With 7 attributes, there are but 2**7 == 128 subsets to consider; and no attribute group with more that 7 attributes.
You could enumerate all subsets of each object. That might total to a few thousand unique attribute groups for the whole problem. In other words, with size and density so low, you can easily afford to construct the powerset of attributes. This way you can transform the 500 by 75 into 500 by few-thousands, search and sort by cardinality or weight, etc.