Transitive Subgroups of S15

TName(s)|G|Parity|CS15(G)|SubfieldsOther RepresentationsResolvents
1C(15)=5[x]315 = 3 · 51153T1, 5T1  3: 3T1
5: 5T1
2D(15)30 = 2 · 3 · 5-113T2, 5T2  2: 2T1
6: 3T2
10: 5T2
3D(5)[x]330 = 2 · 3 · 5133T1, 5T2  2: 2T1
3: 3T1
6: 6T1
10: 5T2
45[x]S(3)30 = 2 · 3 · 5-153T2, 5T1  2: 2T1
5: 5T1
6: 3T2
10: 10T1
5A_5(15)60 = 22 · 3 · 5135T4 5T4, 6T12, 10T7, 12T33, 20T15 
6F(5)[1/2]S(3)60 = 22 · 3 · 5113T2, 5T3  2: 2T1
4: 4T1
6: 3T2
12: 12T5
20: 5T3
7D(5)[x]S(3)60 = 22 · 3 · 5-113T2, 5T2  2: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
10: 5T2
12: 6T3
20: 10T3
8F(5)[x]360 = 22 · 3 · 5-133T1, 5T3  2: 2T1
3: 3T1
4: 4T1
6: 6T1
12: 12T1
20: 5T3
9[5^2]375 = 3 · 52153T1 15T93: 3T1
10S_5(15)120 = 23 · 3 · 5115T5 5T5, 6T14, 10T12, 10T13, 12T74, 20T30, 20T35, 20T322: 2T1
11F(5)[x]S(3)120 = 23 · 3 · 5-113T2, 5T3  2: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
6: 3T2
8: 8T2
12: 6T3
20: 5T3
24: 12T11
40: 10T5
12[5^2:2]3150 = 2 · 3 · 52113T1 15T122: 2T1
3: 3T1
6: 6T1
13[5^2]S(3)150 = 2 · 3 · 52-153T2 15T142: 2T1
6: 3T2
145^2:2[1/2]S(3)150 = 2 · 3 · 52-113T2 15T132: 2T1
6: 3T2
153A_5(15)=[3]A(5)=GL(2,4)180 = 22 · 32 · 5135T4 15T16, 15T15, 18T903: 3T1
60: 5T4
16A(5)[x]3180 = 22 · 32 · 5133T1, 5T4 15T15, 15T15, 18T903: 3T1
60: 5T4
171/2[5^2:4]S(3)300 = 22 · 3 · 52113T2 15T172: 2T1
4: 4T1
6: 3T2
12: 12T5
18[5^2:2]S(3)300 = 22 · 3 · 52-113T2 15T182: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
12: 6T3
19[5^2:4]3300 = 22 · 3 · 52-113T1 15T192: 2T1
3: 3T1
4: 4T1
6: 6T1
12: 12T1
20A_6(15)360 = 23 · 32 · 511  6T15, 6T15, 10T26, 15T20, 20T89 
213S_5(15)360 = 23 · 32 · 5115T5 15T21, 15T22, 18T1462: 2T1
6: 3T2
120: 5T5
22S(5)[1/2]S(3)360 = 23 · 32 · 5113T2, 5T5 15T21, 15T21, 18T1462: 2T1
6: 3T2
120: 5T5
23A(5)[x]S(3)360 = 23 · 32 · 5-113T2, 5T4 18T1452: 2T1
6: 3T2
60: 5T4
120: 10T11
24S(5)[x]3360 = 23 · 32 · 5-133T1, 5T5 18T1442: 2T1
3: 3T1
6: 6T1
120: 5T5
25[5^3]3=5wr3375 = 3 · 53153T1 15T25, 15T25, 15T25, 15T25, 15T25, 15T25, 15T253: 3T1
5: 5T1
15: 15T1
75: 15T9
26[3^4]5405 = 34 · 5135T1 15T26, 15T26, 15T26, 15T26, 15T26, 15T26, 15T265: 5T1
27[5^2:4]S(3)600 = 23 · 3 · 52-113T2 15T272: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
6: 3T2
8: 8T2
12: 6T3
24: 12T11
28S_6(15)720 = 24 · 32 · 511  6T16, 6T16, 10T32, 12T183, 12T183, 15T28, 20T145, 20T149, 20T1492: 2T1
29S(5)[x]S(3)720 = 24 · 32 · 5-113T2, 5T5 18T2272: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
12: 6T3
120: 5T5
240: 10T22
