Why is cyanobacteria [blue green algae] not put under the division thallophyta?
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i dont know
 

Blue-green algae, also known as Cyanobacteria, are a group of photosynthetic bacteria that many people refer to as "pond scum." Blue-green algae are most often blue-green in color, but can also be blue, green, reddish-purple, or brown. Blue-green algae generally grow in lakes, ponds, and slow-moving streams when the water is warm and enriched with nutrients like phosphorus or nitrogen. Blue green algae was put in the kingdom of Monera because they are one celled. 
Monera are bacteria and other mostly tiny, single-celled organisms whose genetic material is loose in the cell. The genetic material of plants, animals, and other eukaryotes, on the other hand, is held in the cell's nucleus. 
Plants are living organisms belonging to the kingdom Plantae. They include familiar organisms such as trees, herbs, bushes, grasses, vines, ferns, mosses, and green algae. 
So I’d have to say it’s in monera and not plantae because of the cell division, where it “can” potentially be grown; and other circumstances.

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