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 In mathematics, the lattice of subgroups of a group formula_1 is the lattice whose elements are the subgroups of formula_1, with the partial order relation being set inclusion. In this lattice, the join of two subgroups is the subgroup generated by their union, and the meet of two subgroups is their intersection. The dihedral group Dih has ten subgroups, counting itself and the trivial subgroup. Five of the eight group elements generate subgroups of order two, and the other two non-identity elements both generate the same cyclic subgroup of order four. In addition, there are two subgroups