If you face this error in SharePoint 2010 “Invalid index. (Exception from HRESULT: 0x80070585)” – this means that indexing needs to be correct for the view of the list to work.
To solve, please follow these steps:
1. Modify view of your list as shown in below screen shot:

2. Uncheck “Last Updated” field

3. Index problem should be resolved with this.

4. Now, repeat step 2 and check “Last Updated” field again.
Hope this helps!
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