Saving intersection matrix as a table

[witszymanski]

Objective
I would like to ask if there is a way to save all the entries of different sets from intersection matrix as separate tables or any other format.

So like here, I would have a 1st table with 5904 entries, 2nd table with 91 etc.

Or just a better way would be to create a table with the intersection number and elements name / row number...

Btw. Awesome package!