Insect

Insects (Insecta) are the predominant group of arthropods, placed within the class Hexapoda along with the Protura, Collembola, and Diplura. Insects are the only group other than vertebrates to have developed flight.

wingless insects

Order Archaeognatha (Jumping bristletails)
Order Monura - extinct
Order Thysanura (Common bristletails: silverfish, firebrats)
Order Mantophasmatodea (newly discovered wingless insects)

Pterygota, the winged insects

Order Palaeodictyoptera - extinct
...
Order Ephemeroptera (Mayflies)
Order Odonata (Dragonflies and damselflies)

Neoptera, insects with folding wings

Order Blattodea (Cockroaches)
Order Mantodea (Mantids)
Order Isoptera (Termites)
Order Zoraptera (Zorapterans)
Order Grylloblattodea (Ice Insects)
Order Dermaptera (Earwigs)
Order Plecoptera (Stoneflies)
Order Orthoptera (Grasshoppers, crickets, and katydids)
Order Phasmatodea (Walking sticks, timemas)
Order Embioptera (Webspinners)

Hemipterodea

Order Psocoptera (Booklice and barklice)
Order Phthiraptera (Sucking lice and chewing lice)
Order Hemiptera (True bugs, cicadas and kin - formerly Heteroptera + Homoptera)
Order Thysanoptera (Thrips)

Endopterygota, insects with complete metamorphosis

Order Miomoptera - extinct
Order Megaloptera (Alderflies, dobsonflies, and fishflies)
Order Raphidioptera (Snakeflies)
Order Neuroptera (Net-veined insects)
Order Coleoptera (Beetles)
Order Strepsiptera (Twisted-winged parasites)
Order Mecoptera (Scorpionflies and kin)
Order Siphonaptera (Fleas)
Order Diptera (Flies)
Order Trichoptera (Caddisflies)
Order Lepidoptera (Butterflies and moths)
Order Hymenoptera (Bees, ants, wasps, sawflies, and kin)