1. Find all the subgroups of Q8. (Q8 = {I, -I, J, -J, K, -K, L, -L}. Different notation can be used as well). Show that Q8 is an example of a nonabelian group with the property that all its proper subgroups are cyclic.

2. a) Let G be a cyclic group of ordern. Show that ifmis a positive integer, then G has an element of ordermIFFmdividesn.

b) Let G be a cyclic group of order 40. List all the possibilities for the orders of elements of G.

3. Let G = <x> be a cyclic group of order 144. How many elements are there in the subgroup <x^26>?

4. Construct a nonabelian group of order 16, and one of order 24.