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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 246 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
40T196 $C_5\times F_8$ $280$ $1$ ✓ $C_5$, $C_2^3:C_7$
40T197 $C_2^4:C_{20}$ $320$ $-1$ ✓ $C_2$, $C_4$, $C_5$, $((C_8 : C_2):C_2):C_2$, $C_{10}$, $C_{20}$ 40T197, 40T232 x 2
40T198 $C_2^4:C_{20}$ $320$ $1$ ✓ $C_2$, $C_4$, $C_5$, $C_{10}$, $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$, $C_{20}$, $C_2\wr C_5$, $C_2^4:C_{20}$ 20T75 x 3, 40T198 x 2, 40T289 x 3, 40T290 x 6, 40T291 x 12
40T199 $(C_2^3\times C_{10}):C_4$ $320$ $-1$ ✓ $C_2$, $C_4$, $D_{5}$, $((C_8 : C_2):C_2):C_2$, $D_5$, $C_5:C_4$ 40T199, 40T230 x 2
40T200 $C_2^5.D_5$ $320$ $1$ ✓ $C_2$, $C_4$, $D_{5}$, $D_5$, $(C_2^4 : C_5) : C_2$, $(C_2^4 : C_5) : C_2$, $C_5:C_4$, $C_2^4:D_5$, $C_2^5.D_5$ 20T82 x 6, 20T84 x 3, 40T200 x 2, 40T283 x 3, 40T285 x 6, 40T287 x 6, 40T294 x 6
40T201 $C_2\wr C_2^2\times C_5$ $320$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $C_5$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_{10}$ x 3, $C_2\times C_{10}$ 40T201, 40T231 x 6
40T202 $C_2^5:C_{10}$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_5$, $C_{10}$ x 3, $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ x 3, $C_2\times C_{10}$, $C_2\wr C_5$ x 3, $C_2^5:C_{10}$ x 3 20T72 x 6, 20T74 x 36, 20T86 x 9, 40T202 x 2, 40T274 x 72, 40T275 x 36, 40T276 x 36, 40T277 x 18, 40T278 x 18, 40T292 x 9
40T203 $C_2^4:D_{10}$ $320$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_5$, $D_{10}$ x 2, $D_{10}$ 40T203, 40T227 x 2, 40T259 x 4
40T204 $C_2\wr D_5$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $D_5$, $D_{10}$ x 2, $(C_2^4 : C_5) : C_2$, $(C_2^4 : C_5) : C_2$, $C_2\times (C_2^4 : D_5)$ x 2, $D_{10}$, $C_2^4:D_5$, $C_2\wr D_5$ x 2, $C_2\wr D_5$ x 2, $C_2\wr D_5$ 10T23 x 6, 20T71 x 6, 20T73 x 6, 20T76 x 6, 20T81 x 3, 20T85 x 6, 20T87 x 6, 32T9313 x 2, 40T204 x 2, 40T270 x 12, 40T271 x 12, 40T272 x 3, 40T273 x 2, 40T284 x 6, 40T286 x 6, 40T288 x 3, 40T293 x 3, 40T295 x 6
40T205 $C_2^4:F_5$ $320$ $-1$ ✓ $C_2$, $C_4$, $F_5$, $((C_8 : C_2):C_2):C_2$, $F_5$, $F_5$ 40T205, 40T265 x 2
40T206 $C_2^4:F_5$ $320$ $1$ ✓ $C_2$, $C_4$, $F_5$, $F_5$, $F_5$, $C_2^4:F_5$, $C_2^4:F_5$ 10T24, 10T25, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88, 32T9312, 40T207, 40T296, 40T297, 40T298, 40T299, 40T300, 40T301, 40T302, 40T303
40T207 $C_2^4:F_5$ $320$ $1$ ✓ $C_2$, $C_4$, $F_5$, $F_5$, $(C_2^4 : C_5):C_4$, $(C_2^4 : C_5):C_4$, $F_5$, $C_2^4:F_5$, $C_2^4:F_5$ 10T24, 10T25, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88, 32T9312, 40T206, 40T296, 40T297, 40T298, 40T299, 40T300, 40T301, 40T302, 40T303
