Hieracium spp; The taxonomy of Hawkweeds is very complicated. Basically, the genus is subdivided into two main sections: the Hieracium section and the Pilosella section. The latter are characterized by pollen-fertilisation or are only facultatively apomictic. In apomictic plants the seeds are not produced by pollen-fertilisation of egg-cells but rather by "normal" cells producing the embryo. Because pollen-ferilisation is the norm, true species can be defined within the Pilosella section. To my knowledge - I am not sure here - there is only one hawkweed species on Iceland representing the Pilosella section. This is Hieracium islandicum which is also known as Pilosella islandica, the Icelandic hawkweed.
The first section (the nominate Hieracium section) consists of plants which are full apomictic species. Because the seeds are genetically pure vegetative copies (clones) of the parent plant, it becomes more or less impossible to define real species. Nevetheless so-called microspecies are defined based on morphological traits. On Iceland no less than 200 microspecies have been defined! Clearly a matter of specialists. In Hörður Kristinsson's popular field guide "Flowering Plants and Ferns of Iceland" this problem is adressed too but he nevertheless treats a few (micro-)species. These, I assume, are the most common hawkweeds. The problem is that the user of the book, trying to identify a hawkweed plant, can never be sure if the if his/her identification is correct even when all the characteristics, given for one of the mentioned micro-species, fit. After all they may also fit one or more of the many other microspecies. Below are links to pages of some possible microspecies. However, one needs to realise that (my) identification of photographed hawkweed plants may be wrong. Finally: the microspecies are differentiated by the many characteristics of a plant. Special emphasis is given to the type of hairs and bristles on the plant especially those on the involucral bracts of the flower head. This is dealt on the pages mentioned below.
Hieracium alpinum (Alpine Hawkweed)
Hieracium thaectolepium (Hillside Hawkweed)
Hieracium aquiliforme (Hearth Hawkweeed)
Hieracium strictophyllum (Stain-leaved Hawkweed)
Another Hieracium spp (a Hawkweed)
Hieracium islandicum, aka Pilosella islandica (Icelandic Hawkweed))
It is member of the Asteraceae (syn.: Compositae) family, i.e. daisy family.