diff --git a/src/click/core.py b/src/click/core.py
index 6f483675d..93c2d177c 100644
--- a/src/click/core.py
+++ b/src/click/core.py
@@ -1180,7 +1180,7 @@ def get_help_option_names(self, ctx: Context) -> list[str]:
         for param in self.params:
             all_names.difference_update(param.opts)
             all_names.difference_update(param.secondary_opts)
-        return list(all_names)
+        return sorted(all_names)
 
     def get_help_option(self, ctx: Context) -> Option | None:
         """Returns the help option object.