Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D32×D5 |
| commutator, Fitting, socle, cosocle | C22×C32×C5 | C23 |
| hypocenter | C32×C5 | #127 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67156 | C2 | semidirect |
| 2. C2×#67152 | C2 | semidirect |
| 3. C2×#67151 | C2 | semidirect |
| 4. C2×C5×#626 | C2 | semidirect |
| 5. C2×#67140 | C2 | semidirect |
| 6. C2×C3×#1203 | C2 | semidirect |
| 7. C3×Dic3×Dic5 | C2 | semidirect |
| 34. C2×#1203 | D3 | semidirect |
| 38. Dic3×Dic5 | D3 | semidirect |
| 52. C3×Dic15 | D4 | semidirect |
| 53. C3×C5×Dic3 | D4 | semidirect |
| 54. C32×Dic5 | D4 | semidirect |
| 61. C2×#626 | D5 | semidirect |
| 156. Dic15 | D12 | semidirect |
| 159. C3×Dic5 | D12 | semidirect |
| 160. C3×Dic5 | #67 | semidirect |
| 161. C5×Dic3 | D12 | semidirect |
| 177. C32×C5 | #127 | semidirect |
| 206. C3×Dic3 | C22⋊D5 | semidirect |
| 272. Dic5 | #626 | semidirect |
| 288. C3×C5 | #874 | semidirect |
| 289. C3×C5 | #940 | semidirect |
| 329. Dic3 | #1203 | semidirect |
| 337. C32 | #4086 | semidirect |
| 370. C5 | #63911 | semidirect |
| 388. C3 | #91451 | semidirect |
| 389. C3 | #91567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67156 | 2 |
| C2×#67152 | 2 |
| C2×#67151 | 2 |
| C2×C5×#626 | 2 |
| C2×#67140 | 2 |
| C2×C3×#1203 | 2 |
| C3×Dic3×Dic5 | 2 |
| #91567 | 3 |
| #91451 | 3 |
| #63911 | 5 |