Plant Biology and Classification

Cryptogams refer to the plants and fungi that do not reproduce by seeds. Besides these, the cryptogams are also known to reproduce by means of spores. All spore producing plants including mosses and ferns do not reproduce by seeds are hence, known as cryptogams.

The name horsetail, often used for the entire group, arose because the branched species somewhat resemble a horse's tail. 
Equisetum is the only living genus in Equisetaceae, a family of vascular plants that reproduce by spores rather than seeds.
Equisetum is a "living fossil" as it is the only living genus of the entire class Equisetopsida, which for over one hundred million years was much more diverse and dominated the understory of late Paleozoic forests. Some Equisetopsida were large trees reaching to 30 meters tall.

A cryptogam is a plant  that reproduces by spores and it is without flowers or seeds. Cryptogamae means hidden reproduction which refers to the fact that no seed is produced, thus cryptogams represent the non-seed bearing plants. Other names, such as "thallophytes", "lower plants", and "spore plants" are also occasionally used.

The phanerogams are the plants which can produce seeds. These are the plants which possess ovule where the fertilisation of male and female gametes takes place to form the zygote. The ovule is transformed into the seed after fertilisation. So, the seeds can be observed in the phanerogams. 

Ectophloic siphonostele, where the phloem is restricted to the outer surface of the xylem, is a characteristic feature found in Osmunda and Equisetum.

The plants exhibit the alternation of generations in their life cycle. The lower plants have a dependent sporophytic generation of the gametophyte. The first plants to develop as an independent sporophytic generation are the pteridophytes. These are the vascular plants which can survive in the terrestrial areas and has a independent diploid sporophytic stage. 

The cryptogams are flowerless (non-flowering) and seedless, spore-bearing plants. Phanerogams are flower bearing, seed producing tracheophytes. Bryophytes and pteridophytes come under cryptogams. 

Lycopodium is a genus of clubmosses which is also known as ground pines or creeping cedar. They are flowerless, vascular, terrestrial or epiphytic plants, with widely branched, erect, prostrate or creeping stems, with small, simple, needle-like or scale-like leaves that cover the stem and branches thickly. Their leaves contain a single, unbranched vascular strand and are microphylls by definition. The kidney-shaped or reniform spore-cases (sporangia) contain spores of one kind only (isosporous, homosporous) and are borne on the upper surface of the leaf blade of specialized leaves (sporophylls) arranged in a cone-like strobilus at the end of upright stems. The club-shaped appearance of these fertile stems gives the clubmosses their common name.

Vascular cryptogams are plants that possess vascular tissues but do not produce seeds, which defines the Pteridophytes. Equisetum is a well-known genus of Pteridophytes.

Equisetum is commonly referred to as the horse-tail plant due to the appearance of its jointed, ribbed stems.

Pteridophytes are vascular plants and have leaves (known as fronds), roots and sometimes true stems, and tree ferns have full trunks. For example, ferns, horsetails and clubmosses. Fronds in the largest species of ferns can reach some six meters in length. Many ferns from tropical rain forests are epiphytes, which means they only grow on other plant species. Their water comes from the damp air or from rainfall running down branches and tree trunks. There are also some purely aquatic ferns such as water fern or water velvet (Salvinia molesta) and mosquito ferns (Azolla species). Thallophytes and bryophytes are not differentiated into roots, stems and leaves. Hydrophytes are differentiated into roots, stems and leaves and bear flowers and seeds. 

The correct answer is 'Pteropsida'

A fern is a member of a group of approximately 12,000 species of vascular plants which reproduce via spores and have neither seeds nor flowers. They differ from mosses by being vascular (i.e., having water-conducting vessels). They have stems and leaves, like other vascular plants. Most ferns have fiddleheads that expand into fronds, which are each delicately divided. Leptosporangiate ferns (sometimes called as true ferns) are by far the largest group, but ferns as defined here (ferns sensu lato) include horsetails, whisk ferns, marattioid ferns, and ophioglossoid ferns. This group may be referred to as monilophytes. The term pteridophyte traditionally refers to ferns plus a few other seedless vascular plants.

Pteridophytes are cryptogamae, they are Non-flowering plants whereas phanerogams are flowering plants and are further classified as monocots and Dicots.

Adiantum -Maiden Hair fern ( because of shining,smooth and blackish hair like petioles ).