System 1 has group of order 8
{0,4,8}{2,6,9}{1,3,5,10,7}
{0,5,9}{2,7,8}{1,6,4,3,10}
{1,4,9}{3,6,8}{0,7,5,2,10}
{1,5,8}{3,7,9}{0,2,4,10,6}
{0,1,2,3}{4,5,6,7}{8,9,10}
-----------------------------------
System 2 has group of order 2
{0,4,8}{1,5,9}{2,6,3,7,10}
{0,5,10}{2,7,8}{1,3,9,6,4}
{1,6,8}{3,4,10}{0,2,5,7,9}
{2,4,9}{3,5,8}{0,6,10,1,7}
{0,1,2,3}{4,5,6,7}{8,9,10}
-----------------------------------
System 3 has group of order 2
{0,2,4}{1,6,8}{3,9,5,7,10}
{0,5,8}{1,3,7}{2,9,6,4,10}
{0,7,9}{3,4,8}{1,5,2,6,10}
{1,4,9}{2,7,8}{0,6,3,5,10}
{0,1,2,3}{4,5,6,7}{8,9,10}
-----------------------------------
System 4 has group of order 2
{0,2,4}{1,6,8}{3,9,5,7,10}
{0,5,8}{1,3,7}{2,9,6,4,10}
{0,6,10}{1,4,9}{2,5,3,8,7}
{0,7,9}{1,5,10}{2,6,3,4,8}
{0,1,2,3}{4,5,6,7}{8,9,10}
-----------------------------------
System 5 has group of order 4
{0,2,4}{1,6,8}{3,5,9,7,10}
{0,5,7}{2,6,10}{1,4,8,3,9}
{1,3,7}{2,5,8}{0,6,9,4,10}
{1,5,10}{3,4,6}{0,8,7,2,9}
{0,1,2,3}{4,5,6,7}{8,9,10}
-----------------------------------
System 6 has group of order 4
{0,2,4}{1,5,8}{3,6,9,7,10}
{0,5,7}{3,4,8}{1,9,2,6,10}
{0,6,8}{1,3,7}{2,5,9,4,10}
{1,4,6}{2,7,8}{0,9,3,5,10}
{0,1,2,3}{4,5,6,7}{8,9,10}
-----------------------------------
System 7 has group of order 1
{0,2,4}{1,5,8}{3,6,9,7,10}
{0,5,7}{2,6,10}{1,3,8,4,9}
{0,6,8}{2,5,9}{1,7,3,4,10}
{1,4,6}{2,7,8}{0,9,3,5,10}
{0,1,2,3}{4,5,6,7}{8,9,10}
-----------------------------------