Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
410 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 91 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×C3×C4×D15 | C2 | semidirect |
| 3. C2×#67155 | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 5. C3×#6712 | C2 | semidirect |
| 6. #10623829 | C2 | semidirect |
| 7. #10623828 | C2 | semidirect |
| 18. #67156 | C4 | semidirect |
| 21. C2×C4×D15 | D3 | semidirect |
| 27. #6712 | D3 | semidirect |
| 39. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 42. C2×C3×D15 | C2×C4 | semidirect |
| 46. C3×Dic15 | C2×C4 | semidirect |
| 47. C3×Dic15 | D4 | semidirect |
| 52. #3752 | D5 | semidirect |
| 108. C2×D15 | C4×D3 | semidirect |
| 125. Dic15 | C4×D3 | semidirect |
| 126. Dic15 | #67 | semidirect |
| 148. C32×C5 | C4×D4 | semidirect |
| 162. C2×C3⋊D3 | C4×D5 | semidirect |
| 234. C3×C5 | #893 | semidirect |
| 235. C3×C5 | C4×#67 | semidirect |
| 271. C32 | #4027 | semidirect |
| 296. C5 | #63904 | semidirect |
| 310. C3 | #91406 | semidirect |
| 311. C3 | #91440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C2×#67156 | 2 |
| C2×#67155 | 2 |
| C5×#3752 | 2 |
| C3×#6712 | 2 |
| #10623829 | 2 |
| #10623828 | 2 |
| #91440 | 3 |
| #91406 | 3 |
| #63904 | 5 |