AM is not used with 24 hour time. 1300 is 1pm.
0000 = 12:00am
0100 = 1:00am
1259 = 12:59 am
1300 = 1:00pm
1800 = 6:00pm
2359 = 11:59pm
Easiest way to convert is if you see a time greater than 12:59, subtract 12 from it. That will give you the "PM" time.
Longer, more detailed explanation
HERE.