I need an aerial adaptor for my 4G modem. What are the names of these types of coax connectors?
If you want to replace your tiny antenna with the big one, the part with the outer thread nut is the Male connector and it normally has a center pin unless it is Reverse Polarity RP.

Match this up to your required connections. It is best  to use the big coax with Type N for lowest loss on long cables and then small adapters at the modem.

Here is an example of type N female to SMA Male adapter worth about $5 or more.





Looks like an SMA connector with an 8mm hex nut which has a defined torque spec.

Sounds like you got a Type N connector.

To be more precise it is an SMA  Male plug that you show  and not a reverse polarity RP-SMA  Male plug.