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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (1-50 of 76 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
2T1 $C_2$ $2$ $-1$ ✓
3T1 $C_3$ $3$ $1$ ✓
4T1 $C_4$ $4$ $-1$ ✓ $C_2$
4T2 $C_2^2$ $4$ $1$ ✓ $C_2$ x 3
5T1 $C_5$ $5$ $1$ ✓
6T1 $C_6$ $6$ $-1$ ✓ $C_2$, $C_3$
7T1 $C_7$ $7$ $1$ ✓
8T1 $C_8$ $8$ $-1$ ✓ $C_2$, $C_4$
8T2 $C_4\times C_2$ $8$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$
8T3 $C_2^3$ $8$ $1$ ✓ $C_2$ x 7, $C_2^2$ x 7
9T1 $C_9$ $9$ $1$ ✓ $C_3$
9T2 $C_3^2$ $9$ $1$ ✓ $C_3$ x 4
10T1 $C_{10}$ $10$ $-1$ ✓ $C_2$, $C_5$
11T1 $C_{11}$ $11$ $1$ ✓
12T1 $C_{12}$ $12$ $-1$ ✓ $C_2$, $C_3$, $C_4$, $C_6$
12T2 $C_6\times C_2$ $12$ $1$ ✓ $C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3
13T1 $C_{13}$ $13$ $1$ ✓
14T1 $C_{14}$ $14$ $-1$ ✓ $C_2$, $C_7$
15T1 $C_{15}$ $15$ $1$ ✓ $C_3$, $C_5$
16T1 $C_{16}$ $16$ $-1$ ✓ $C_2$, $C_4$, $C_8$
16T2 $C_4\times C_2^2$ $16$ $1$ ✓ $C_2$ x 7, $C_4$ x 4, $C_2^2$ x 7, $C_4\times C_2$ x 6, $C_2^3$
16T3 $C_2^4$ $16$ $1$ ✓ $C_2$ x 15, $C_2^2$ x 35, $C_2^3$ x 15
16T4 $C_4^2$ $16$ $1$ ✓ $C_2$ x 3, $C_4$ x 6, $C_2^2$, $C_4\times C_2$ x 3
16T5 $C_8\times C_2$ $16$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$
17T1 $C_{17}$ $17$ $1$ ✓
18T1 $C_{18}$ $18$ $-1$ ✓ $C_2$, $C_3$, $C_6$, $C_9$
18T2 $C_6 \times C_3$ $18$ $-1$ ✓ $C_2$, $C_3$ x 4, $C_6$ x 4, $C_3^2$
19T1 $C_{19}$ $19$ $1$ ✓
20T1 $C_{20}$ $20$ $-1$ ✓ $C_2$, $C_4$, $C_5$, $C_{10}$
20T3 $C_2\times C_{10}$ $20$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_5$, $C_{10}$ x 3
21T1 $C_{21}$ $21$ $1$ ✓ $C_3$, $C_7$
22T1 $C_{22}$ $22$ $-1$ ✓ $C_2$, $C_{11}$
23T1 $C_{23}$ $23$ $1$ ✓
24T1 $C_{24}$ $24$ $-1$ ✓ $C_2$, $C_3$, $C_4$, $C_6$, $C_8$, $C_{12}$
24T2 $C_2\times C_{12}$ $24$ $1$ ✓ $C_2$ x 3, $C_3$, $C_4$ x 2, $C_2^2$, $C_6$ x 3, $C_4\times C_2$, $C_{12}$ x 2, $C_6\times C_2$
24T3 $C_2^2\times C_6$ $24$ $1$ ✓ $C_2$ x 7, $C_3$, $C_2^2$ x 7, $C_6$ x 7, $C_2^3$, $C_6\times C_2$ x 7
25T1 $C_{25}$ $25$ $1$ ✓ $C_5$
25T2 $C_5^2$ $25$ $1$ ✓ $C_5$ x 6
26T1 $C_{26}$ $26$ $-1$ ✓ $C_2$, $C_{13}$
27T1 $C_{27}$ $27$ $1$ ✓ $C_3$, $C_9$
27T2 $C_3\times C_9$ $27$ $1$ ✓ $C_3$ x 4, $C_9$ x 3, $C_3^2$
27T4 $C_3^3$ $27$ $1$ ✓ $C_3$ x 13, $C_3^2$ x 13
28T1 $C_{28}$ $28$ $-1$ ✓ $C_2$, $C_4$, $C_7$, $C_{14}$
28T2 $C_2\times C_{14}$ $28$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_7$, $C_{14}$ x 3
29T1 $C_{29}$ $29$ $1$ ✓
30T1 $C_{30}$ $30$ $-1$ ✓ $C_2$, $C_3$, $C_5$, $C_6$, $C_{10}$, $C_{15}$
31T1 $C_{31}$ $31$ $1$ ✓
32T32 $C_2\times C_{16}$ $32$ $1$ ✓ $C_2$ x 3, $C_4$ x 2, $C_2^2$, $C_8$ x 2, $C_4\times C_2$, $C_{16}$ x 2, $C_8\times C_2$
32T33 $C_{32}$ $32$ $-1$ ✓ $C_2$, $C_4$, $C_8$, $C_{16}$
32T34 $C_2^3\times C_4$ $32$ $1$ ✓ $C_2$ x 15, $C_4$ x 8, $C_2^2$ x 35, $C_4\times C_2$ x 28, $C_2^3$ x 15, $C_4\times C_2^2$ x 14, $C_2^4$
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Results are complete for degrees $\leq 23$.