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 on no generators), this result can be seen as a special case of the Nielsen–Schreier theorem that every subgroup of a free group is itself free. The fundamental theorem for finite cyclic groups can be established from the same theorem for the infinite cyclic groups, by viewing each finite cyclic group as a quotient group of the infinite cyclic group. In both the finite and the infinite case, the lattice of subgroups of a cyclic group is isomorphic to the dual of a divisibility lattice. In the finite case, the lattice of subgroups of a cyclic group of order "n"