In the Laws, his unfinished final work, Plato outlines a kind of hierarchy of worship or reverence, in the following order: (1) Olympian and city-keeping gods, (2) chthonic (=earthly/underworld) gods, (3) daemons, (4) heroes, (5) ancestral gods, and (6) living parents. As one can see, this list is neither based purely on spatial order, or the chthonic gods should come after the living; nor purely on the rank of the beings in questions, since in that case, chthonic and ancestral gods should be included among the first group. Rather, Plato combines spatial and hierarchical considerations with an order based on the social fabric of a city, in which the city-keeping gods are naturally more important than the ancestral gods of certain groups within the city or the parents of a given person.
This order does not seem to have made much of an impact on later thought, precisely because of its complexity. In a Latin summary of the Laws, for example, we can see it being drastically simplified to a tripartite schema of (1) celestial gods, (2) underworld gods, and (3) aethereal daemons. In this case, aether is understood as the elemental space between the fiery stars and the lower air around the Earth.
With the inclusion of living parents in the Laws after the gods, Plato’s order has some relations to what I call the Principal Maxims of ethical literature. Also see the Golden Verses and Pythagoras’ Advice to his Students.
2 Plato, Laws 717a
After the Olympian gods and the gods who keep the state, we will hit straight upon the mark of piety by assigning the even, secondary and left-hand things as honors to the chthonic gods, but the opposite of these to the former. After these gods, the rational person will make celebrations for the daemons, and after them to the heroes. Next follow the private shrines of ancestral gods, celebrated according to law, and after these, the honors for living parents.
3 Pseudo-Apuleius, On Plato and his Doctrines 3, summary of the Laws
“Plato arranged the order of worship such that we should first honor the celestial gods, then the gods below [inferni = in the underworld], and after these, the ethereal Manes [=daemons].