Women in positions of power have a lot less trouble than men at finding other female executives for key roles, according to an analysis of 1,000 U.S. corporate boardrooms.

When women hold key leadership posts like CEO or board chairman, companies have women in more than 27 percent of director seats, compared with less than 18 percent when men are in charge, according to a study released Monday by the advocacy group 2020 Women on Boards. The group wants women to hold at least 20 percent of all board seats at U.S. companies by 2020, up from 17.9 percent now. Almost 90 percent of businesses led by women already meet that goal.

"Women-led companies are doing better in the gender diversity on boards than male-led companies, but in general we're also seeing a better level of women serving on boards," said Malli Gero, co-founder and president of 2020 Women on Boards. "When you have a woman on the board, they are going to be able to help find more women."