Private equity firm Clearlake Capital Group LP has completed the purchase of online retailer Bluefly Inc. The transaction, announced in May, follows Clearlake’s $35 million acquisition of Agilysys Inc.’s retail services unit in July and the purchase of Chicago data service Inventus LLC for an undisclosed amount in June.

New York-based Bluefly sells designer clothes, accessories and beauty products at discounts through its website. Founded in 1998, the company sells more than 350 brands, discounted up to 75 percent off. In 2011, Bluefly expanded, launching Belle & Clive, a members-only shopping website, and Eyefly, an online glasses retailer.

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