Hello maphillips0912,
I understand Reminders don't look the same on iCloud.com as they do on your iPhone, and you're not seeing the same options either. I'm happy to help you resolve this.
It's normal for Reminders to look slightly different on iCloud.com than they appear in the Reminders app on your iPhone since you're using two different applications to view them. However, you should still be able to view all of the same reminders in both places, and many of the features you have available in the Reminders iOS app are also available in the online version. For example, it is possible to create a subtask for a reminder on iCloud.com, and in order to do so you would select the reminder and then press the Tab key on your keyboard as explained here: Create and delete reminders on iCloud.com - iCloud User Guide. I recommend taking a look at the rest of the sections in that user guide to learn more about using Reminders on iCloud.com. Click on the Table of Contents link near the top to do so.
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Take care.