Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
670 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 88 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×C5×C4⋊S4 | C2 | semidirect |
| 2. C2×C5×C8×A4 | C2 | semidirect |
| 3. C5×#5402 | C2 | direct (N × H) |
| 8. C5×C4⋊S4 | C22 | semidirect |
| 10. C5×C8×A4 | C22 | semidirect |
| 11. C2×#5402 | C5 | direct (N × H) |
| 13. C23×C5×C8 | D3 | semidirect |
| 27. C2×C4⋊S4 | C2×C5 | semidirect |
| 28. C2×C8×A4 | C2×C5 | semidirect |
| 29. #5402 | C2×C5 | direct (N × H) |
| 40. C22×C5×C8 | C2×D3 | semidirect |
| 51. C2×C5×A4 | D8 | semidirect |
| 61. C4⋊S4 | C22×C5 | semidirect |
| 63. C8×A4 | C22×C5 | semidirect |
| 90. C2×C5×C8 | S4 | semidirect |
| 96. C23×C8 | C5×D3 | semidirect |
| 105. C5×A4 | C2×D8 | semidirect |
| 124. C23×C5 | D24 | semidirect |
| 145. C5×C8 | C2×S4 | semidirect |
| 156. C22×C8 | C2×C5×D3 | semidirect |
| 169. C2×A4 | C5×D8 | semidirect |
| 188. C22×C5 | C2×D24 | semidirect |
| 221. C2×C8 | C5×S4 | semidirect |
| 230. A4 | C2×C5×D8 | semidirect |
| 237. C2×C5 | #5402 | direct (N × H) |
| 247. C23 | C5×D24 | semidirect |
| 268. C8 | C2×C5×S4 | semidirect |
| 272. C5 | C2×#5402 | direct (N × H) |
| 285. C22 | C2×C5×D24 | semidirect |
| 297. C2 | C5×#5402 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊S4 | 2 |
| C2×C5×C8×A4 | 2 |
| C5×#5402 | 2 |
| C2×C5×#466 | 3 |
| C2×C5×D24 | 4 |
| C2×#5402 | 5 |