All subgroups of index up to 43929600 (order at least 2769091920) are shown, as well as all normal subgroups of any index.
| Order 121645100408832000: $S_{19}$ |
| Order 60822550204416000: $A_{19}$ |
| Order 6402373705728000: $S_{18}$ |
| Order 3201186852864000: $A_{18}$ |
| Order 711374856192000: $C_2\times S_{17}$ |
| Order 355687428096000: $S_{17}$ x 2, $C_2\times A_{17}$ |
| Order 177843714048000: $A_{17}$ |
| Order 125536739328000: $S_3\times S_{16}$ |
| Order 62768369664000: $C_3.A_{16}.C_2$ x 2, $S_3.A_{16}$ |
| Order 41845579776000: $C_2.S_{16}$ |
| Order 31384184832000: $S_4\times S_{15}$, $C_3.A_{16}$ |
| Order 20922789888000: $S_{16}$ x 2, $C_2.A_{16}$ |
| Order 15692092416000: $A_4.A_{15}.C_2$ x 2, $S_4.A_{15}$ |
| Order 10461394944000: $S_5\times S_{14}$, $D_4.A_{15}.C_2$, $A_{16}$ |
| Order 7846046208000: $A_4.A_{15}$, $S_3\times S_{15}$ |
| Order 5230697472000: $C_2^2.A_{15}.C_2$ x 3, $C_4.A_{15}.C_2$ x 2, $A_{14}.S_5$ x 2, $D_4.A_{15}$, $C_2^2\times S_{15}$, $A_{14}.A_5.C_2$ |
| Order 4483454976000: $S_6\times S_{13}$ |
| Order 3923023104000: $C_3.S_{15}$, $C_3.S_{15}$, $S_3\times A_{15}$ |
| Order 2615348736000: $C_2\times S_{15}$ x 5, $C_2^2.A_{15}$ x 2, $C_4.A_{15}$, $C_2.A_{15}.C_2$, $A_{14}.A_5$ |
| Order 2414168064000: $S_7\times S_{12}$ |
| Order 2241727488000: $A_{13}.A_6.C_2$ x 3 |
| Order 2092278988800: $S_4.A_{14}.C_2$ |
| Order 1961511552000: $C_3.A_{15}$ |
| Order 1743565824000: $F_5.A_{14}.C_2$ |
| Order 1609445376000: $S_8\times S_{11}$ |
| Order 1316818944000: $S_9\times S_{10}$ |
| Order 1307674368000: $S_{15}$ x 3, $C_2.A_{15}$ x 2 |
| Order 1207084032000: $A_{12}.A_7.C_2$ x 3 |
| Order 1120863744000: $A_{13}.A_6$ |
| Order 1046139494400: $A_4.A_{14}.C_2$ x 2, $S_4.A_{14}$, $D_6.A_{14}.C_2$ |
| Order 871782912000: $S_{14}\times D_5$, $F_5\times A_{14}$, $D_5.A_{14}.C_2$ |
| Order 804722688000: $A_{11}.A_8.C_2$ x 3 |
| Order 747242496000: $S_{13}\times S_5$, $A_5.A_{13}.C_2^2$ |
| Order 697426329600: $D_4.A_{14}.C_2$ |
| Order 658409472000: $A_{10}.A_9.C_2$ x 3 |
| Order 653837184000: $A_{15}$ |
| Order 603542016000: $A_{12}.A_7$ |
