After “Wikispecies”, 2008

<==o Capitata Kühn, 1913 [Hydroida: Anthomedusae (in partim); incl. Chondrophora]
   |--o Acaulidae [Hydroida: Anthomedusae:]
   |  `--o Acauloides
   |     |-- A. primarius
   |     |-- A. ammisatum
   |     `-- A. ilonae
   |--o Boreohydridae
   |  |-- Boreohydra simplex
   |  |-- Meiorhopalon arenicolum
   |  `-- Psammohydra nana
   |--o Candelabridae Stechow, 1921  [Hydroida: Anthomedusae:]
   |  |-- Monocoryne gigantea Broch, 1909
   |  `--o Candelabrum de Blainville, 1830 [Myriothela Sars, 1851]
   |     |-- C. cocksii
   |     |-- C. minutum
   |     |-- C. mitra
   |     |-- C. phrygium
   |     |-- C. serpentarii
   |     `-- C. verrucosum
   |--o Cladocorynidae [Hydroida: Anthomedusae:]
   |  `-- Cladocoryne
   |--o Cladonematidae [Hydroida: Anthomedusae:]
   |  `-- Cladonema timmsii Gershwin & Zeidler, 2008
   |--o Corymorphidae [Hydroida: Anthomedusae:]
   |  |-- Amalthaea
   |  |-- Branchiocerianthus
   |  |-- Corymorpha
   |  |-- Eucodonium
   |  |-- Eugotoea
   |  |-- Euphysora
   |  |-- Paragotoea
   |  |-- Plotocnide
   |  `-- Vannuccia
   |--o Corynidae [Hydroida: Anthomedusae:]
   |  |-- Actigia
   |  |-- Coryne
   |  |-- Dicodonium
   |  |-- Dipurena
   |  `-- Sarsia
   |--o Eleutheriidae [Hydroida: Anthomedusae:]
   |  |-- Eleutheria
   |  `-- Staurocladia
   |--o Euphysidae
   |  |-- Euphysa
   |  |-- Gymnogonos
   |  `-- Siphonohydra
   |--o Halocorynidae
   |  `-- Halocoryne
   |--o Margelopsidae [Hydroida: Anthomedusae:]
   |  `-- Margelopsis
   |--o Moerisiidae [Hydroida: Limnomedusae:]
   |  |-- Halmomises lacustris
   |  |-- Moerisia
   |  |-- Odessia
   |  |-- Ostroumovia
   |  `-- Tiaricodon
   |--o Paracorynidae
   |  `-- Paracoryne
   |--o Pennariidae McCrady, 1859 [Codonidae Haeckel, 1879; Halocordylidae Stechow, 1921] [Hydroida: Anthomedusae:]
   |  `-- Pennaria
   |--o Porpitidae Goldfuss, 1818 [Velellidae] [Chondrophora:] (uimapolyypit)
   |  |-- Porpema prunella (Haeckel, 1888)
   |  |-- Porpita porpita (Linnaeus, 1758) Lesson, 1826 [Porpita pacifica Lesson, 1826; Porpita linneana Lesson, 1843 (nomen dubium); Porpita umbela Müller, 1776 (nomen dubium)] (Portugese Man of War)
   |  `-- Velella velella (Linnaeus, 1758) Lamarck, 1801 [Velella spirans (Forskal); Velella lata Chamisso & Eysenhardt, 1821 (nomen dubium)]
   |--o Rosalindidae
   |  `-- Rosalinda
   |--o Sphaerocorynidae
   |  `-- Sphaerocoryne
   |--o Tubulariidae [Hydroida: Anthomedusae:]
   |  |-- Ectopleura
   |  |-- Hybocodon
   |  |-- Rhabdoon
   |  `-- Tubularia
   `--o Zancleidae [Hydroida: Anthomedusae:]
      `-- Zanclea

Reference(s):