SELECT 
  category_id, 
  parent_id 
FROM 
  q_categories 
WHERE 
  parent_id IN(
    551, 191, 192, 193, 194, 195, 196, 197, 
    199, 200, 201, 202, 204, 206, 386, 420, 
    424, 428, 429, 556
  )

Query time 0.00032

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "49.41"
    },
    "table": {
      "table_name": "q_categories",
      "access_type": "range",
      "possible_keys": [
        "parent"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id"
      ],
      "key_length": "3",
      "rows_examined_per_scan": 21,
      "rows_produced_per_join": 21,
      "filtered": "100.00",
      "index_condition": "(`portal`.`q_categories`.`parent_id` in (551,191,192,193,194,195,196,197,199,200,201,202,204,206,386,420,424,428,429,556))",
      "cost_info": {
        "read_cost": "45.21",
        "eval_cost": "4.20",
        "prefix_cost": "49.41",
        "data_read_per_join": "55K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ]
    }
  }
}