Green Pozole

Name: Green Pozole
Ingredients: 2 (25-ounce) cans Mexican-style hominy, drained and rinsed; 1 small whole chicken, cut into serving pieces; 1 head garlic, plus 2 additional peeled garlic cloves; 10–12 cups water; ¼ medium white onion, left whole, plus 1 medium white onion, chopped; 1 pound tomatillos; 2 serrano peppers; 1 large bunch cilantro; 1 tablespoon dried Mexican oregano, plus more for serving; 1 tablespoon salt, plus more to taste; 1 head iceberg lettuce head, sliced; 1 bunch red radishes, sliced; 3 large avocados; 5 limes, cut in half; 16–20 tostada shells