It’s almost fall, which means we are just weeks away from college application season and the start of our national obsession with the country’s elite colleges.

A new data point making its way around the internet reminds us that those schools are just that: elite. Despite the cultural space they occupy, they educate only a small, rarefied group of today’s college students.

About 30% of Harvard College’s class of 2021 has some sort of familial connection to the school, such as a parent, grandparent or other relative who attended the college, according to a survey of the class conducted by the school’s student newspaper, the Harvard Crimson. It’s hard to say whether the figure is accurate (the Crimson did correct an earlier, higher figure); more than 50% of the class responded to the survey, according to the newspaper, but it didn’t use official admissions data.

So-called legacy can play a role in the Harvard admissions process, according to a frequently asked questions page the school’s website. “Among a group of similarly distinguished applicants, the daughters and sons of Harvard College alumni/ae may receive an additional look,” the site reads. Still, a Harvard spokeswoman wrote in an email that the school considers “a range of academic and personal factors as part of a whole-person admissions process.”

Nonetheless, the Crimson survey adds to the growing body of evidence that the nation’s most prestigious colleges aren’t fulfilling what we think of as one of the most important roles a higher education institution can serve — as engines of economic and social mobility.

Mark Huelsman, a senior policy analyst at Demos, a left-leaning think tank, described the propensity of elite institutions to admit wealthy students or those with a familial connection as “the affirmative action we just don’t talk about.”

“We have a country where our titans of industry, or government, or law come from a select few institutions and that’s a problem in and of itself,” he said. “But as long as those institutions entrench privilege in a pretty severe way, that’s a major problem. It means that the ladders of opportunity aren’t there for the vast majority of people.”

Harvard and other prestigious colleges do provide generous financial aid packages to the low-income students they admit, but it’s a small share of the needy students who attend college in the U.S. At 346 colleges across the country, the share of students receiving a Pell grant — the money the federal government provides low-income students to attend college — is less than 20%, according to an analysis by Georgetown University’s

Center for Education and the Workforce. More than half those schools are among the nation’s most selective 500 colleges.

Though Ivy League and other elite schools, like Harvard, are often derided or have long been derided as bastions of elitism, research indicates that prestigious colleges of all types, including flagship public universities, are increasingly catering to wealthy and otherwise advantaged students. That’s partly due to cuts in state funding over the past several years that have pushed state schools to lure wealthy students. But it’s also the result of efforts by these schools to attract students with the kinds of qualifications that will make the schools appear more prestigious. Wealthier students often have a better shot at achieving higher test scores thanks to tutoring and other resources.

All of this means that low-income and marginalized students are more likely to end up at regional public and less-selective colleges that make do with fewer resources. That can make it harder for these students to persist and graduate and to get a decent job afterward, in many cases reproducing the inequality that existed before they entered college.

But there are some bright spots. Research indicates that public universities, like Cal State-Los Angeles and the City University of New York, do a better job than the nation’s most selective colleges at educating students from low-income backgrounds and helping them move into higher income brackets.