Bob's resource is really well organized. This next listing of "parroquias" has a different format:
http://www.vivirasturias.com/00htm/00/i ... uias.shtml
And this long, long page on "poblaciones" might give hints about smaller unofficial communities:
http://www.vivirasturias.com/00htm/00/i ... ones.shtml
But this short list of "concejos" is a jumping off place if you want to see only the parroquias or poblaciones for a specific concejo, and easily get to more detailed information on each:
http://www.vivirasturias.com/index2.shtml
Look to the right column of links for poblaciones. Oddly, there is no link for associated parroquia. Also the parroquia listing seems to have somewhat different data than the one Bob found, so check them both.
The individual pages give info on the number of households and inhabitants, population density, surface area, distance from the capital, min and max altitude, traditional name, etc. This is a very useful resource!
The pages on concejos also offer information on famous people, fairs and festivals, maps, museums, historical sites, parks, food and lodging, sports, shopping, etc.
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An attempt at definitions:
concejo: town council, town government, so that might refer in this case to incorporated towns and cities. But I believe that Asturias is divided into areas much like our counties, or more accurately our townships. So Avilés could be both a township and a city.
parroquia: parish church, parish (in the sense of territory), so this probably refers to districts of the concejo.
población: population, town, city, village, center of population, built-up area. I equate this with neighborhood. I assume that these are named villages and barrios, but that they may not be official governmental divisions.
If anyone has better definitions, or insights, or corrections, I'd love to hear about them!