Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 106 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. C4×D120 | C2 | semidirect |
| 2. C4×C5×D24 | C2 | semidirect |
| 4. C3×C4×#672 | C2 | semidirect |
| 5. #11745939 | C2 | semidirect |
| 6. #11745896 | C2 | semidirect |
| 7. #11745894 | C2 | semidirect |
| 20. #90939 | C4 | direct (N × H) |
| 28. C4×#672 | D3 | semidirect |
| 39. D120 | C2×C4 | semidirect |
| 43. C5×D24 | C2×C4 | semidirect |
| 45. C3×#672 | C2×C4 | semidirect |
| 48. C4×D24 | D5 | semidirect |
| 110. #672 | C4×D3 | semidirect |
| 126. C3×C4×C5 | D16 | semidirect |
| 145. D24 | C4×D5 | semidirect |
| 206. C4×C5 | D48 | semidirect |
| 227. C3×C5 | C4×D16 | semidirect |
| 236. C3×C4 | #3958 | semidirect |
| 267. C5 | C4×D48 | semidirect |
| 278. C4 | #90939 | direct (N × H) |
| 281. C3 | C4×#3958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D120 | 2 |
| C4×C5×D24 | 2 |
| C2×#90939 | 2 |
| C3×C4×#672 | 2 |
| #11745939 | 2 |
| #11745896 | 2 |
| #11745894 | 2 |
| C4×#3958 | 3 |
| C4×D48 | 5 |