Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 80 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. C5×#5768 | C2 | semidirect |
| 2. #11751294 | C2 | semidirect |
| 3. #11747920 | C2 | semidirect |
| 4. #11747548 | C2 | semidirect |
| 5. C3×#64786 | C2 | semidirect |
| 6. #11745911 | C2 | semidirect |
| 7. #11745883 | C2 | semidirect |
| 11. C2×D120 | C22 | semidirect |
| 22. #91096 | C22 | semidirect |
| 23. C3×#3949 | C22 | semidirect |
| 24. C3×#3944 | C22 | semidirect |
| 34. #64786 | D3 | semidirect |
| 49. C3×C5×Q16 | D4 | semidirect |
| 51. C3×C5×D8 | D4 | semidirect |
| 60. C5×Dic12 | D4 | semidirect |
| 61. C5×D24 | D4 | semidirect |
| 69. #5768 | D5 | semidirect |
| 92. #3949 | C2×D3 | semidirect |
| 94. #3944 | C2×D3 | semidirect |
| 159. C5×Q16 | D12 | semidirect |
| 166. C5×D8 | D12 | semidirect |
| 212. C3×Q16 | C22⋊D5 | semidirect |
| 214. C3×D8 | C22⋊D5 | semidirect |
| 223. Dic12 | C22⋊D5 | semidirect |
| 226. D24 | C22⋊D5 | semidirect |
| 345. Q16 | #1203 | semidirect |
| 354. D8 | #1203 | semidirect |
| 363. C3×C5 | #2190 | semidirect |
| 420. C5 | #69252 | semidirect |
| 436. C3 | #10602905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5768 | 2 |
| #11751294 | 2 |
| #11747920 | 2 |
| #11747548 | 2 |
| C3×#64786 | 2 |
| #11745911 | 2 |
| #11745883 | 2 |
| #10602905 | 3 |
| #69252 | 5 |