You can move an individual Display from one Display Group to another. Do this to avoid the trouble of deleting and adding the Display back in the new group.
Moving Your Device
1. Click the "Display Groups" drop-down at the top of the page and select the Display Group where your Device is currently assigned
2. Next to the Device you want to move, click the button
3. You will be prompted to select another Display Group to move your Device to. Once you make your selection click on "ASSIGN"