All species of Liverworts and Hornworts to be found in Europe.

Liverworts and Hornworts are two divisions of non vascular plants, often grouped together with mosses.

The scientific name of the Liverworts is Hepaticophyta or Marchantiophyta. They are assumed to have about 7500 species world wide.
About 85% of the world wide Liverworts are leafy.

The scientific name of the Hornworts is Anthocerotophyta. They are assumed to have about 150 species world wide.

Classification of the Liverworts up to order, taken mainly from Wikipedia ( https://en.wikipedia.org/wiki/Marchantiophyta ), and complemented with estimated numbers of current species (W: world, Eu: Europe, CE: Central Europe).

Class Haplomitriopsida

• Order Haplomitriales (W: 8, CE: 1)
• Treubiales (W: 10)

Class Marchantiopsida

• Blasiidae
  -- Order Blasiales (W: 2, Eu: 1)

• Marchantiidae (W: 350)
  -- Neohodgsoniales (W: 1)
  -- Sphaerocarpales (bottle liverworts) (W: ~20)
  -- Lunulariales (W: 1)
  -- Marchantiales (complex thalloids) (W: 180)

Jungermanniopsida

• Pelliidae
  -- Pelliales (W: 6?, Eu: 3?)
  -- Pallaviciniales
  -- Fossombroniales

• Metzgeriidae
  -- Pleuroziales
  -- Metzgeriales

• Jungermanniidae (leafy liverworts)
  -- Porellales
  -- Ptilidiales
  -- Jungermanniales

Orders of the Hornworts, again from Wikipedia, with about 215 species world wide.

• order Leiosporocerotales (W: 1)
• order Anthocerotales (W: ~100, De: 2?)
• order Notothyladales (W: ~65)
• order Phymatocerotales (W: 2)
• order Dendrocerotales (W: ~60)
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