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
Lattice of subgroups of the form Z × Z, generated by pairs of order-two elements. The lattice formed by these ten subgroups is shown in the illustration. This example also shows that the lattice of all subgroups of a group is not a modular lattice in general. Indeed, this particular lattice contains the forbidden "pentagon" "N" as a sublattice. For any "A", "B", and "C" subgroups of a group with "A" ≤ "C" ("A" subgroup of "C") then "AB" ∩ "C" = "A(B ∩ C)"; the multiplication here is the product of subgroups. This property has been called the "modular property of groups"