An inspection report on Low Moss Prison in Bishopbriggs disclosed that in 2012-13, there were 15 serious attacks by prisoners on other criminals in the jail.
There were a further 140 assaults by prisoners on fellow inmates where the victim suffered minor injury or no injury, and 10 such assaults on prison staff.
There were also "five incidents of concerted indiscipline" during the year, most of which were said to be a form of sit down protest.
The report, by HM Chief Inspector of Prison David Strang, said Low Moss had "appropriate staffing levels" to "ensure good order is maintained", adding "most prisoners reported that they feel safe".
A Scottish Prison Service spokesman said: "We will consider and respond to all the recommendations."