Split Group

Hi, I have a grid of lines in a group, and I want to split them using a square, so that I have two groups, one that is a small cut-out portion of the grid and another that is the donut-shaped remainder. When I split, the objects split but remained grouped. Is there any way to have the command also split the objects into two groups?

You may need to ungroup all , then regroup the ones you want in each group