Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
546 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 92 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×C5×C8×A4 | C2 | semidirect |
| 3. C5×#5409 | C2 | semidirect |
| 4. C5×#5400 | C2 | semidirect |
| 5. C5×C8×S4 | C2 | semidirect |
| 16. #85437 | C5 | direct (N × H) |
| 18. C23×C5×C8 | D3 | semidirect |
| 39. C2×C8×A4 | C2×C5 | semidirect |
| 40. #5409 | C2×C5 | semidirect |
| 41. #5400 | C2×C5 | semidirect |
| 42. C8×S4 | C2×C5 | semidirect |
| 132. C2×C5×C8 | S4 | semidirect |
| 144. C23×C8 | C5×D3 | semidirect |
| 156. C5×A4 | #131 | semidirect |
| 262. C22×C5 | #901 | semidirect |
| 306. C2×C8 | C5×S4 | semidirect |
| 320. A4 | C5×#131 | semidirect |
| 368. C5 | #85437 | direct (N × H) |
| 379. C22 | C5×#901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5912 | 2 |
| C2×C5×C8×A4 | 2 |
| C5×#5409 | 2 |
| C5×#5400 | 2 |
| C5×C8×S4 | 2 |
| C5×#2929 | 3 |
| C5×#901 | 4 |
| #85437 | 5 |