| Order 523069747200: $S_3\times S_{14}$ x 4, $C_6.A_{14}.C_2$ x 2, $D_6.A_{14}$, $A_4.A_{14}$ |
| Order 448345497600: $S_{13}\times S_3\wr C_2$ |
| Order 435891456000: $C_5.A_{14}.C_2$ x 2, $D_5.A_{14}$ |
| Order 402361344000: $A_{11}.A_8$ |
| Order 373621248000: $A_5.A_{13}.C_2$ x 3, $A_{13}.S_5$ x 2, $A_{13}.A_5.C_2$ |
| Order 348713164800: $C_2^2.A_{14}.C_2$ x 3, $C_4.A_{14}.C_2$ x 2, $D_4.A_{14}$, $C_2^2\times S_{14}$ |
| Order 344881152000: $A_6.A_{12}.C_2^2$ |
| Order 329204736000: $A_{10}.A_9$ |
| Order 298896998400: $(C_2\times S_4).A_{13}.C_2$ x 2 |
| Order 263363788800: $S_9\wr C_2$ |
| Order 261534873600: $C_3.S_{14}$ x 2, $C_3.S_{14}$ x 2, $S_3.A_{14}$ x 2, $C_6.A_{14}$ |
| Order 224172748800: $S_3^2.A_{13}.C_2$ x 4, $C_3:S_3.C_2.A_{13}.C_2$ x 2, $A_{13}\times S_3\wr C_2$ |
| Order 217945728000: $C_5.A_{14}$ |
| Order 201180672000: $A_7.A_{11}.C_2^2$ |
| Order 186810624000: $A_{13}.A_5$, $A_5.A_{13}$ |
| Order 174356582400: $C_2.S_{14}$ x 5, $C_2^2.A_{14}$ x 2, $C_4.A_{14}$, $C_2.A_{14}.C_2$ |
| Order 172440576000: $A_6.A_{12}.C_2$ x 3 |
| Order 149448499200: $S_4.A_{13}.C_2$ x 8, $(C_2\times A_4).A_{13}.C_2$ x 4, $C_2\times S_4.A_{13}$, $A_{13}\times C_2\times S_4$ |
| Order 146313216000: $A_8.A_{10}.C_2^2$ |
| Order 131681894400: $A_9.A_9.C_2^2$, $A_9^2.C_2^2$, $A_9^2.C_4$ |
| Order 130767436800: $C_3.A_{14}$ |
| Order 124540416000: $F_5.A_{13}.C_2$ |
| Order 114960384000: $C_2.A_{12}.A_5.C_2^2$ |
| Order 112086374400: $C_3:S_3.A_{13}.C_2$ x 4, $(C_3\times S_3).A_{13}.C_2$ x 4, $S_3^2.A_{13}$ x 2, $C_3:S_3.C_2.A_{13}$ |
| Order 100590336000: $A_7.A_{11}.C_2$ x 3 |
| Order 99632332800: $(C_2\times D_4).A_{13}.C_2$ |
| Order 87178291200: $S_{14}$ x 3, $C_2.A_{14}$ x 2 |
| Order 86220288000: $A_6.A_{12}$ |
| Order 80472268800: $S_{12}\times \PSL(2,7)$ |
| Order 74724249600: $A_4.A_{13}.C_2$ x 8, $S_4.A_{13}$ x 4, $(C_2\times A_4).A_{13}$ x 2, $D_6.A_{13}.C_2$, $C_2\times S_3.A_{13}.C_2$ |
| Order 73156608000: $A_8.A_{10}.C_2$ x 3 |
| Order 68976230400: $S_3.A_{12}.C_2\times S_4$ |
| Order 65840947200: $A_9.A_9.C_2$ x 2, $A_9\wr C_2$ |
