SELECT 
  category_id, 
  parent_id 
FROM 
  q_categories 
WHERE 
  parent_id IN(
    551, 169, 134, 3, 2, 145, 139, 249, 96, 
    13, 251, 6, 170, 100, 5, 50, 546, 38, 77, 
    252, 366, 12, 136, 454, 171, 10, 168, 
    44, 460, 11, 133, 190, 253, 387, 184, 
    95, 523, 138, 207, 248, 144, 389, 299, 
    393, 177, 438, 544, 434, 519, 552, 180, 
    181, 484, 533, 183, 386, 379, 244, 518, 
    513, 428
  )

Query time 0.00099

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "134.53"
    },
    "table": {
      "table_name": "q_categories",
      "access_type": "ALL",
      "possible_keys": [
        "parent"
      ],
      "rows_examined_per_scan": 598,
      "rows_produced_per_join": 277,
      "filtered": "46.49",
      "cost_info": {
        "read_cost": "78.93",
        "eval_cost": "55.60",
        "prefix_cost": "134.53",
        "data_read_per_join": "734K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ],
      "attached_condition": "(`portal`.`q_categories`.`parent_id` in (551,169,134,3,2,145,139,249,96,13,251,6,170,100,5,50,546,38,77,252,366,12,136,454,171,10,168,44,460,11,133,190,253,387,184,95,523,138,207,248,144,389,299,393,177,438,544,434,519,552,180,181,484,533,183,386,379,244,518,513,428))"
    }
  }
}