For ten points, identify this group with four elements named after a mathematician who also names a bottle.
Eight of the eleven rings with the same number of elements as this group have its operation as their additive operation, and all of this group's 5 subgroups are normal. This group names an a cappella singing group at Northwestern University best known for their song  Finite Simple Group of Order Two . This group is isomorphic to   D2, the second dihedral group, and to Z2 Ã— Z2. This group is equal to the symmetry group of a rectangle which is not a square. This group is the smallest non-cyclic group, and every element's square is equal to the identity. For ten points, identify this group with four elements named after a mathematician who also names a bottle.
Eight of the eleven rings with the same number of elements as this group have its operation as their additive operation, and all of this group's 5 subgroups are normal.
Klein four-group [prompt on four-group, accept vierergruppe, accept D2 and Z2 Ã— Z2 before read]