The Smithsonian has compiled a list of the 41 states in the United States which have officially designated State Insects.
Illinois has the Monarch Butterfly:
Most of the states who have an official State Insect have selected a butterfly of some sort, but New Mexico is very unusual.
The State Insect of New Mexico is the Tarantula Hawk Wasp:
Read more about the Tarantula Hawk Wasp at Durango Nature Studies