The two subphyla of invertebrate chordates, the subphylum Urochordata (1250 species) and the subphylum Cephalochordata (45 species), lack a vertebral column.hey differ from the invertebrate chordates in possessing 1  : an internal skeleton, including a vertebral column which encloses the nerve cord; 2  a brain enclosed in a skull; 3  a pumping heart and efficient blood circulation.