k5_g3 := List([1..12], i -> []);

k5_g3[8,1] := [ [ 4, 5, 6, 7, 8 ], [ 3, 4, 6, 7, 8 ], [ 2, 5, 6, 7, 8 ], [ 1, 2, 5, 6, 8 ], [ 1, 3, 4, 7, 8 ], [ 1, 2, 3, 4, 7 ], 
  [ 1, 2, 3, 5, 6 ], [ 1, 2, 3, 4, 5 ] ];

k5_g3[10,1] := [ [ 3, 7, 8, 9, 10 ], [ 6, 7, 8, 9, 10 ], [ 1, 5, 8, 9, 10 ], [ 6, 7, 8, 9, 10 ], [ 3, 6, 7, 8, 10 ], [ 2, 4, 5, 7, 9 ], 
  [ 1, 2, 4, 5, 6 ], [ 1, 2, 3, 4, 5 ], [ 1, 2, 3, 4, 6 ], [ 1, 2, 3, 4, 5 ] ];

k5_g3[12,1] := [ [ 8, 9, 10, 11, 12 ], [ 3, 4, 5, 6, 7 ], [ 2, 9, 10, 11, 12 ], [ 2, 8, 10, 11, 12 ], [ 2, 7, 10, 11, 12 ], [ 2, 8, 9, 11, 12 ], 
  [ 2, 5, 8, 9, 10 ], [ 1, 4, 6, 7, 9 ], [ 1, 3, 6, 7, 8 ], [ 1, 3, 4, 5, 7 ], [ 1, 3, 4, 5, 6 ], [ 1, 3, 4, 5, 6 ] ];