I’ve never seen anything in the lore go into very much detail about the rank structure of the covenant and what their versions of platoons and battalions etc. would be so here’s a place to discuss all of that.
I think your right I don’t remember reading about a specific rank structure. My guess the E1-E5 are the grunts and jackals, meaning they are the lower enlisted making up the bulk of a platoon element. The elites ranging from ranger to zealot would be your E6-E9, making a smaller portion of the platoon. They would be the command element as well. I feel that the brutes would fall somewhere between E4-E7, at least until the take over the elites position in halo 3. Then you have the elites that are ship commanders. They would probably be most of the officer ranks. My guess would be there is around 100 per platoon and probably 70-100 platoons per battalion. For the shear size of the covenant army I would say there is 100 battalions. Just my two cents from what I’ve seen in game and read in the books.
I don’t think it’s as rigid as human militaries. The Covenant military isn’t centralized like most militaries we know of on Earth, with different government organizations/ministries having their own armies and fleets. But generally, an Elite Minor will lead a squad of Grunt Minors and Majors and a couple of Jackal Minors, maybe a Major. An Elite Major will lead a multitude of these squads, probably with additional Grunt Majors/Ultras or Jackal Majors spruced in. A multitude of these larger units will in turn be lead by an Elite Ultra. I assume special troops like a Hunter pair, Skirmishers, Jackal snipers, Elite rangers and stealth Elites probably could fall under the command of Majors or Ultras where needed. Ultras will then fall under the command of a General or any Zealot in some leadership role (Shipmaster, Fleetmaster, Field Master/Marshal, etc.).
Fleetmasters and equivalent may report directly to whatever ministry they fall under, though even larger fleets can be lead by a Supreme Commander or Imperial Admiral, the latter being the highest known military rank for an Elite. Any of the aforementioned fleet-commanding officers will presumably be beholden to whatever Prophet(s), or possibly Elite Councilors, who make up the Ministry they serve. And of course, they are all ultimately beholden to the High Council, which is beholden to the three Hierarchs.
EDIT: Should reemphasize that this is all highly variable because the Covenant doesn’t follow as rigid or organized subdivisions that the US/UNSC typically use. An Elite Major, for example, may command as a few as a dozen individuals in a small ground squad, or a few hundred as a junior officer onboard a ship.