Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1106 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 1106 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13107548 | C2 | semidirect |
| 3. #13104862 | C2 | semidirect |
| 4. C2×C8×#1043 | C2 | semidirect |
| 5. #13103946 | C2 | semidirect |
| 6. #13103872 | C2 | semidirect |
| 7. #13103871 | C2 | semidirect |
| 14. #11717358 | C22 | semidirect |
| 17. C5×#4050 | C4 | semidirect |
| 18. #11716940 | C4 | semidirect |
| 21. #11716920 | C4 | semidirect |
| 22. #11716915 | C4 | semidirect |
| 23. #11716914 | C4 | semidirect |
| 24. #11716889 | C22 | semidirect |
| 25. #11716888 | C22 | semidirect |
| 26. C8×#1043 | C22 | semidirect |
| 27. C8×#1043 | C22 | semidirect |
| 28. #11716770 | C22 | semidirect |
| 57. C5×Dic20 | C2×C4 | semidirect |
| 58. C5×D40 | C2×C4 | semidirect |
| 59. C5×#677 | C2×C4 | semidirect |
| 60. #87775 | C2×C4 | semidirect |
| 61. #87772 | C2×C4 | semidirect |
| 62. #87770 | C2×C4 | semidirect |
| 117. #4050 | AGL(1,𝔽5) | semidirect |
| 185. Dic20 | C2×AGL(1,𝔽5) | semidirect |
| 186. D40 | C2×AGL(1,𝔽5) | semidirect |
| 187. #677 | C2×AGL(1,𝔽5) | semidirect |
| 206. C5⋊D5 | #443 | semidirect |
| 276. C52 | C2×#443 | semidirect |
| 370. C5 | D5⋊#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107548 | 2 |
| #13105775 | 2 |
| #13104862 | 2 |
| C2×C8×#1043 | 2 |
| #13103946 | 2 |
| #13103872 | 2 |
| #13103871 | 2 |
| D5⋊#443 | 5 |