| Order 62270208000: $D_5.A_{13}.C_2$ x 2, $A_{13}\times F_5$ |
| Order 57480192000: $A_{12}.S_5.C_2$ x 4, $C_2.A_{12}.S_5$ x 2, $C_2\times S_{11}\times S_6$, $C_2.A_{12}.A_5.C_2$, $A_5.A_{12}.C_2^2$ |
| Order 56043187200: $C_3^2.A_{13}.C_2$ x 4, $(C_3\times S_3).A_{13}$ x 2, $C_3:S_3.A_{13}$ |
| Order 53648179200: $S_{11}\times C_2^3.\PSL(2,7)$ |
| Order 50295168000: $A_7.A_{11}$ |
| Order 49816166400: $D_4.A_{13}.C_2$ x 8, $C_2^3.A_{13}.C_2$ x 3, $(C_2\times C_4).A_{13}.C_2$ x 2, $C_2^3\times S_{13}$, $(C_2\times D_4).A_{13}$ |
| Order 45984153600: $A_4^2.D_4.A_{11}.C_2$ |
| Order 43589145600: $A_{14}$ |
| Order 40236134400: $A_{12}\times \PSL(2,7)$ |
| Order 37362124800: $S_3\times S_{13}$ x 8, $C_6.A_{13}.C_2$ x 3, $D_6.A_{13}$ x 2, $A_4.A_{13}$ x 2, $C_2\times C_3.A_{13}.C_2$ |
| Order 36578304000: $C_2.A_{10}.A_7.C_2^2$, $A_8.A_{10}$ |
| Order 34488115200: $C_3:S_4.A_{12}.C_2$ x 2, $(S_3\times A_4).A_{12}.C_2$ x 2, $(C_3\times S_4).A_{12}.C_2$ x 2, $S_3\wr C_2.A_{12}.C_2$, $(S_3\times S_4).A_{12}$ |
| Order 32920473600: $A_9.A_9$ |
| Order 31135104000: $C_5.A_{13}.C_2$ x 2, $D_5.A_{13}$ |
| Order 29262643200: $C_2\times S_9\times S_8$ |
| Order 28740096000: $S_{11}\times S_6$ x 3, $C_2.A_{11}.A_6.C_2$ x 3, $A_{12}.S_5$ x 3, $A_5.A_{12}.C_2$ x 3, $S_{12}\times A_5$, $C_2.A_{12}.A_5$, $A_{12}\times S_5$, $A_{12}.A_5.C_2$, $A_{11}.A_6.C_2^2$, $(S_3\times A_5).A_{11}.C_2^2$ |
| Order 28021593600: $C_3^2.A_{13}$ |
| Order 26824089600: $A_{11}\times C_2^3.\PSL(2,7)$ |
| Order 24908083200: $C_2^2.A_{13}.C_2$ x 18, $C_4.A_{13}.C_2$ x 8, $D_4.A_{13}$ x 4, $C_2^3.A_{13}$ x 2, $C_2^2\times S_{13}$ x 2, $(C_2\times C_4).A_{13}$ |
| Order 22992076800: $A_4^2.C_2^2.A_{11}.C_2$ x 4, $A_4^2.C_4.A_{11}.C_2$ x 2, $(C_2\times S_4).A_{12}.C_2$ x 2, $A_{11}\times A_4^2.D_4$, $(S_3\times D_4).A_{12}.C_2$ |
| Order 20118067200: $F_7.A_{12}.C_2$ |
| Order 19508428800: $S_3.A_8^2.D_4$ |
| Order 19160064000: $(C_2\times F_5).A_{12}.C_2$ |
| Order 18681062400: $C_3.S_{13}$ x 4, $C_3.S_{13}$ x 4, $A_{13}\times S_3$ x 4, $C_6.A_{13}$ x 2 |
| Order 18289152000: $S_{10}\times S_7$ x 3, $C_2.A_{10}.A_7.C_2$ x 3, $A_{10}.A_7.C_2^2$ |
