An administrator of an Office 365 organization can add one of your users or contacts to a distribution list/group.
First, open a web browser and go to https://admin.microsoft.com and sign in.
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On the left pane of the screen go down and click Exchange. You will be redirected to the Exchange Admin Center.
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From here click groups under recipients.
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Double click on the group you would like to add members to.
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Click membership on the left side of the dialogue box.
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Click the '+' sign next to add members.
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You can select users and click add then click OK.
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You can add them one at a time, or select multiple by holding the control or shift keys.
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After adding the users you want to the group click save.