A bit of historical information on the setting, which I learned while I was looking for information for my story. Maybe someone will be interested
Since the plot has become very dependent, in a sense, on the politics of the demons and the plot unfolds at their top (all the main characters are demons - Moloch, Lucifer, Asmodeus, Belial), I had to delve into the details of how their society and hierarchy are built. Because I have demons copied from Greek democracy I decided to take the structure of the hierarchy from the same place, only to slightly correct their function and naming for my own plot. After all, the story is about fictional characters who have lived for centuries, and in such conditions, their society could have developed quite differently and adapted to their mores.
So, the Greeks had at the top of a democratic state, if i greatly simplify the information i found, brush aside all sorts of boole, the council of 500 - 9 archons at the top. Three archons had a unique name and their own area of influence and responsibility, while the rest of the archons had a generic name for all. These are unique: eponyms (as I understand it, the most important archon and responsible for the legal affairs of the state of the population, to summarize), polemarch and basileus (the chief priest of the polis, who organizes religious rituals). The rest are called thesmophetes, dealing with the judicial system.
I got a little more of these archons in the setting and with a different name. Since the word "archon" is already used to refer to angels / demons who control the water element, it is no longer suitable for the hierarchy of the position of the demons. I couldn't find a better name for the angelic "water" caste, so it was just easier to change or invent a different job title for the demons. By analogy with the name "archangel" - the main ones of the angels, I replaced the name "archon" with "archipag", combining the part from the archangel with the word areopagus - the assembly of the top among the ancient Greeks.
And I have redistributed responsibilities to these archipags. As the head of the demons, Lucifer will be an Eponym. Lucifer will control the rest of the archipags. Lucifer himself is also required to deal with administrative and legal matters and partially judicial statements. Among themselves, the other archipags are conceived to be hierarchically equal and able to manage only their sphere of responsibility throughout the demon polis. Moloch is more about external security, an analogue of the army, and the internal security and order of the policy are given to Asmodeus, an analogue of the executive branch.
For the latter, there was no head among the archons. Among the Greeks, the equivalent of the police were slaves and there were also astinomes. While I was looking for information, I still didn't understand whether they were recruited from slaves or whether they were already citizens separately, but I liked the title of the position and their functions fit those prescribed to the character Asmodeus, so I entered such a unique name among the archipags.
Basileus is given to Belial. Of course, it is ridiculous to introduce any kind of priesthood to characters who themselves know what religious propaganda is, because demons will not have any religion like the human society. But the functions of the basileus, as responsible for organizing any celebrations, instead of religious service, are very suitable for Belial and for demons + as part of some shadow side and gray areas for demons (the distribution of intoxicating substances by archaic demons separately, among their own area, among people serving demons, the presence of analogues of a hedonistic cult).
Archai demons were invented from succubi, and given their hedonistic lifestyle, they are well suited to be used more mundane, following the example of the cliche about demons stealing human souls - there will be no souls in the setting, because death will be the last end, as in reality.
But demons will need humans for the same purpose as slaves of the ancient Greeks - to provide a way of life for demons and to relieve them of the need to personally perform their daily routine. But since demons are prescribed by tempters, then this role can be used by archaic demons to lure people into their service and keep them not by force, but by offering better conditions than they can get from other people or by seduction. This will perfectly explain who is involved in the demons' daily routine and provides some kind of parallel with their images from the myth, only pragmatic and realistic.
The fesmophet archipelago will be responsible for the judicial system of the demons, and it will be for the crowd character, some kind of cherub demon. And the last archipag will be an archon demon, so that each type of 4 types of demons will be at the top. There is also no separate name for the latter archipag, so the name is taken by analogy with the astinome - agoran. They were engaged in ancient Greek surveillance of order in the agora square and trade. I will slightly change the vector of surveillance for the demons, it will not be purely related to the agora, but to trade in general and surveillance of the work of people summoned by archaic demons to the demon polis.
That's all with the arhipags, and the remaining top of the demons will be the nomarchs. Nomarchs in ancient Hellenistic Egypt were the administrative managers/representatives of the pharaoh in the nomes, an analogue of one of the districts/ territories of Egypt. Although the demons will have a small polis, up to about 800 demons, they will have a polis divided into 4 districts, where their own type of demons will live separately: seraphs separately, archai, kerubi and archons separately, and each district will have its own head - nomarch.
They will be identical in function to the local administration and order. In the hierarchy, they will be lower after the archipags, but equal to each other. Unlike archipags, their area of responsibility will be only their districts. The nomarchs will report to the eponym, not to the other archipags, but only if this is not related to the area of responsibility of the archipags.
Something like that. I hope the educational program didn't seem boring. I understand that there is a lot of text, but it took even more reading before we could find the necessary data suitable for the setting and plot, and then systematize them. There will be a reason for the demons to have such a top position. Some characters, more precisely more than half, will be in ideological conflict with each other and diverge in values. In order for the conflict to be open, the characters must be hierarchically on equal terms, otherwise it will be difficult to show an open conflict without violating the logic of the characters' behavior.
For example, the basis of the society of demons will be a conflict between the demons seraphs and archaea on the basis of their contrasting nature and directly opposite values. This conflict will not develop separately in the plot, but it will enliven the setting quite well and will be most vividly shown through Asmodeus and Belial, whose line will be involved in the plot