Google Calendar does not automatically sync calendar subscriptions to iOS devices unless explicitly enabled.
This help covers all four steps needed, but you'll likely only need Step 3.
Add your Google account to your iOS device.
Open SettingsCalendarAccountsAdd accountGoogle and add your Google account if not already added.
Please make sure you've checked to sync calendars.
Google wants you to select which subscribed calendars you wish to see on your mobile device.
Please go to Google Calendar Sync Settings. Log in if necessary.
Select all calendars under Shared Calendars
Your calendar will soon show your calendar subscriptions from Google.
You may also tell your iOS device to update immediately.
To do that, please take a look at How do I force my calendar application to refresh a calendar subscription?