${Group.name} is solvable because it is abelian.
${Group.name} is a solvable group by the following solvable decomposition:
In summary, ${decompositionDisplay}.
You can see a diagram of all the groups in the solvable decomposition, including quotient maps, by Cayley diagram, cycle graph, or multiplication table.
${Group.name} is not a solvable group.
In fact, it does not even have a normal subgroup that can be used to form an abelian quotient group.
Group Explorer is currently unable to determine whether ${Group.name} is a solvable group because it does not have access to all the groups it needs. For example, there is a normal subgroup of order ${unknown_subgroup.order} that yields an abelian quotient group, but that is not isomorphic to any group in the library currently loaded.
You will need to more groups loaded (see options window for starters) to make this computation possible.
${G.name}