Animal mesoderm forms by enterocoelic pouching, through invagination of the endoderm. The main deuterostome phyla are the Echinodermata and the Chordata. Echinoderms are exclusively marine and include starfish, sea urchins, and sea cucumbers. The chordates are dominated by the vertebrates (animals with backbones), which consist of fishes, amphibians, reptiles, birds, and mammals. The deuterostomes also include the Hemichordata (acorn worms). The Ecdysozoa are protostomes, named after their shared trait of ecdysis, growth by moulting. They include the largest animal phylum, the Arthropoda, which contains insects, spiders, crabs, and their kin. All of these have a body divided into repeating segments, typically
Subgroups of cyclic groups on no generators), this result can be seen as a special case of the Nielsen–Schreier theorem that every subgroup of a free group is itself free. The fundamental theorem for finite cyclic groups can be established from the same theorem for the infinite cyclic groups, by viewing each finite cyclic group as a quotient group of the infinite cyclic group. In both the finite and the infinite case, the lattice of subgroups of a cyclic group is isomorphic to the dual of a divisibility lattice. In the finite case, the lattice of subgroups of a cyclic group of order "n"