Being a Latter Day Saint myself, I can assure you we are Christians. I cannot speak for Jehovah's Witnesses, however.
Christians believe that Christ was the literal son of God. That he was conceived in the body of a virgin by the holy spirit. That is different than being a prophet. That means that Islam and Judaisim are not subsets of Christianity. In fact, Judaism is separate from Islam because Islam believes that Ishmael is supposed to be the birthright child and trace their lineage through him, while Judaism traces it through Issac (who according to the Torah/Old Testament is the birthright child). Christianity is a branch of Judaism because Christ was a Jew, as well as his original followers.
I have read the LDS books, some of the other spinoffs as well, and find myself generally aware of proceedings there* (going back a fair while various family were members, some still are). Does not function like any of the other setups I have seen -- Roman Catholicism and the various flavours of Protestantism may have some fundamental disagreements (transubstantiation is always a good time there) but to the casual outside observer** would appear broadly similar (the biggest differences you will get reported back would be in terms of musical style favoured) in terms of local structure. I doubt anybody would say the same about LDS and the related movements. Spin it another way a Catholic could wander into a Anglican service and probably follow along well enough, do it for a LDS one and at best it is one of those "preacher is relating something to the modern world moments" (though given the phrasing maybe going through old papal edicts or something). I can do something similar for the first part for Islam between the major sects save for modern Sufism to relate them together.
I know LDS like to say they Christian and this would probably fall under claim what you want to claim but we may be operating under different definitions, especially if we are discussing the word denomination as was originally started with. Some in the past have claimed I am denying them their religion which is a) hard to do and b) not true from where I sit; have Jesus as a/the fundamental character, the bible (though which translation could get fun) as a holy book, and believe Jesus was a magic righteous dude if you want.
"Christians believe that Christ was the literal son of God. That he was conceived in the body of a virgin by the holy spirit. That is different than being a prophet."
If the former are true then the latter would presumably follow, however I don't know I can get to the former.
Right from the start (or at least living memory of the start of it all) you have the gnostic sects (a bit different to modern takes but went along the lines of "this bible lark, not bad advice, let's run with it"). More modernly you have the literalist vs liberalist either debate or spectrum (or higher than 3 dimensional graph for the really fun stuff) wherein one could conceivably follow a morality from the bible, consider Jesus a very important historical figure (perhaps no different to me studying the writings of Sun Tzu) and creator/leader of the faith, and believe none of the supernatural stuff.
*others reading the formation is taken care of 17.40 or so of the video below (or watch the whole thing as it is good stuff), current setup and practice we can go elsewhere for. If you want to read the extra works then it is online
https://www.lds.org/scriptures/bofm?lang=eng
**someone that might not necessarily know the titles, the difference between a lectern and a pulpit and all the other jazz I got to do as part of high school religious studies but knows enough to compare a book/play/film.
I would not have placed Judaism as a subset, indeed I avoided mentioned it in that for just that reason. It predates it and does not seem to recognise Jesus in any real capacity. From their perspective it could just be someone running around doing a remix, one that got surprisingly popular and even spawned a few remixes of its own.