Cyclic subgroups of U(30): why are <17> and <23> not included?

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patelnjigar
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Please help me.

The question is: List the cyclic Subgroups of U(30)

My answer {<1>,<7>,<13>,<17>,<19>,<23>,<29>} however the answer key tells me {<1>,<7>,<13>,<19>,<29>} (leaving out <17>,<23>)

Where am I erroneous?
 
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where is erroneous?

The question is: List the cyclic Subgroups of U(30)

My answer {<1>,<7>,<13>,<17>,<19>,<23>,<29>} however the answer key tells me {<1>,<7>,<13>,<19>,<29>} (leaving out <17>,<23>)

Where am I erroneous?