The correct classification of cockroach is :
Kingdom: Animalia
Phylum: Arthropoda
Class: Insecta
Order: Blattodea
Family: Blattidae
Genus: Periplaneta
It is included in the Phylum Arthropoda because of the presence of these characteristic features: An Exoskeleton, Segmented Bodies, Jointed Appendages, Bilateral Symmetry and Open Circulatory System.
So, the correct answer is option D.