Can Anybody tell me how the Inc plasmids are categorized? on what basis inc plasmids were grouped?How many groups and subgroups of Inc plasmids are there?
Inc groups are defined by the replication/copy number control system of plasmids. Plasmids in the same Inc group share this machinery and hence interfere with each others replication (or to be more accurate the cell can not distinguish between two plasmids of the same group). Plasmids in different Inc groups can normally coexist stably.
I have no idea how many Inc groups there are any longer, but it would be a large number if you include plasmids from outside the enterobacteria.
The Inc typing system was historically based on the phenotypical finding that related plasmids could not stably reside in the same cell as described above by Michael Benedik. Nowadays, people mainly look at the genotype for epidemiological study as described in the first link.
Especially the IncF plasmids have a lot of subtypes due to genetic differences which is explained further in the second link.