The Suborder Blattodea belongs to the insect order Blattaria, which includes cockroaches. There are several synonyms used to describe this suborder, including Dictyoptera, which was used in the past and is still sometimes used, and Blattaria, which is sometimes used as an overall term for the order. Other synonyms for the Suborder Blattodea include Blattoptera, Blatodea, and Blattodictya. It is important to note that while there may be different names used to describe this suborder, the scientific community recognizes Suborder Blattodea as the correct and accepted term.