[math-fun] Simple finite group problem

This is a simple finite group problem, not to be confused with a finite simple group problem. It's a simple problem about finite groups, not a difficult problem about finite simple groups. List all multiplicative groups of integers mod ten. For instance {1,9} is one of them, and {1} is another. I noticed that the number of multiplicative groups of integers mod N is not in OEIS. I plan to add it.