[Perdition]

Solitary doesn't just mean single occupancy cells, it means separation from most human contact.

They could easily have groups of cells where inmates are confined individually but can still have non-physical contact with other prisoners.

And as most of those in solitary aren't raving psychotics (mostly they attacked guards or rival gang members, an issue largely due to prison overcrowding) they could be allowed monitored time in the yard with other prisoners.