How to get sub categories by parent category id in Magento?

You can try below code for display all sub category of one particular category by category id.

<?php 

$category_id = 13;   // you can change category id according to you

$parentCat = Mage::getModel('catalog/category')->load($category_id); 

$subCat = explode(',',$parentCat ->getChildren()); 

$collection  = $parentCat
             ->getCollection()
             ->addAttributeToSelect("*")
             ->addFieldToFilter("entity_id", array("in", $subCat) );

foreach($collection as $catname)

{

     echo $catname->getName();

}

?>