Based on the nature of the leaf and the position of sporangia, they are classified into four classes - psilopsida, lycopsida, sphenopsida, and pteropsida.
Psilopsida:
They are the most primitive group of pteridophytes.
The plants are dichotomously branched.
They have rhizoids, but most of them do not possess leaves.
They have a homosporous sporophyte.
Example- Psilotum.
Lycopsida:
They are also called club mosses.
The plant body is differentiated into adventitious roots, stems, rhizophores, and leaves.
They can have homosporous and heterosporous sporophytes.
Example- Lycopodium
Sphenopsida:
They are also called horsetail.
The plant body is differentiated into roots, stems, and scaly leaves.
The homosporous sporophyte is born on the strobilus.
Example- Equisetum.
Pteropsida:
They are also called ferns.
The plant body is differentiated into roots, stems, and leaves.
The sporophyte can be both homosporous and heterosporous.