Rinse the pork and cut it into large chunks. Place it in a large pot along with the hominy and cover with water.
Add salt, the whole garlic cloves, and the onion. Bring to a boil, then reduce heat and simmer for 2-3 hours, or until the pork is tender.
Soak the dried chiles in hot water for 15 minutes. Remove the seeds and veins.
Blend the chiles with a little of the soaking water until smooth. Strain the mixture and add it to the soup.
Let the soup simmer gently for another 30 minutes to allow the flavors to meld.
When serving, slice the radishes, shred the lettuce, and serve with lime wedges and tortilla chips.
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