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It's a minorly bothersome thing to be in a group of friends getting ready to play a game, someone goes to get a drink or you take a brief break after playing several matches in a row, then you get multiple invites from other friends because they don't know you're in a group.
My proposition is to have something show when a player is in a group just like you can put your mouse over a player and see "in queue" or "in game" or "spectating". It may even be wise to have a message appear when you try to invite a player in a group say "This player is in another party currently". Or remove the ability to add a player during that time.
These are just suggestions but I think it'd be a really good idea since I've encountered this, again minor, annoyance since joining the game. Hope riot's listening.