40T208 $(C_2^2\times D_{10}):C_4$ $320$ $-1$ ✓ $C_2$, $C_4$, $D_{5}$, $((C_8 : C_2):C_2):C_2$, $D_{10}$, $C_4\times D_5$ 40T208, 40T212 x 2
40T209 $C_2^3:C_4\times D_5$ $320$ $1$ ✓ $C_2$, $C_4$, $D_{5}$, $C_2^3: C_4$, $D_{10}$, $C_4\times D_5$ 40T209, 40T219 x 2, 40T257 x 4
40T210 $C_2^3.D_{20}$ $320$ $-1$ ✓ $C_2$, $C_4$, $D_{5}$, $((C_8 : C_2):C_2):C_2$, $D_{10}$, $C_4\times D_5$ 40T210, 40T225 x 2
40T211 $\OD_{16}:D_{10}$ $320$ $-1$ ✓ $C_2$, $C_4$, $D_{5}$, $(C_8:C_2):C_2$, $D_{10}$, $C_4\times D_5$ 40T211 x 3
40T212 $(C_2^2\times D_{10}):C_4$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$, $C_5:D_4$ 40T208 x 2, 40T212
40T213 $(C_2\times C_{20}):D_4$ $320$ $1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$, $C_5:D_4$ 40T213 x 5, 40T217 x 2
40T214 $C_2^3.D_{20}$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$, $C_5:D_4$ 40T214, 40T224 x 2
40T215 $(C_5\times D_4):D_4$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(C_4^2 : C_2):C_2$, $D_{10}$, $C_5:D_4$ 40T215 x 3
40T216 $D_{20}:C_2^3$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $Q_8:C_2^2$, $D_{10}$ x 3, $C_2\times D_{10}$ 40T216 x 11
40T217 $(C_2\times C_{20}):D_4$ $320$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$ x 3, $C_2\times D_{10}$ 40T213 x 6, 40T217
40T218 $C_2^3:D_{20}$ $320$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$ x 3, $C_2\times D_{10}$ 40T218, 40T226 x 2, 40T256 x 4
40T219 $C_2^3:C_4\times D_5$ $320$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $D_{5}$, $C_2^3: C_4$, $D_{10}$ x 3, $C_2\times D_{10}$ 40T209 x 2, 40T219, 40T257 x 4
40T220 $(C_2\times D_{20}).C_4$ $320$ $-1$ ✓ $C_2$, $C_4$, $F_5$, $(C_8:C_2):C_2$, $F_5$, $C_2\times F_5$ 40T220 x 3
40T221 $(C_4\times D_{10}):C_4$ $320$ $1$ ✓ $C_2$, $C_4$, $F_5$, $C_2^3: C_4$, $F_5$, $C_2\times F_5$ 40T221, 40T236 x 2, 40T248 x 4
40T222 $(C_2^2\times D_{10}):C_4$ $320$ $-1$ ✓ $C_2$, $C_4$, $F_5$, $((C_8 : C_2):C_2):C_2$, $F_5$, $C_2\times F_5$ 40T222, 40T268 x 2
40T223 $D_{20}:D_4$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(C_4^2 : C_2):C_2$, $D_{10}$, $D_{20}$ 40T223 x 3
40T224 $C_2^3.D_{20}$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$, $D_{20}$ 40T214 x 2, 40T224
40T225 $C_2^3.D_{20}$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$, $D_{20}$ 40T210 x 2, 40T225
40T226 $C_2^3:D_{20}$ $320$ $1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_{10}$, $D_{20}$ 40T218 x 2, 40T226, 40T256 x 4
40T227 $C_2^4:D_{10}$ $320$ $1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_5$, $C_5:D_4$ 40T203 x 2, 40T227, 40T259 x 4
40T228 $(C_4\times C_{20}):C_4$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_5$, $C_5:D_4$ 40T228 x 3
