diff --git a/mysql-test/main/group_min_max.result b/mysql-test/main/group_min_max.result
index d1bd4d8cedb7e..a87a79fbc56de 100644
--- a/mysql-test/main/group_min_max.result
+++ b/mysql-test/main/group_min_max.result
@@ -4083,5 +4083,17 @@ MIN(pk)
 1
 DROP TABLE t1, t2;
 #
+# MDEV-30605 Wrong result while using index for group-by
+#
+CREATE TABLE t1 (pk INT primary key, a int, key(a)) engine=innodb;
+INSERT INTO t1 VALUES (1,-1),(2,8),(3,5),(4,-1),(5,10), (6,-1);
+SELECT MIN(pk), a FROM t1 WHERE pk <> 1 GROUP BY a;
+MIN(pk)	a
+4	-1
+3	5
+2	8
+5	10
+DROP TABLE t1;
+#
 # End of 10.5 tests
 #
diff --git a/mysql-test/main/group_min_max.test b/mysql-test/main/group_min_max.test
index 7de57d75d36f1..5f7981b8b3075 100644
--- a/mysql-test/main/group_min_max.test
+++ b/mysql-test/main/group_min_max.test
@@ -1737,6 +1737,17 @@ SELECT SQL_BUFFER_RESULT MIN(pk) FROM t1, t2;
 SELECT MIN(pk) FROM t1, t2;
 DROP TABLE t1, t2;
 
+--echo #
+--echo # MDEV-30605 Wrong result while using index for group-by
+--echo #
+
+CREATE TABLE t1 (pk INT primary key, a int, key(a)) engine=innodb;
+INSERT INTO t1 VALUES (1,-1),(2,8),(3,5),(4,-1),(5,10), (6,-1);
+
+SELECT MIN(pk), a FROM t1 WHERE pk <> 1 GROUP BY a;
+
+DROP TABLE t1;
+
 --echo #
 --echo # End of 10.5 tests
 --echo #
diff --git a/sql/opt_range.cc b/sql/opt_range.cc
index 223799a3235f6..82b19e23fd402 100644
--- a/sql/opt_range.cc
+++ b/sql/opt_range.cc
@@ -461,7 +461,7 @@ void print_range_for_non_indexed_field(String *out, Field *field,
 static void print_min_range_operator(String *out, const ha_rkey_function flag);
 static void print_max_range_operator(String *out, const ha_rkey_function flag);
 
-static bool is_field_an_unique_index(RANGE_OPT_PARAM *param, Field *field);
+static bool is_field_an_unique_index(Field *field);
 
 /*
   SEL_IMERGE is a list of possible ways to do index merge, i.e. it is
@@ -7752,8 +7752,13 @@ SEL_TREE *Item_func_ne::get_func_mm_tree(RANGE_OPT_PARAM *param,
     If this condition is a "col1<>...", where there is a UNIQUE KEY(col1),
     do not construct a SEL_TREE from it. A condition that excludes just one
     row in the table is not selective (unless there are only a few rows)
+
+    Note: this logic must be in sync with code in
+    check_group_min_max_predicates(). That function walks an Item* condition
+    and checks if the range optimizer would produce an equivalent range for
+    it.
   */
-  if (is_field_an_unique_index(param, field))
+  if (param->using_real_indexes && is_field_an_unique_index(field))
     DBUG_RETURN(NULL);
   DBUG_RETURN(get_ne_mm_tree(param, field, value, value));
 }
@@ -7865,7 +7870,7 @@ SEL_TREE *Item_func_in::get_func_mm_tree(RANGE_OPT_PARAM *param,
          - if there are a lot of constants, the overhead of building and
            processing enormous range list is not worth it.
       */
-      if (is_field_an_unique_index(param, field))
+      if (param->using_real_indexes && is_field_an_unique_index(field))
         DBUG_RETURN(0);
 
       /* Get a SEL_TREE for "(-inf|NULL) < X < c_0" interval.  */
@@ -8574,24 +8579,18 @@ SEL_TREE *Item_equal::get_mm_tree(RANGE_OPT_PARAM *param, Item **cond_ptr)
     In the future we could also add "almost unique" indexes where any value is
     present only in a few rows (but necessarily exactly one row)
 */
-static bool is_field_an_unique_index(RANGE_OPT_PARAM *param, Field *field)
+static bool is_field_an_unique_index(Field *field)
 {
   DBUG_ENTER("is_field_an_unique_index");
-
-  // The check for using_real_indexes is there because of the heuristics
-  // this function is used for.
-  if (param->using_real_indexes)
+  key_map::Iterator it(field->key_start);
+  uint key_no;
+  while ((key_no= it++) != key_map::Iterator::BITMAP_END)
   {
-    key_map::Iterator it(field->key_start);
-    uint key_no;
-    while ((key_no= it++) != key_map::Iterator::BITMAP_END)
+    KEY *key_info= &field->table->key_info[key_no];
+    if (key_info->user_defined_key_parts == 1 &&
+        (key_info->flags & HA_NOSAME))
     {
-      KEY *key_info= &field->table->key_info[key_no];
-      if (key_info->user_defined_key_parts == 1 &&
-          (key_info->flags & HA_NOSAME))
-      {
-        DBUG_RETURN(true);
-      }
+      DBUG_RETURN(true);
     }
   }
   DBUG_RETURN(false);
@@ -13475,7 +13474,7 @@ cost_group_min_max(TABLE* table, KEY *index_info, uint used_key_parts,
          - (C between const_i and const_j)
          - C IS NULL
          - C IS NOT NULL
-         - C != const
+         - C != const  (unless C is the primary key)
     SA4. If Q has a GROUP BY clause, there are no other aggregate functions
          except MIN and MAX. For queries with DISTINCT, aggregate functions
          are allowed.
@@ -14358,6 +14357,17 @@ check_group_min_max_predicates(Item *cond, Item_field *min_max_arg_item,
         if (!simple_pred(pred, args, &inv))
           DBUG_RETURN(FALSE);
 
+        /*
+          Follow the logic in Item_func_ne::get_func_mm_tree(): condition
+          in form "tbl.primary_key <> const" is not used to produce intervals.
+
+          If the condition doesn't have an equivalent interval, this means we
+          fail LooseScan's condition SA3. Return FALSE to indicate this.
+        */
+        if (pred_type == Item_func::NE_FUNC &&
+            is_field_an_unique_index(min_max_arg_item->field))
+          DBUG_RETURN(FALSE);
+
         if (args[0] && args[1]) // this is a binary function or BETWEEN
         {
           DBUG_ASSERT(pred->fixed_type_handler());