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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 365 matches)

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Label Name Order Parity Solvable Subfields Low Degree Siblings
25T54 $F_5\times A_5$ $1200$ $-1$ $F_5$, $A_5$ 30T245
25T55 $A_5:F_5$ $1200$ $1$ $F_5$, $S_5$ 30T250
25T56 $\AGammaL(1,25)$ $1200$ $-1$ ✓ 30T239
25T57 $C_5^2:\SL(2,3):C_2$ $1200$ $1$ ✓ 30T233
25T58 $D_5\times S_5$ $1200$ $-1$ $D_{5}$, $S_5$ 30T252
25T59 $C_5^3:C_{10}$ $1250$ $1$ ✓ $C_5$ 25T59 x 4
25T60 $C_5^3:D_5$ $1250$ $1$ ✓ $D_{5}$ 25T60 x 4
25T61 $C_5^3.D_5$ $1250$ $1$ ✓ $D_{5}$ 25T61 x 4
25T62 $C_5^3:D_5$ $1250$ $1$ ✓ $D_{5}$ 25T62 x 4
25T63 $\He_5:C_4^2$ $2000$ $-1$ ✓ $F_5$ 25T63
26T16 $D_{13}\wr C_2$ $1352$ $-1$ ✓ $C_2$ 26T16, 26T19
26T17 $C_{13}^2:Q_8$ $1352$ $-1$ ✓ $C_2$ 26T17 x 2
26T18 $D_{13}^2.C_2$ $1352$ $-1$ ✓ $C_2$ 26T18 x 5
26T19 $D_{13}\wr C_2$ $1352$ $-1$ ✓ $C_2$ 26T16 x 2
26T20 $C_{13}^2:C_8$ $1352$ $1$ ✓ $C_2$ 26T20 x 6
26T21 $C_{13}:F_{13}$ $2028$ $-1$ ✓ $C_2$ 26T21 x 5
26T22 $D_{13}^2:C_3$ $2028$ $-1$ ✓ $C_2$ 26T22 x 5
26T23 $C_{13}^2:D_6$ $2028$ $-1$ ✓ $C_2$ 39T34 x 2
26T24 $C_{13}^2:C_3:C_4$ $2028$ $-1$ ✓ $C_2$ 39T35 x 2
27T292 $C_3^3:C_{13}:C_3$ $1053$ $1$ ✓ 39T29, 39T30 x 2
27T293 $C_3^3:\GL(2,3)$ $1296$ $-1$ ✓ $C_3$, $((C_3^2:Q_8):C_3):C_2$ 24T2917, 36T2273
27T294 $\He_3:\GL(2,3)$ $1296$ $1$ ✓ $((C_3^2:Q_8):C_3):C_2$ 27T294 x 2, 36T2302 x 3
27T295 $S_3\times \PGU(3,2)$ $1296$ $-1$ ✓ $S_3$, $(C_3^2:Q_8):C_3$ 24T2936, 36T2269
27T296 $S_3\wr S_3$ $1296$ $-1$ ✓ 9T31, 12T213, 18T300, 18T303, 18T311, 18T312, 18T314, 18T315, 18T319, 18T320, 24T2893, 24T2894, 24T2895, 24T2912, 27T298, 36T2197, 36T2198, 36T2199, 36T2201, 36T2202, 36T2210, 36T2211, 36T2212, 36T2213, 36T2214, 36T2215, 36T2216, 36T2217, 36T2218, 36T2219, 36T2220, 36T2225, 36T2226, 36T2229, 36T2305
27T297 $C_3^3:\GL(2,3)$ $1296$ $1$ ✓ $S_3$, $((C_3^2:Q_8):C_3):C_2$ 24T2918 x 3, 27T297 x 2, 36T2271 x 3
27T298 $S_3\wr S_3$ $1296$ $1$ ✓ $S_3$ 9T31, 12T213, 18T300, 18T303, 18T311, 18T312, 18T314, 18T315, 18T319, 18T320, 24T2893, 24T2894, 24T2895, 24T2912, 27T296, 36T2197, 36T2198, 36T2199, 36T2201, 36T2202, 36T2210, 36T2211, 36T2212, 36T2213, 36T2214, 36T2215, 36T2216, 36T2217, 36T2218, 36T2219, 36T2220, 36T2225, 36T2226, 36T2229, 36T2305
