This takes a little bit on your part but isn’t too hard to set up. Get everyone to “check in” as they arrive. Check their names off a list and hand out name tags. All pretty normal stuff. But pay attention to them as you do this and note the color of their eyes. Have a sheet that they can’t see. Have this prepared ahead of time with all the names and columns for eye colors so you can just quickly put a check mark in the right place.
An alternative to the chart and so a bit easier is to just hand them a colored balloon after you know which eye color they have. While I don't think too many people would make the connection between the color of the balloon they have and their eye color, you might want to just assign a different balloon color to each eye color.
Now when you are ready to play the game, you are going to group them by eye color without them knowing how you are forming the groups. So just go down your list and call off the names of everyone with the blue eyes and tell them they are on a team. Then do the same for the other eye colors. (green, gray, brown) Or if you used the balloons you just say find everyone with the same color of balloon as you.
Tell everyone that they have something in common with everyone in their group. They have 5 minutes to figure out what it is. At the end of the time, go around to each group and quietly ask them what they have in common. You want to do this quietly so to not tip off the other teams if one group figures it out before you ask another.
After you talk to all the groups award the group(s) that figured it out.
Since they don’t know what they have in common, they will have to talk to each other to try to figure it out. This is a great sneaky way to get them interacting with each other.