30[5^3:2]3750 = 2 · 3 · 53113T1 15T30, 15T30, 15T30, 15T30, 15T30, 15T30, 15T302: 2T1
3: 3T1
6: 6T1
10: 5T2
30: 15T3
150: 15T12
311/2[5^3:2]S(3)750 = 2 · 3 · 53-113T2 15T31, 15T31, 15T312: 2T1
6: 3T2
10: 5T2
30: 15T2
150: 15T13
32[5^3]S(3)750 = 2 · 3 · 53-153T2 15T32, 15T32, 15T322: 2T1
5: 5T1
6: 3T2
10: 10T1
30: 15T4
150: 15T13
33[3^4:2]5810 = 2 · 34 · 5-115T1 15T33, 15T33, 15T33, 15T33, 15T33, 15T33, 15T332: 2T1
5: 5T1
10: 10T1
34[3^4]D(5)810 = 2 · 34 · 5135T2 15T35, 15T35, 15T35, 15T35, 15T34, 15T34, 15T342: 2T1
10: 5T2
351/2[3^4:2]D(5)810 = 2 · 34 · 5-115T2 15T34, 15T34, 15T34, 15T34, 15T35, 15T35, 15T352: 2T1
10: 5T2
36[3^5]5=3wr51215 = 35 · 5135T1 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T36, 15T363: 3T1
5: 5T1
15: 15T1
405: 15T26
371/2[5^3:4]S(3)1500 = 22 · 3 · 53113T2 15T37, 15T37, 15T372: 2T1
4: 4T1
6: 3T2
12: 12T5
20: 5T3
60: 15T6
300: 15T17
38[5^3:4]31500 = 22 · 3 · 53-113T1 15T38, 15T38, 15T38, 15T38, 15T38, 15T38, 15T382: 2T1
3: 3T1
4: 4T1
6: 6T1
12: 12T1
20: 5T3
60: 15T8
300: 15T19
39[1/2.D(5)^3]31500 = 22 · 3 · 53113T1 20T2093: 3T1
12: 4T4
40[5^3:2]S(3)1500 = 22 · 3 · 53-113T2 15T40, 15T40, 15T402: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
10: 5T2
12: 6T3
20: 10T3
60: 15T7
300: 15T18
41[3^4]F(5)1620 = 22 · 34 · 5-135T3 15T422: 2T1
4: 4T1
20: 5T3
421/2[3^4:2]F(5)1620 = 22 · 34 · 5115T3 15T412: 2T1
4: 4T1
20: 5T3
43[3^4:2]D(5)1620 = 22 · 34 · 5-115T2 15T43, 15T43, 15T43, 15T43, 15T43, 15T43, 15T432: 2T1, 2T1, 2T1
4: 4T2
10: 5T2
20: 10T3
44[3^5:2]52430 = 2 · 35 · 5-115T1 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T44, 15T442: 2T1
5: 5T1
6: 3T2
10: 10T1
30: 15T4
810: 15T33
451/2[3^5:2]D(5)2430 = 2 · 35 · 5-115T2 15T45, 15T45, 15T45, 15T45, 15T45, 15T45, 15T452: 2T1
6: 3T2
10: 5T2
30: 15T2
810: 15T34
46[3^5]D(5)=3wrD(5)2430 = 2 · 35 · 5135T2 15T46, 15T46, 15T46, 15T46, 15T46, 15T46, 15T462: 2T1
3: 3T1
6: 6T1
10: 5T2
30: 15T3
810: 15T34
47A_7(15)2520 = 23 · 32 · 5 · 711  7T6, 15T47, 21T33 
481/2[D(5)^3]S(3)3000 = 23 · 3 · 53-113T2 20T2702: 2T1
6: 3T2
24: 4T5
49[5^3:4]S(3)3000 = 23 · 3 · 53-113T2 15T49, 15T49, 15T492: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
6: 3T2
8: 8T2
12: 6T3
20: 5T3
24: 12T11
40: 10T5
120: 15T11
600: 15T27
50[D(5)^3]3=D(5)wr33000 = 23 · 3 · 53113T1 20T2692: 2T1
3: 3T1
6: 6T1
12: 4T4
24: 6T6
51[1/2.D(5)^3]S(3)3000 = 23 · 3 · 53-113T2 20T2682: 2T1
6: 3T2
24: 4T5
52[3^4:2]F(5)3240 = 23 · 34 · 5-115T3 15T522: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
8: 8T2
20: 5T3
40: 10T5
