Are there extended partitions in GPT partition table?

128 partitions is the default limit for GPT, and it's probably painful in practice to use half that many...

Linux itself originally also had some limitations in its device namespace. For /dev/sdX it assumes no more than 15 partitions (sda is 8,0, sdb is 8,16, etc.). If there are more partitions, they will be represented using 259,X aka Block Extended Major.

You could certainly still do more partitions in various ways. Loop devices, LVM, or even GPT inside GPT. Sometimes this happens naturally when handing partitions as block devices to virtual machines, they see the partition as virtual disk drive and partition that.

Just don't expect such partitions inside partitions to be picked up automatically.

As @fpmurphy1 pointed out in the comments, I was wrong: You can change the limit, using gdisk, expert menu, resize partition table. This can also be done for existing partition tables, provided there is unpartitioned space (a 512-byte sector for 4 additional partition entries) at the start and end of the drive. However I'm not sure how widely supported this is; there doesn't seem to be an option for it in parted or other partitioners I've tried.

And the highest limit you can set with gdisk seems to be 65536 but it's bugged:

Expert command (? for help): s   
Current partition table size is 128.
Enter new size (4 up, default 128): 65536
Value out of range

And then...

Expert command (? for help): s   
Current partition table size is 128.
Enter new size (4 up, default 128): 65535
Adjusting GPT size from 65535 to 65536 to fill the sector

Expert command (? for help): s
Current partition table size is 65536.

Eeeh? Whatever you say.

But try to save that partition table and gdisk is stuck in a loop for several minutes.

Expert command (? for help): w

--- gdisk gets stuck here ---
      PID USER      PR  NI    VIRT    RES    SHR S  %CPU %MEM     TIME+ COMMAND    
    22253 root      20   0   24004  11932   3680 R 100.0  0.1   1:03.47 gdisk      
--- unstuck several minutes later ---

Final checks complete. About to write GPT data. THIS WILL OVERWRITE EXISTING
PARTITIONS!!

Do you want to proceed? (Y/N): Your option? (Y/N): y
OK; writing new GUID partition table (GPT) to /dev/loop0.
Warning: The kernel is still using the old partition table.
The new table will be used at the next reboot or after you
run partprobe(8) or kpartx(8)
The operation has completed successfully.

And here's what parted has to say about the successfully completed operation:

# parted /dev/loop0 print free
Backtrace has 8 calls on stack:
  8: /usr/lib64/libparted.so.2(ped_assert+0x45) [0x7f7e780181f5]
  7: /usr/lib64/libparted.so.2(+0x24d5e) [0x7f7e7802fd5e]
  6: /usr/lib64/libparted.so.2(ped_disk_new+0x49) [0x7f7e7801d179]
  5: parted() [0x40722e]
  4: parted(non_interactive_mode+0x92) [0x40ccd2]
  3: parted(main+0x1102) [0x405f52]
  2: /lib64/libc.so.6(__libc_start_main+0xf1) [0x7f7e777ec1e1]
  1: parted(_start+0x2a) [0x40610a]


You found a bug in GNU Parted! Here's what you have to do:

Don't panic! The bug has most likely not affected any of your data.
Help us to fix this bug by doing the following:

Check whether the bug has already been fixed by checking
the last version of GNU Parted that you can find at:

    http://ftp.gnu.org/gnu/parted/

Please check this version prior to bug reporting.

If this has not been fixed yet or if you don't know how to check,
please visit the GNU Parted website:

    http://www.gnu.org/software/parted

for further information.

Your report should contain the version of this release (3.2)
along with the error message below, the output of

    parted DEVICE unit co print unit s print

and the following history of commands you entered.
Also include any additional information about your setup you
consider important.

Assertion (gpt_disk_data->entry_count <= 8192) at gpt.c:793 in function
_parse_header() failed.

Aborted                                                                   

So parted refuses to work with GPT that has more than 8192 partition entries. Nobody ever does that, so it has to be corrupt, right?

This is what happens when you don't stick to defaults.