40T229 $C_4^2:D_{10}$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(C_4^2 : C_2):C_2$, $D_5$, $C_5:D_4$ 40T229 x 3
40T230 $(C_2^3\times C_{10}):C_4$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $D_{5}$, $(((C_4 \times C_2): C_2):C_2):C_2$, $D_5$, $C_5:D_4$ 40T199 x 2, 40T230
40T231 $C_2\wr C_2^2\times C_5$ $320$ $1$ ✓ $C_2$, $D_{4}$, $C_5$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_{10}$, $C_5\times D_4$ 40T201 x 2, 40T231 x 5
40T232 $C_2^4:C_{20}$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $C_5$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_{10}$, $C_5\times D_4$ 40T197 x 2, 40T232
40T233 $C_4^2:C_{20}$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $C_5$, $(((C_4 \times C_2): C_2):C_2):C_2$, $C_{10}$, $C_5\times D_4$ 40T233 x 3
40T234 $C_5\times D_4:D_4$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $C_5$, $(C_4^2 : C_2):C_2$, $C_{10}$, $C_5\times D_4$ 40T234 x 3
40T235 $D_{10}.C_2^4$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $Q_8:C_2^2$, $F_5$, $F_{5}\times C_2$ x 2, $C_2\times F_5$ 40T235 x 3, 40T238 x 8
40T236 $(C_4\times D_{10}):C_4$ $320$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $C_2^3: C_4$, $F_5$, $F_{5}\times C_2$ x 2, $C_2\times F_5$ 40T221 x 2, 40T236, 40T248 x 4
40T237 $(C_2^2\times F_5):C_4$ $320$ $-1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $C_2^3: C_4$, $F_5$, $F_{5}\times C_2$ x 2, $C_2\times F_5$ 40T237, 40T244 x 2, 40T250 x 2, 40T263 x 2
40T238 $D_{10}.C_2^4$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $Q_8:C_2^2$, $F_{5}\times C_2$ x 3, $C_2^2\times F_5$ 40T235 x 4, 40T238 x 7
40T239 $D_{10}.C_2^4$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $Q_8:C_2^2$, $F_{5}\times C_2$ x 3, $C_2^2\times F_5$ 40T239 x 5
40T240 $D_{10}.C_2^4$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $F_5$, $Q_8:C_2$, $F_{5}\times C_2$ x 3, $C_2^2\times F_5$ 40T240 x 11
40T241 $D_{10}.C_2^4$ $320$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $F_5$, $D_4\times C_2$, $F_{5}\times C_2$ x 3, $C_2^2\times F_5$, $D_4\times F_5$ x 2 40T241 x 15
40T242 $\OD_{16}:F_5$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $F_5$, $C_4\wr C_2$, $F_{5}\times C_2$, $C_{20}:C_4$ 40T242 x 3
40T243 $\OD_{16}:F_5$ $320$ $-1$ ✓ $C_2$, $D_{4}$, $F_5$, $Z_8 : Z_8^\times$, $F_{5}\times C_2$, $C_{20}:C_4$ 40T243
40T244 $(C_2^2\times F_5):C_4$ $320$ $1$ ✓ $C_2$, $D_{4}$, $F_5$, $C_2^3 : C_4 $, $F_{5}\times C_2$, $C_{20}:C_4$ 40T237 x 2, 40T244, 40T250 x 2, 40T263 x 2
40T245 $C_{10}.(C_4\times D_4)$ $320$ $1$ ✓ $C_2$, $D_{4}$ x 3, $F_5$, $C_2^2 \wr C_2$, $F_{5}\times C_2$, $C_{20}:C_4$, $D_4\times F_5$ x 2 40T245 x 7
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Results are complete for degrees $\leq 23$.