php mysql html表单选择循环父和子

Hope that all doing fine

I m working to build html form based on php and mysql.

What I m stuck in is: Select sub category based on category

For example I have 2 parent categories games and software and I have 4 sub categories 2 for games(action and stragedy ) and 2 for software(internet and anti-virus).

What I m looking for is when I select the games in category the sub-category only show the (action and stragedy) and when I select the software the sub-category only show the (Internet and anti-virus)

Parent games child1 action, child2 stragedy

Parent software child1 internet, child2 anti-virus

Here is the mysql table

And here is php code

<?php
$conn=mysqli_connect("localhost","root","root","mene");
if (mysqli_connect_errno())
{
  echo "Failed to connect to MySQL: " . mysqli_connect_error();
}
$sql = "SELECT * from cates WHERE parent_name = 'main'";
$result = mysqli_query($conn,$sql);
$sql1 = "SELECT * from cates WHERE parent_name = 'category'";
$result1 = mysqli_query($conn,$sql1);
$sql2 = "SELECT * from cates WHERE parent_name = 'games'";
$result2 = mysqli_query($conn,$sql2);
$sql3 = "SELECT * from cates WHERE parent_name = 'software'";
$result3 = mysqli_query($conn,$sql3);
?>
<form action="action.php">
  <a>choose the operating system</a>
  <select name="main">
    <option value="main">-----</option>
    <?php 
            while($row = mysqli_fetch_array($result)) {     
         ?>
    <option value="<category"><?php echo $row['name']; ?></option>
    <?php } ?>
  </select>
  <br><br>
  <a>choose the category</a>
  <select name="parent">
    <option value="parent">-----</option>
    <?php 
            while($row = mysqli_fetch_array($result1)) { 
         ?>
    <option value="<category"><?php echo $row['name']; ?></option>
    <?php } ?>
  </select>
  <br><br>
  <a>choose sub category</a>
  <select name="child">
    <option value="child">-----</option>
    <php  ?>
    <?php 
            while($row1 = mysqli_fetch_array($result2)) {
         ?>
    <option value="sub_category"><?php echo $row1['name']; ?></option>
    <?php } ?>
  </select>
  <br><br>
  <input type="submit">
</form>
<?php mysqli_close($conn); ?>
<php } ?>

any help?