53[3^4]A(5)4860 = 22 · 35 · 5135T4 15T53, 15T5360: 5T4
541/2[3^5:2]F(5)4860 = 22 · 35 · 5115T3 15T542: 2T1
4: 4T1
6: 3T2
12: 12T5
20: 5T3
60: 15T6
1620: 15T41
55[3^5:2]D(5)4860 = 22 · 35 · 5-115T2 15T55, 15T55, 15T55, 15T55, 15T55, 15T55, 15T552: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
10: 5T2
12: 6T3
20: 10T3
60: 15T7
1620: 15T43
56[3^5]F(5)=3wrF(5)4860 = 22 · 35 · 5-135T3 15T562: 2T1
3: 3T1
4: 4T1
6: 6T1
12: 12T1
20: 5T3
60: 15T8
1620: 15T41
57[1/4.F(5)^3]36000 = 24 · 3 · 53113T1  3: 3T1
12: 4T4
48: 12T31
581/2[D(5)^3:2]S(3)6000 = 24 · 3 · 53113T2 20T3602: 2T1
4: 4T1
6: 3T2
12: 12T5
24: 4T5
48: 12T27
59[D(5)^3:2]36000 = 24 · 3 · 53-113T1 20T3592: 2T1
3: 3T1
4: 4T1
6: 6T1
12: 4T4, 12T1
24: 6T6
48: 12T29
60[D(5)^3]S(3)=D(5)wrS(3)6000 = 24 · 3 · 53-113T2 20T3612: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
12: 6T3
24: 4T5
48: 6T11
61[3^4:2]A(5)9720 = 23 · 35 · 5-115T4  2: 2T1
60: 5T4
120: 10T11
621/2[3^4:2]S(5)9720 = 23 · 35 · 5115T5 15T62, 15T622: 2T1
120: 5T5
63[3^4]S(5)9720 = 23 · 35 · 5-135T5  2: 2T1
120: 5T5
64[3^5:2]F(5)9720 = 23 · 35 · 5-115T3 15T642: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
6: 3T2
8: 8T2
12: 6T3
20: 5T3
24: 12T11
40: 10T5
120: 15T11
3240: 15T52
651/2[1/2.F(5)^3]S(3)12000 = 25 · 3 · 53-113T2  2: 2T1
6: 3T2
24: 4T5
96: 12T62
66[1/4.F(5)^3]S(3)12000 = 25 · 3 · 53-113T2  2: 2T1
6: 3T2
24: 4T5
96: 12T62
67[1/2.F(5)^3]312000 = 25 · 3 · 53113T1  2: 2T1
3: 3T1
6: 6T1
12: 4T4
24: 6T6
48: 12T31
96: 12T55
68[D(5)^3:2]S(3)12000 = 25 · 3 · 53-113T2 20T4542: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
6: 3T2
8: 8T2
12: 6T3
24: 4T5, 12T11
48: 6T11
96: 12T53
69[3^5]A(5)=3wrA(5)14580 = 22 · 36 · 5135T4 15T69, 15T69, 15T69, 15T69, 15T693: 3T1
60: 5T4
180: 15T15
4860: 15T53
70[3^4:2]S(5)19440 = 24 · 35 · 5-115T5  2: 2T1, 2T1, 2T1
4: 4T2
120: 5T5
240: 10T22
71[1/2.S(3)^5]519440 = 24 · 35 · 5115T1  5: 5T1
80: 10T8
72L(15)=A_8(15)=PSL(4,2)20160 = 26 · 32 · 5 · 711  8T49, 15T72 
731/2[F(5)^3]S(3)24000 = 26 · 3 · 53113T2  2: 2T1
4: 4T1
6: 3T2
12: 12T5
24: 4T5
48: 12T27
96: 12T62
192: 12T98
74[1/2.F(5)^3]S(3)24000 = 26 · 3 · 53-113T2  2: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
12: 6T3
24: 4T5
48: 6T11
96: 12T62
192: 12T95
75[F(5)^3]3=F(5)wr324000 = 26 · 3 · 53-113T1  2: 2T1
3: 3T1
4: 4T1
6: 6T1
12: 4T4, 12T1
24: 6T6
48: 12T29, 12T31
96: 12T55
192: 12T94
76[3^5:2]A(5)29160 = 23 · 36 · 5-115T4 15T762: 2T1
6: 3T2
60: 5T4
120: 10T11
360: 15T23
9720: 15T61
771/2[3^5:2]S(5)29160 = 23 · 36 · 5115T5 15T77, 15T77, 15T77, 15T77, 15T772: 2T1
