How do I separate one of a group of Vector Graphics on a page of many?

I downloaded a page of free vector images. In Illustrator, they are all combined together into one group. If I "ungroup" them, each image is then separated into it's many parts. For example, if one of the images is a flower made up of lots of separate pieces, how do I get just those flower pieces combined so I can separate the flower? Thanks.

That's why they were "free." Make sure to check the terms of usage, as it may be limited. You're going to have to select all the pieces of the flower either individually or using an area-select tool and then group those pieces.