| Order 17244057600: $S_3^2.A_{12}.C_2$ x 4, $(C_3\times A_4).A_{12}.C_2$ x 4, $C_3:S_3.C_2.A_{12}.C_2$ x 2, $S_3\wr C_2\times A_{12}$, $C_3:S_4.A_{12}$, $(S_3\times A_4).A_{12}$, $(C_3\times S_4).A_{12}$ |
| Order 15676416000: $S_3.A_6.A_{10}.C_2^2$ |
| Order 15567552000: $C_5.A_{13}$ |
| Order 15328051200: $S_{11}\times C_2\wr A_4.C_2$ |
| Order 14631321600: $A_9.A_8.C_2^2$ x 4, $C_2.A_9.A_8.C_2$ x 3 |
| Order 14370048000: $A_{11}.A_6.C_2$ x 4, $(C_3\times A_5).A_{11}.C_2^2$ x 4, $(S_3\times A_5).A_{11}.C_2$ x 3, $S_{11}\times A_6$, $C_2.A_{11}.A_6$, $A_{12}.A_5$, $A_{11}\times S_6$, $A_5.A_{12}$ |
| Order 13412044800: $A_{11}.\SO(3,7).C_2$ |
| Order 12454041600: $C_2\times S_{13}$ x 12, $C_2^2.A_{13}$ x 5, $C_4.A_{13}$ x 2, $C_2.A_{13}.C_2$ x 2 |
| Order 11496038400: $S_4.A_{12}.C_2$ x 9, $\PSOPlusPlus(4,3).A_{11}.C_2$ x 4, $C_3:D_4.A_{12}.C_2$ x 4, $(C_2^2\times S_3).A_{12}.C_2$ x 4, $(C_2\times A_4).A_{12}.C_2$ x 4, $D_{12}.A_{12}.C_2$ x 2, $A_4^2.C_2^2.A_{11}$ x 2, $A_4\wr C_2.A_{11}.C_2$ x 2, $(C_4\times S_3).A_{12}.C_2$ x 2, $(C_3\times D_4).A_{12}.C_2$ x 2, $(A_4\times S_4).A_{11}.C_2$ x 2, $C_2\times S_4\times A_{12}$, $A_4^2.C_4.A_{11}$, $(S_3\times D_4).A_{12}$, $(C_2\times S_4).A_{12}$ |
| Order 10973491200: $S_3.A_9.C_2\times S_7$ |
| Order 10450944000: $S_9\times A_5^2.D_4$, $S_4.A_{10}.A_5.C_2^2$ |
| Order 10059033600: $C_7:C_3.A_{12}.C_2$ x 2, $F_7\times A_{12}$ |
| Order 9754214400: $C_3.A_8^2.D_4$ x 4, $S_3.A_8^2.C_4$, $S_3.A_8^2.C_2^2$, $S_3.A_8.C_2\times S_8$ |
| Order 9580032000: $F_5.A_{12}.C_2$ x 4, $D_{10}.A_{12}.C_2$ x 2, $C_2\times F_5\times A_{12}$, $C_2.A_{11}.A_5.C_2^2$, $(C_2\times A_5).A_{11}.C_2^2$ |
| Order 9340531200: $C_3\times A_{13}$ x 2 |
| Order 9144576000: $A_{10}.A_7.C_2$ x 4, $S_{10}\times A_7$, $C_2.A_{10}.A_7$, $A_{10}\times S_7$ |
| Order 8622028800: $C_3:S_3.A_{12}.C_2$ x 4, $(C_3\times S_3).A_{12}.C_2$ x 4, $S_3^2.A_{12}$ x 2, $C_3:S_3.C_2.A_{12}$, $(C_3\times A_4).A_{12}$ |
| Order 7838208000: $C_3.A_6.A_{10}.C_2^2$ x 4, $S_3.A_6.A_{10}.C_2$ x 3 |
