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
Subgroups of cyclic groups is isomorphic to the dual of the lattice of divisors of "n", with a subgroup of order "n"/"d" for each divisor "d". The subgroup of order "n"/"d" is a subgroup of the subgroup of order "n"/"e" if and only if "e" is a divisor of "d". The lattice of subgroups of the infinite cyclic group can be described in the same way, as the dual of the divisibility lattice of all positive integers. If the infinite cyclic group is represented as the additive group on the integers, then the subgroup generated by "d" is a subgroup of the subgroup generated