also:
<?php
$db = new mysqli($host,$user,$pass,$name);
$query = "SELECT * FROM Sublist WHERE 1 LIMIT 0 , 30";
$result = $mysqli->query($query);
# as brad says, you need to be using mysqli_fetch_array.
# **However**
# you also need to pass the $result to the function, not the $query
# (_and_ use mysqli flags, not mysql).
while($info = mysql_fetch_array($query, MYSQL_ASSOC)) {
/** etc... */
I would also recommend against using both the procedural and object-oriented APIs - you start by creating a mysqli object and running a query, but then switch to procedural functions to try to access the results.
This is going to cause confusion down the line (if it hasn't already). Choose one or the other (I prefer OO).