How can I edit distribution lists in Office 365?

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Log in to Office 365 by going to https://outlook.office365.com.
Click on the Gear icon in the top-right, then click on Mail under Your app settings. You may need to scroll down to see the options.
When the Options page loads, expand the General group on the left side, then click on Distribution groups. From here, you should be able to see all the groups you are a member of plus the groups you own. To edit a group you own, you can either double-click the group name or click on the group and click the Pencil icon.
When the edit window appears, click on Membership. From here, you can click on the Plus (+) or Minus (-) buttons to either add or remove members from the distribution group. When you're done, don't forget to hit the Save button at the bottom of the page.