The glass ceiling is firmly intact among America's wealthiest 1 percent.

Women earn enough on their own to qualify for 1 percent status in only one in 20 elite households, according to new research in American Sociological Review. That gap hasn't narrowed in over 20 years.

A woman's best shot at reaching 1 percent status is not through a high-paying job or advanced education, but rather by marrying a man with "good income prospects," researchers said. In contrast, men's chances at reaching 1 percent status are closely associated with career and educational achievements.

"In the last two decades, women have made virtually no progress relative to men in earning top 1 percent income," Jill Yavorsky, a University of North Carolina-Charlotte professor who authored the study, tells CNBC Make It.

"This is despite the fact that women now earn half of all law and medical degrees and are starting businesses in greater numbers today than in the past," she says. "Unfortunately, these educational and entrepreneurship accomplishments have not resulted in securing them the same kind of access to high income positions as they have for men."

Women were 84 percent less likely than men to have a personal 1 percent status, and only 4.5 percent of women could earn enough themselves to qualify for the top 1 percent, according to the analysis of Federal Reserve data from 1995 to 2016.

Married women, on the other hand, had much higher odds, largely due to their spouse's incomes. They were 991 percent more likely than single women to be in the top 1 percent, compared to married men at 71 percent.

Income inequality between the 1 percent and remaining 99 percent of the American population has been on the rise since the 1980s, with the top 1 percent owning more wealth than the country's bottom 90 percent. In 2016, the U.S. median household income was $51,000, while households in the top 1 percent earned a minimum of $845,000, according to the 2016 Survey of Consumer Finances.

Prior research shows that since 1 percent households have such tremendous financial resources, they yield significant political, economic and social power. If women's income is inconsequential in these households, then men are dominating the economy, Yavorsky says.

"It's primarily men's interests being reflected in this influence, which, as other research indicates, can differ from women's interests."

Higher education and self-employment do increase women's income, but those factors alone are not enough to secure women equal opportunity to a 1 percent position, researchers said — 1.8 percent of self-employed and highly-educated married women earn enough on their own to be in the top 1 percent, compared to 7.3 percent of men.

Men still dominate high-paying fields like finance, consulting and law, are more likely to start their own businesses than women and have more opportunity to rise up corporate ranks. Women face career obstacles and have lower earnings at all educational levels, researchers noted, and therefore take longer to achieve a high income status than men.

Since the research showed a strong connection between entrepreneurship and high incomes, Yavorsky says that expanding female entrepreneurs' access to financial capital to start their companies would help narrow the pay gap in the 1 percent.

She also suggests passing federal legislation that could jump-start gender progress, such as state-sponsored childcare, both paid maternity and paternity leave and gender quotas that could increase women's representation in leadership roles.

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