Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
544 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. C2×C16×D15 | C2 | semidirect |
| 3. D15×#107 | C2 | semidirect |
| 4. C3×C5×#357 | C2 | semidirect |
| 5. #11746383 | C2 | semidirect |
| 6. #11746330 | C2 | semidirect |
| 7. #11746312 | C2 | semidirect |
| 13. D8×D15 | C4 | semidirect |
| 17. C2×C3×C5×C16 | C22 | semidirect |
| 18. C3×C5×#107 | C22 | semidirect |
| 19. #91102 | C22 | semidirect |
| 20. C2×C3⋊#672 | C22 | semidirect |
| 27. C5×#357 | D3 | semidirect |
| 40. C3×C5×D8 | C2×C4 | semidirect |
| 48. D120 | C2×C4 | semidirect |
| 56. C3×#357 | D5 | semidirect |
| 68. C2×C5×C16 | C2×D3 | semidirect |
| 69. C5×#107 | C2×D3 | semidirect |
| 104. C2×C3×C16 | C2×D5 | semidirect |
| 105. C3×#107 | C2×D5 | semidirect |
| 119. C5×D8 | C4×D3 | semidirect |
| 138. #357 | D15 | direct (N × H) |
| 164. C3×D8 | C4×D5 | semidirect |
| 208. C2×C16 | C2×D15 | semidirect |
| 211. #107 | C2×D15 | semidirect |
| 217. D15 | #357 | direct (N × H) |
| 267. D8 | C4×D15 | semidirect |
| 277. C3×C5 | C2×#357 | semidirect |
| 327. C5 | D3×#357 | semidirect |
| 344. C3 | D5×#357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D15 | 2 |
| C2×C16×D15 | 2 |
| D15×#107 | 2 |
| C3×C5×#357 | 2 |
| #11746383 | 2 |
| #11746330 | 2 |
| #11746312 | 2 |
| D5×#357 | 3 |
| D3×#357 | 5 |