Societies are, almost by nessecity, to some extent, Lawful. Having a viewpoint beyond the individual is Lawful, to some extent.
A Chaotic view would be something like "We're all Individuals!" Everyone is largely the same, with a multitude of variations, and there is no internal ranking system. From a "pure" CN perspective, no outside system should stop someone from doing something -- there are no authority figures, no leaders, no people whose place it is at the head. Nobody deserves any more respect than you by any swing of the fish. The only way you give people leeway is if they show you that they deserve it -- which is why CN beings like Slaad can have a sort of loose ranking system -- there is a respect for actual raw power, because they can force you to listen to them. But, laregley, Gray Slaad won't care if a Red Slaad calls itself "King of Limbo," because he has a right to call himself whatever he pleases. But the moment he starts trying to enforce his edicts on the Gray, the Gray will have to kill him -- just because he can't be subordinated to anyone. And if the Gray goes up against a White in an attempt to prove that, he knows he's going to die horribly...so he doesn't. Keep a respectful distance, and maybe be willing to be bullied a little bit.
It's hard to have anything more than a purely anarchic society with Chaotics. Elves do it fairly well, because they're all Good and thus they're all concerned with each other's well being. They want people to be happy, so not having anyone enforce that edict makes sense for them. Slaadi, as has been pointed out, don't really care one way or the other what the others do, as long as they don't invade each other's individual space, and, in that case, a ranking system emerges simply based on raw power. More powerful/religious/philosophical Slaads may even be interested in spreading that delightful freedom to other lands, seeing themselves as above the power of the 2nd level Aristocrat king because they *can*. In their book, now they're kinda in control of it, at least until someone shows them otherwise. For orcs and the like, it's similar but more brutal. The freedom isn't just for individuals any more -- an orc doesn't care what his makes his cousin happy. It becomes selfish, and delighting in the pain of others. If hurting Grok makes me happy, I hurt Grok. If that makes Grok unhappy, all the better. If he wants to change it, he's welcome to try. It's still fairly egaltarian, because an orc chieftan is aware that he's not nessecarily better than the rest of the orcs...but he can boss them around. Chaotic Evil is very, very selfish, but isn't so much concerned with power. As long as they can make themselves happy (by hurting others around them), they're content.
Any form of happy deference to any form of authority is, at the very least, neutral. In addition, Lawful types would try to maintain and ensure that the authority remains in place, because, in the mind of a Lawful, the differences created by reality need to be categorized and ranked. Sight is better than blindness, but a blind woman's touch is better than a sighted woman's.
Lawful types don't need to always obey the codified laws of their nation, but they should respect them in spirit at all times. A lawful revolutionary would work "within the system."
Clans can be quite lawful, if they are led and governed by order and ranking. If there is a clan head, and he is respected simply for being a clan head, and the head is a desired constant as a position. If the clan is chaotic, then the head of the clan is probably loathed for his position, and people only listen to him as far as he can make them (or, if they're CG, if he has a good idea others may listen to him...but would never feel obligated to).
Don't so narrowly define what is and isn't in-alignment. In reality, they're quite flexible tools.