Generally, according to the article below, the subsites will inherit the theme from the parent site. Here is the article link: http://office.microsoft.com/en-us/office365-sharepoint-online-enterprise-help/choose-a-theme-for-your-publishing-site-HA102891580.aspx
If subsite is from another template, then follow the instruction below:
1) Since the link of Master page setting is hidden, you can change the URL to the setting page by two steps.
Copy your site URL and remove the target of URL after the default URL. See the example below:
Root URL : https://XXX.sharepoint.com/SitePages/Home.aspx
Change to : https://XXX.sharepoint.com/
Add the ‘_layouts/15/ChangeSiteMasterPage.aspx’ behind the URL from step a. See the example below:
Root URL: https://XXX.sharepoint.com/
Change to : https://XXX.sharepoint.com/_layouts/15/ChangeSiteMasterPage.aspx
Note: if you get the error message, please go to check the Publishing Features on Team Site.
2) Then you will see the two inherit feature, please choose them.
The options include:
a. Site Master Page
b. System Master Page
d. Alternate CSS URL