Check your transfer settings, by default it demands they fit all requirements to transfer. So not being a gang member, passing a program, low reoffending rate, etc.
You can fine-tune the settings for each prisoner category if you want more transfers. For example, I don't allow Super Max to do any programs, so I removed that requirement, and also allow gang members to go from SM to Max so I removed that requirement. Conversely, for Normal to Min I require they pass at least two programs, so I upped that.