| Order 7664025600: $C_2^3:S_4.A_{11}.C_2$ x 2, $C_2^3:A_4:C_2.A_{11}.C_2$ x 2, $C_2\wr A_4.A_{11}.C_2$ x 2, $C_2^2:S_4:C_2.A_{11}.C_2$, $C_2\wr A_4.C_2.A_{11}$, $(D_4\times S_4).A_{11}.C_2$, $(C_2\times D_4).A_{12}.C_2$ |
| Order 7315660800: $A_9.A_8.C_2$ x 4, $S_9\times A_8$, $C_2.A_9.A_8$, $A_9\times S_8$ |
| Order 7185024000: $(C_3\times A_5).A_{11}.C_2$ x 6, $A_{11}\times A_6$, $(S_3\times A_5).A_{11}$ |
| Order 6706022400: $A_{11}.\SO(3,7)$ x 2, $\PSL(2,7).A_{11}.C_2$, $F_8:C_3.A_{11}.C_2$, $D_7.A_{12}.C_2$, $A_{11}.\PSL(2,7).C_2$ |
| Order 6502809600: $C_2.A_8^2.D_4$ |
| Order 6270566400: $S_4.A_9.A_6.C_2^2$ |
| Order 6227020800: $S_{13}$ x 4, $C_2\times A_{13}$ x 3 |
| Order 6096384000: $A_5.A_7^2.D_4.C_2$ |
| Order 5748019200: $D_6.A_{12}.C_2$ x 16, $A_4.A_{12}.C_2$ x 10, $(C_2\times C_6).A_{12}.C_2$ x 8, $S_4.A_{12}$ x 5, $C_{12}.A_{12}.C_2$ x 4, $C_3:C_4.A_{12}.C_2$ x 4, $A_4^2.A_{11}.C_2$ x 4, $C_3:D_4.A_{12}$ x 2, $(C_2^2\times S_3).A_{12}$ x 2, $(C_2\times A_4).A_{12}$ x 2, $\PSOPlusPlus(4,3).A_{11}$, $D_{12}.A_{12}$, $C_2\times S_{12}\times S_3$, $A_4\wr C_2.A_{11}$, $(S_3\times S_4).A_{11}.C_2$, $(C_4\times S_3).A_{12}$, $(C_3\times D_4).A_{12}$, $(C_2\times S_3\wr C_2).A_{11}.C_2$, $(A_4\times S_4).A_{11}$ |
| Order 5486745600: $S_3.A_7.A_9.C_2$ x 3, $C_3.A_7.A_9.C_2^2$ x 3, $S_{10}\times \SL(2,8).C_3$, $C_3.A_9.C_2\times S_7$ |
| Order 5225472000: $A_9.A_5^2.D_4$ x 4, $A_4.A_{10}.S_5.C_2$ x 3, $S_4.A_{10}.S_5$ x 2, $S_4.A_{10}.A_5.C_2$, $C_2.A_6.A_{10}.C_2^2$, $A_9.A_5^2.C_4.C_2$, $A_9.A_5^2.C_2^3$, $A_7.A_6^2.D_4.C_2$, $A_5.A_5.A_9.C_2^3$, $A_4.A_{10}.A_5.C_2^2$ |
| Order 5109350400: $D_4^2.C_2.A_{11}.C_2$ |
| Order 5029516800: $C_7:C_3.A_{12}$ |
| Order 4877107200: $C_3.A_8^2.C_2^2$ x 3, $C_3.A_8.A_8.C_2^2$ x 3, $S_3.A_8.A_8.C_2$ x 2, $C_3.A_8^2.C_4$ x 2, $S_4.A_8.A_7.C_2^2$, $S_3.A_8^2.C_2$, $C_2^3.A_{10}.\PSL(2,7).C_2$ |
| Order 4790016000: $D_5.A_{12}.C_2$ x 6, $A_5.A_{11}.C_2^2$ x 4, $A_{11}.S_5.C_2$ x 3, $(C_2\times A_5).A_{11}.C_2$ x 3, $C_{10}.A_{12}.C_2$ x 2, $C_2.A_{11}.S_5$ x 2, $F_5.A_{12}$, $D_{10}.A_{12}$, $C_2.A_{11}.A_5.C_2$, $A_{12}\times F_5$, $A_{11}.A_5.C_2^2$, $(S_3\times F_5).A_{11}.C_2$ |
