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The groupings are based on distinct physical traits and life cycles that define each order. Cockroaches belong to Blattodea, a category that circles around flat-bodied insects with broad pronota and chewing mouthparts; modern classifications even include termites in Blattodea, so this order covers these roaches and their close relatives. Praying mantises, on the other hand, are in Mantodea, an order noted for their elongated bodies, triangular heads, and especially their grasping, spiny forelegs used to catch prey. Because these two groups are placed in different orders, there isn’t a single order that includes both cockroaches and praying mantises. (If you’ve seen termites listed separately as Isoptera in older tables, note that current taxonomy moves termites into Blattodea, not Mantodea.)