- Mantidfly - Neuroptera
Mantidflies may resemble mantids or wasps, but belong with the lacewings in the order Neuroptera. - Pillbug - Isopoda
Woodlice, or pillbugs are related to crustaceans in the Isopoda and are not insects. - Twisted-wing parasites - Strepsiptera.
Twisted wing parasites like this one may be parasites of wasps or leafhoppers and belong to the order Strepsiptera. - Lacewing - Neuroptera.
Lacewings, antlions and owlflies belong to the order Neuroptera. - Silverfish - Thysanura
Silverfish and firebrats belong to the order Thysanura. - Webspinner - Embioptera
Webspinners or foot spinners make silk with their feet and belong to the order Embioptera or Embiodea or Embiidina, depending on who you ask. - Jumping Bristletail - Microcoryphia
Jumping bristletails are similar to silverfish and belong to the order Microcoryphia. - Beetle - Coleoptera
Beetles outnumber all other animal species on earth and they belong to the order Coleoptera. - Mantid - Mantodea
Mantids belong to the order Mantodea. - Fly - Diptera
Flies belong to the order Diptera. - Damselfly - Odonata
Damselflies and dragonflies belong to the order Odonata. - Roach - Blattodea
Roaches belong to the order Blattodea. - Earwig - Dermaptera
Earwigs belong to the order Dermaptera. - Scorpionfly - Mecoptera.
Scorpionflies, snow fleas, and hangflies belong to the order Mecoptera. - Centipede - Myriapoda
Centipedes are not insects, but rather belong to a related group in the Myriapoda (many legs).