| Order 4702924800: $S_{10}\times C_3^3:C_2^2.D_6$ |
| Order 4572288000: $A_7\times A_{10}$ |
| Order 4311014400: $C_3^2.A_{12}.C_2$ x 4, $(C_3\times S_3).A_{12}$ x 2, $C_3:S_3.A_{12}$ |
| Order 4180377600: $A_4^2.D_4.A_{10}.C_2$ |
| Order 3919104000: $C_3.A_6.A_{10}.C_2$ x 6, $S_3.A_6.A_{10}$ |
| Order 3832012800: $D_4.A_{12}.C_2$ x 8, $(C_2^2\times S_4).A_{11}.C_2$ x 5, $\GL(2,\mathbb{Z}/4).A_{11}.C_2$ x 4, $C_2^3:A_4.A_{11}.C_2$ x 4, $C_2^3.A_{12}.C_2$ x 4, $C_2^2:S_4.A_{11}.C_2$ x 4, $C_4:S_4.A_{11}.C_2$ x 2, $C_2^2\wr C_2:C_3.A_{11}.C_2$ x 2, $(D_4\times A_4).A_{11}.C_2$ x 2, $(C_4\times S_4).A_{11}.C_2$ x 2, $(C_2\times C_4).A_{12}.C_2$ x 2, $C_2^3:S_4.A_{11}$, $C_2^3:A_4:C_2.A_{11}$, $C_2^2:S_4:C_2.A_{11}$, $C_2\wr A_4.A_{11}$, $(D_4\times S_4).A_{11}$, $(C_2\times D_4).A_{12}$ |
| Order 3657830400: $C_2\times S_7\times S_9$, $A_8\times A_9$ |
| Order 3592512000: $(C_3\times A_5).A_{11}$ |
| Order 3483648000: $D_4.A_{10}.S_5.C_2$, $A_6.A_8.A_5.C_2^3$ |
| Order 3353011200: $A_{11}\times \PSL(2,7)$ x 2, $D_7.A_{12}$, $C_7\times S_{12}$, $C_7.A_{12}.C_2$, $A_{11}\times F_8:C_3$ |
| Order 3251404800: $S_8\wr C_2$ x 4, $C_2.A_8^2.C_4$, $C_2.A_8^2.C_2^2$, $C_2.A_8.A_8.C_2^2$ |
| Order 3135283200: $A_4.A_9.A_6.C_2^2$ x 4, $S_4.A_9.A_6.C_2$ x 3 |
| Order 3113510400: $A_{13}$ |
| Order 3048192000: $A_5.A_7^2.D_4$ x 4, $A_5.A_7^2.C_4.C_2$, $A_5.A_7^2.C_2^3$, $A_5.A_7.C_2^2\times S_7$ |
| Order 2874009600: $S_3\times S_{12}$ x 15, $C_6.A_{12}.C_2$ x 14, $S_3\wr C_2.A_{11}.C_2$ x 8, $D_6.A_{12}$ x 6, $(C_2\times S_3^2).A_{11}.C_2$ x 4, $A_4.A_{12}$ x 3, $C_3:S_4.A_{11}.C_2$ x 2, $(S_3\times A_4).A_{11}.C_2$ x 2, $(C_3\times S_4).A_{11}.C_2$ x 2, $(C_2\times C_6).A_{12}$ x 2, $(C_2\times C_3:S_3.C_2).A_{11}.C_2$ x 2, $C_{12}.A_{12}$, $C_3:C_4.A_{12}$, $C_2\times S_3\wr C_2\times A_{11}$, $A_4^2.A_{11}$, $(S_3\times S_4).A_{11}$ |
| Order 65536: $C_2\times C_2^5.C_2^5.C_2^4.C_2$ |
| Order 6561: $C_3^4.C_3^4$ |
| Order 342: $F_{19}$ |
| Order 125: $C_5^3$ |
| Order 49: $C_7^2$ |
| Order 19: $C_{19}$ |
| Order 17: $C_{17}$ |
| Order 13: $C_{13}$ |
| Order 11: $C_{11}$ |
| Order 1: $C_1$ |