6: 3T2
120: 5T5
360: 15T21
9720: 15T62
78[3^5]S(5)=3wrS(5)29160 = 23 · 36 · 5-135T5 15T782: 2T1
3: 3T1
6: 6T1
120: 5T5
360: 15T24
9720: 15T63
791/2[S(3)^5]D(5)38880 = 25 · 35 · 5-115T2  2: 2T1
10: 5T2
160: 10T15
80[1/2.S(3)^5]D(5)38880 = 25 · 35 · 5115T2  2: 2T1
10: 5T2
160: 10T15
81[S(3)^5]5=S(3)wr538880 = 25 · 35 · 5-115T1  2: 2T1
5: 5T1
10: 10T1
80: 10T8
160: 10T14
82[F(5)^3]S(3)=F(5)wrS(3)48000 = 27 · 3 · 53-113T2  2: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
6: 3T2
8: 8T2
12: 6T3
24: 4T5, 12T11
48: 6T11
96: 12T53, 12T62
192: 12T95
384: 12T150
83[3^5:2]S(5)58320 = 24 · 36 · 5-115T5 15T832: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
12: 6T3
120: 5T5
240: 10T22
720: 15T29
19440: 15T70
841/2[S(3)^5]F(5)77760 = 26 · 35 · 5115T3  2: 2T1
4: 4T1
20: 5T3
320: 10T24
85[1/2.S(3)^5]F(5)77760 = 26 · 35 · 5-115T3  2: 2T1
4: 4T1
20: 5T3
320: 10T24
86[S(3)^5]D(5)=S(3)wrD(5)77760 = 26 · 35 · 5-115T2  2: 2T1, 2T1, 2T1
4: 4T2
10: 5T2
20: 10T3
160: 10T15
320: 10T23
87[S(3)^5]F(5)=S(3)wrF(5)155520 = 27 · 35 · 5-115T3  2: 2T1, 2T1, 2T1
4: 4T1, 4T1, 4T2
8: 8T2
20: 5T3
40: 10T5
320: 10T24
640: 10T29
88[1/2.S(3)^5]A(5)233280 = 26 · 36 · 5115T4  60: 5T4
960: 10T34
891/2[S(3)^5]S(5)466560 = 27 · 36 · 5115T5  2: 2T1
120: 5T5
1920: 10T37
90[S(3)^5]A(5)=S(3)wrA(5)466560 = 27 · 36 · 5-115T4  2: 2T1
60: 5T4
120: 10T11
960: 10T34
1920: 10T36
91[1/2.S(3)^5]S(5)466560 = 27 · 36 · 5-115T5  2: 2T1
120: 5T5
1920: 10T37
92[A(5)^3]3=A(5)wr3648000 = 26 · 34 · 53113T1 18T9113: 3T1
93[S(3)^5]S(5)=S(3)wrS(5)933120 = 28 · 36 · 5-115T5  2: 2T1, 2T1, 2T1
4: 4T2
120: 5T5
240: 10T22
1920: 10T37
3840: 10T39
941/2[A(5)^3:2]S(3)1296000 = 27 · 34 · 53113T2 18T9352: 2T1
6: 3T2
95[A(5)^3:2]31296000 = 27 · 34 · 53-113T1 18T9332: 2T1
3: 3T1
6: 6T1
96[A(5)^3]S(3)=A(5)wrS(3)1296000 = 27 · 34 · 53-113T2 18T9342: 2T1
6: 3T2
97[A(5)^3:2]S(3)2592000 = 28 · 34 · 53-113T2 18T9462: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
12: 6T3
98[1/2.S(5)^3]32592000 = 28 · 34 · 53113T1 18T9473: 3T1
12: 4T4
991/2[S(5)^3]S(3)5184000 = 29 · 34 · 53113T2 18T9542: 2T1
6: 3T2
24: 4T5
100[1/2.S(5)^3]S(3)5184000 = 29 · 34 · 53-113T2 18T9552: 2T1
6: 3T2
24: 4T5
101[S(5)^3]3=S(5)wr35184000 = 29 · 34 · 53-113T1 18T9532: 2T1
3: 3T1
6: 6T1
12: 4T4
24: 6T6
102[S(5)^3]S(3)=S(5)wrS(3)10368000 = 210 · 34 · 53-113T2 18T9582: 2T1, 2T1, 2T1
4: 4T2
6: 3T2
12: 6T3
24: 4T5
48: 6T11
103A15653837184000 = 210 · 36 · 53 · 72 · 11 · 1311    
104S151307674368000 = 211 · 36 · 53 · 72 · 11 · 13-11   2: 2T1