category, click the up/down arrow on the right and drag your category to the correct location.

If you need to move more than one category at a time, check the box to the left of each, then click the purple Change Group button at the bottom of the screen