When teaching elementary group theory, the ideas of coset, normal subgroup and quotient group are difficult to introduce.

A possible approach is to make use of the patterns which appear on the multiplication of a group.

It is easy to pick out from the multiplication table of a group the elements which form a subgroup. All that is needed is to find a set of elements which is closed under the operation.

In the group of Table 1, clearly {I, C} form a subgroup.