Which order is known for containing cockroaches and termites?

Blattodea is the correct order associated with cockroaches and termites. This classification is significant because it highlights the biological relationship and characteristics shared by these two groups of insects. Both cockroaches and termites belong to the same order, indicating they have similarities in their anatomy, development, and behavior.

Cockroaches are often recognized for their durability and ability to thrive in various environments, while termites are known for their social structures and role in decomposing wood and plant material. The grouping under Blattodea illustrates their evolutionary connection and common traits, such as their flat bodies and similar life cycles.

In contrast, the other options represent different orders of insects. For instance, Diptera encompasses flies and mosquitoes, which are completely unrelated to both cockroaches and termites. Hemiptera, known as the "true bugs," includes insects like aphids and cicadas, which have different feeding habits and ecological roles. Lepidoptera consists of butterflies and moths, known for their unique life stages and wing structures.

Understanding these classifications helps in recognizing the biological relationships and environmental roles of various insect species.