Endoskeleton three phyla and one subclass of animals, endoskeletons of various complexity are found: Chordata, Echinodermata, Porifera, and Coleoidea. An endoskeleton may function purely for support (as in the case of sponges), but often serves as an attachment site for muscle and a mechanism for transmitting muscular forces. A true endoskeleton is derived from mesodermal tissue. Such a skeleton is present in echinoderms and chordates. The poriferan 'skeleton' consists of microscopic calcareous or siliceous spicules or a spongin network. The Coleoidae do not have a true endoskeleton in the evolutionary sense; there, a mollusk exoskeleton evolved into several sorts of internal
Lattice of subgroups lattice of subgroups can sometimes be used to infer information about the original group, an idea that goes back to the work of . For instance, as Ore proved, a group is locally cyclic if and only if its lattice of subgroups is distributive. If additionally the lattice satisfies the ascending chain condition, then the group is cyclic. The groups whose lattice of subgroups is a complemented lattice are called complemented groups , and the groups whose lattice of subgroups are modular lattices are called Iwasawa groups or modular groups . Lattice-theoretic characterizations of this type also exist for solvable