Plant Kingdom

Cryptogams are plants that do not produce seeds (algae, bryophytes and pteridophytes).
Pteridophytes are the first terrestrial plants to possess vascular tissues, xylem and phloem, but they reproduce by spores; they are therefore called vascular cryptogams.
$Equisetum$ (horsetail) is a pteridophyte.
$Cedrus$ and $Ginkgo$ are gymnosperms, which are seed plants (phanerogams).
$Marchantia$ is a liverwort (bryophyte), a non-vascular cryptogam.
Hence the vascular cryptogam is $Equisetum$.

Heterospory is the production of two kinds of spores, small microspores and large megaspores, as in $Selaginella$ and $Salvinia$.
The megaspores germinate into female gametophytes that are retained on the parent sporophyte for variable periods.
The development of the zygote into a young embryo takes place within the female gametophyte.
This retention and protected development is a precursor to the seed habit and is considered an important step in evolution.
A free-living gametophyte or a haplontic life cycle works against, not towards, the seed habit.
Hence heterospory is important in the development of the seed habit.

The three classes of algae differ in their stored food.
Phaeophyceae (brown algae): food is stored as complex carbohydrates, laminarin or mannitol. Examples: $Ectocarpus$, $Dictyota$, $Laminaria$, $Sargassum$ and $Fucus$.
Rhodophyceae (red algae): food is stored as floridean starch. $Gracilaria$ and $Porphyra$ are red algae.
Chlorophyceae (green algae): food is stored as starch. $Chara$ is a green alga.
Hence mannitol is the stored food in $Fucus$.

Artificial systems (e.g., that of Linnaeus) were based on a few morphological characters such as the androecium structure.
Natural systems (e.g., Bentham and Hooker) were based on natural affinities, considering many external and internal features.
Phylogenetic classification systems are based on evolutionary relationships between organisms; they assume that organisms belonging to the same taxa have a common ancestor.
Classification based on chemical constituents is chemotaxonomy.
Hence the phylogenetic system is based on evolutionary relationships.