27T299 $C_3^3:C_9:S_3$ $1458$ $1$ ✓ $S_3$, $(C_3^3:C_3):C_2$ 27T299 x 17, 27T329 x 3
27T300 $C_9^2.(C_3\times S_3)$ $1458$ $-1$ ✓ $S_3$, $C_3^2 : C_6$
27T301 $C_3^4.(C_3\times S_3)$ $1458$ $-1$ ✓ $S_3$, $C_3 \wr S_3 $ 27T301 x 2, 27T344 x 3, 27T354
27T302 $C_3^4:D_9$ $1458$ $1$ ✓ $S_3$, $D_{9}$ 27T302 x 8, 27T371 x 3
27T303 $C_3^4.(C_3\times S_3)$ $1458$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T303 x 2
27T304 $(C_3^2\times C_9):C_{18}$ $1458$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T304 x 2
27T305 $C_3^5:C_6$ $1458$ $-1$ ✓ $C_3$, $C_3^2:C_3$, $(C_3^3:C_3):C_2$ 18T327 x 9, 27T305 x 8
27T306 $C_3^5.S_3$ $1458$ $-1$ ✓ $S_3$, $(C_9:C_3):C_2$, $(C_3^3:C_3):C_2$ x 3 27T306 x 8
27T307 $C_3^5:S_3$ $1458$ $-1$ ✓ $S_3$, $C_3^2 : C_6$, $(C_3^3:C_3):C_2$ x 3 27T307 x 8
27T308 $C_3^5:S_3$ $1458$ $-1$ ✓ $S_3$, $(C_3^2:C_3):C_2$, $C_3 \wr S_3 $ x 3 27T308 x 8
27T309 $C_3^4:(C_3\times S_3)$ $1458$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T309 x 2, 27T340 x 3
27T310 $C_3^4:(C_3\times C_6)$ $1458$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T310 x 2, 27T379 x 3
27T311 $C_3^4:C_{18}$ $1458$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T311 x 2, 27T378 x 3
27T312 $C_3^5:S_3$ $1458$ $1$ ✓ $S_3$, $(C_3^2:C_3):C_2$, $(C_3^3:C_3):C_2$ 18T333 x 9, 27T312 x 26
27T313 $C_9^2:(C_3\times C_6)$ $1458$ $1$ ✓ $C_3$, $C_3^2 : S_3 $ 27T313 x 2
27T314 $C_3^4:D_9$ $1458$ $1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T314 x 2, 27T327 x 3
27T315 $(C_3^2\times \He_3):C_6$ $1458$ $-1$ ✓ $C_3$, $C_3^2 : S_3 $ 27T315 x 8, 27T372 x 3
27T316 $C_3^4:C_3:S_3$ $1458$ $1$ ✓ $S_3$, $C_3^2 : C_6$ 27T316 x 17, 27T330 x 3
27T317 $C_3^4:(C_3\times S_3)$ $1458$ $-1$ ✓ $C_3$, $S_3$, $S_3\times C_3$ 27T317 x 11
27T318 $C_3^4:(C_3\times S_3)$ $1458$ $-1$ ✓ $S_3$, $C_3^2 : C_6$ 27T333, 27T367
27T319 $C_9^2:(C_3\times S_3)$ $1458$ $-1$ ✓ $S_3$, $(C_3^2:C_3):C_2$
27T320 $(C_3\times C_9^2):C_6$ $1458$ $1$ ✓ $C_3$, $C_3^2 : S_3 $ 27T320 x 8
27T321 $C_3^5:S_3$ $1458$ $1$ ✓ $S_3$, $C_3^2 : C_6$, $C_3 \wr S_3 $ 18T329 x 9, 27T321 x 26
27T322 $C_3^4:C_3:S_3$ $1458$ $1$ ✓ $S_3$, $(C_3^2:C_3):C_2$ 27T322 x 2, 27T382 x 3
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Results are complete for degrees $\leq 23$.