Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 68 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×#5919 | C2 | semidirect |
| 2. C5×A4×Q16 | C2 | semidirect |
| 3. C5×#5417 | C2 | semidirect |
| 4. C5×#5402 | C2 | semidirect |
| 5. C5×C8×S4 | C2 | semidirect |
| 15. #85465 | C5 | direct (N × H) |
| 17. C22×C5×Q16 | D3 | semidirect |
| 37. #5919 | C2×C5 | semidirect |
| 38. A4×Q16 | C2×C5 | semidirect |
| 39. #5417 | C2×C5 | semidirect |
| 40. #5402 | C2×C5 | semidirect |
| 41. C8×S4 | C2×C5 | semidirect |
| 108. C5×Q16 | S4 | semidirect |
| 133. C22×Q16 | C5×D3 | semidirect |
| 145. C5×A4 | #135 | semidirect |
| 241. C22×C5 | #919 | semidirect |
| 267. Q16 | C5×S4 | semidirect |
| 294. A4 | C5×#135 | semidirect |
| 337. C5 | #85465 | direct (N × H) |
| 346. C22 | C5×#919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5919 | 2 |
| C5×A4×Q16 | 2 |
| C5×#5417 | 2 |
| C5×#5402 | 2 |
| C5×C8×S4 | 2 |
| C5×#3285 | 3 |
| C5×#919 | 4 |
| #85465 | 5 |