Name: Janessa Gramson

Group: U(24)

Group Description: The set of integers less than 24 and relatively prime to 24 with multiplication modulo 24.

We'll call the set R. R = {1,5,7,11,13,17,19,23}.

Because every element of R is its own inverse, any subset of R, which is not all of R and which includes 1 and at least one other element is a non-trivial, proper subgroup. I hope you don't want me to list them all out because there are a lot; 2^7 if I remember my Combinatorics correctly. A few examples though are:

{1,5,7}, {1,13,19}, {1,5,7,11,13,17,19}, {1,11,17,23}