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 or "(Dedekind's) modular law" (, ). Since for two normal subgroups the product is actually the smallest subgroup containing the two, the normal subgroups form a modular lattice. The Lattice theorem establishes a Galois connection between the lattice of subgroups of a group and that of its quotients. The Zassenhaus lemma gives an isomorphism between certain combinations of quotients and products in the lattice of subgroups. In general, there is no restriction on the shape of the lattice of subgroups, in the sense that every lattice is isomorphic to a sublattice of the subgroup lattice of some group. Furthermore, every