155660

You can have ten sets of numbers of at least four members from the box.

1) Prime numbers 2,3,13,17
2) Even numbers 2,8,36,56,64,136
3)Odd numbers 3,13,17,27,39,49,51,91,121,125
4) Multiples of Four 8,38,56,64,136
5)Multiples of Three 3,27,36,39,51
6)Multiples of Eight 8,56,64,136
7)Cubed Numbers 8,27,64,125
8) Squared Numbers 36,49,64,121
9) Fibonacci Numbers 2,3,8,13
10) Triangular numbers 3,36,91,136

If you wanted to you could have eleven sets by including multiples of 1.