SELECT 
  category_id, 
  parent_id 
FROM 
  q_categories 
WHERE 
  parent_id IN(
    375, 376, 377, 390, 410, 430, 534, 572, 
    573, 574, 575, 581, 588, 606
  )

Query time 0.00034

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "36.41"
    },
    "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": 16,
      "rows_produced_per_join": 16,
      "filtered": "100.00",
      "index_condition": "(`portal`.`q_categories`.`parent_id` in (375,376,377,390,410,430,534,572,573,574,575,581,588,606))",
      "cost_info": {
        "read_cost": "33.21",
        "eval_cost": "3.20",
        "prefix_cost": "36.41",
        "data_read_per_join": "42K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ]
    }
  }
}