Select field not appending data

hi. I have a dependent dropdown. when selecting division it will show the districts included in that division but it is not appending select data. Blade file:

<div class="form-group">
                <label for="division">Division</label>
                <select class="form-control" name="division" id="division">
                    @foreach($division as $div)
                        <option value="{{ $div->division }}">{{ $div->division }}</option>
                    @endforeach
                </select>
            </div>
            <div class="form-group">
                <label for="district">District</label>
                <select class="form-control" name="district" id="district">
                   
                </select>
  </div>
              		

script:

    <script>
            $(document).ready(function() {
            $('#division').on('change', function() {
               var division = $(this).val();
               if(division) {
                   $.ajax({
                       url: "<?= url('/admin/getdistrict/') ?>/" + division,
                       type: "GET",
                       data : {"_token":"{{ csrf_token() }}"},
                       dataType: "json",
                       success:function(data)
                       {
                        console.log(data);
                         if(data){
                            $('#district').empty();
                            $('#district').append('<option hidden>Choose district</option>'); 
                            $.each(data, function(key, district){
                                $('select[name="district"]').append('<option value="'+ district.district +'">' + district.district+ '</option>');
                            });
                        }else{
                            $('#district').empty();
                        }
                     }
                   });
               }else{
                 $('#district').empty();
               }
            });
            
</script>

the data is showing in the console. and if i append it in a div then also the data are showing. only when i use select the data is not appending.