Player Collision Group Not working

You may want to check if the parts you want to have CollisionGroups with have CanCollide set to true?

If that doesn’t work I would use this script where it will print the collision group of part your mouse is hovering over:

repeat task.wait(1) until game:IsLoaded() == true

local Mouse = game.Players.LocalPlayer:GetMouse()

while (true) do
	task.wait(1)
	if (Mouse.Target ~= nil) then
		warn(Mouse.Target.CollisionGroup)
	end
end

I would check the players parts and see if those are correct and the mobs part.
Also what do you exactly want to achieve with the collision groups?