Many private health insurers are reaping between three and 13 times the profits on student subscribers than on their typical enrollees, according to a new state report.

While private insurers posted a 2 percent average profit in 2008, student health plans offered by Aetna, which covered 32,737 students that year, resulted in an 11 percent profit margin for the company, according to the Division of Health Care Finance and Policy report. United saw profit margins of 27 percent, while HPIC took in 26 percent profits, and Security Mutual earned 22 percent margins.

All of the plans exhibited higher administrative costs for student insurance plans than the 10 percent average for all private insurance. BCSI spent the most on administrative costs, 34 percent, while Security Mutual spent 32 percent and seven other plans spent 27 percent on administration. Not all the companies posted profits, however. BCSI saw losses of 13 percent and Tufts yielded a 2 percent loss.

On average, $11 of students’ monthly premiums went toward company profits between the 2005 and 2008 school years, $21 went toward administrative costs and $72 paid for medical services.

Although three-quarters of Massachusetts’s 360,000 students obtain health insurance through a parent, spouse or employer, the rest – more than 97,000 – are required to purchase student health plans offered by 14 Massachusetts providers, according to the report.. Average yearly premiums for student health plans are $1,216, and benefits must meet minimum standards but can vary widely from schools to school.

The report also concluded that 951 students exceeded their outpatient benefit maximums in the 2007-2008 school year, 0.9 percent of those enrolled. Consumer groups blasted the report and called for the Patrick administration to “rein in” administrative costs and profits. “Insurers shouldn’t be using students as cash cows to pad their bottom line,” said Brian Rosman, Health Care for All research director, in a statement.