Pick random option in particle settings? It is under "Render" when you select the "Group" option. How does this work? I cannot see any meaningful difference when I turn it on. It looks like it only randomizes the particles a bit differently, like a different seed.
Basically it picks a random object from the group for each particle, instead of selecting them in order.

With an already randomized particle distribution this doesn't make much of a difference, but when particles are consecutively organized the effect is more obvious: