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5. For C locate the one subgroup of order 4. The group D has three subgroups of order 4.
Select one of the three subgroups of D that has a different structure than the subgroup you
obtained from C.
The . subgroups () method will give you a list of all of the subgroups to help you get started.
A Cayley table will help you tell the difference between the two subgroups. What properties
of these tables did you use to determine the difference in the structure of the subgroups?
6. The . subgroup(elt_list) method of a group will create the smallest subgroup containing
the specified elements of the group, when given the elements as a list elt_list. Use this
command to discover the shortest list of elements necessary to recreate the subgroups you
found in the previous exercise. The equality comparison, ==, can be used to test if two
subgroups are equal.

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