diff --git a/src/sage/combinat/root_system/cartan_matrix.py b/src/sage/combinat/root_system/cartan_matrix.py
index 23da5ab2e4b..0a784548781 100644
--- a/src/sage/combinat/root_system/cartan_matrix.py
+++ b/src/sage/combinat/root_system/cartan_matrix.py
@@ -388,6 +388,14 @@ def _CM_init(self, cartan_type, index_set, cartan_type_check):
 
             sage: C = CartanMatrix(['A',1,1])  # indirect doctest                       # needs sage.graphs
             sage: TestSuite(C).run(skip=["_test_category", "_test_change_ring"])        # needs sage.graphs
+
+        Check that :issue:`37979` is fixed::
+
+            sage: C = CartanMatrix([[2]], index_set=(4,))
+            sage: C.index_set()
+            (4,)
+            sage: CartanType("A3").subtype((2,)) is CartanType("A1").relabel({1:2})
+            True
         """
         self._index_set = index_set
         self.set_immutable()
@@ -396,6 +404,8 @@ def _CM_init(self, cartan_type, index_set, cartan_type_check):
             cartan_type = CartanType(cartan_type)
         elif self.nrows() == 1:
             cartan_type = CartanType(['A', 1])
+            if index_set != (1,):
+                cartan_type = cartan_type.relabel({1: index_set[0]})
         elif cartan_type_check:
             # Placeholder so we don't have to reimplement creating a
             #   Dynkin diagram from a Cartan matrix