Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×D5×D24 | C2 | semidirect |
| 2. C3×#65172 | C2 | semidirect |
| 3. C2×#90938 | C2 | semidirect |
| 4. C2×#90937 | C2 | semidirect |
| 5. #11746312 | C2 | semidirect |
| 6. C5×#4491 | C2 | semidirect |
| 7. #11745879 | C2 | semidirect |
| 12. C2×C3×D40 | C22 | semidirect |
| 18. C3×C5×#107 | C22 | semidirect |
| 19. C2×C3⋊#672 | C22 | semidirect |
| 20. C2×C5×C3⋊C16 | C22 | semidirect |
| 28. #65172 | D3 | semidirect |
| 44. D120 | D4 | semidirect |
| 46. C5×D24 | D4 | semidirect |
| 62. #4491 | D5 | semidirect |
| 69. C2×D40 | C2×D3 | semidirect |
| 73. C5×#107 | C2×D3 | semidirect |
| 111. C3×#107 | C2×D5 | semidirect |
| 116. C2×C3⋊C16 | C2×D5 | semidirect |
| 160. C2×C3×D5 | D16 | semidirect |
| 187. D24 | D20 | semidirect |
| 226. #107 | D3×D5 | semidirect |
| 271. C2×D5 | #826 | semidirect |
| 300. C3×C5 | #2184 | semidirect |
| 356. C5 | #71075 | semidirect |
| 375. C3 | #10599984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D24 | 2 |
| C3×#65172 | 2 |
| C2×#90938 | 2 |
| C2×#90937 | 2 |
| #11746312 | 2 |
| C5×#4491 | 2 |
| #11745879 | 2 |
| #10599984 | 3 |
| #71075 | 5 |