Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D15 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C23×C32×C5 | C22 |
| hypercenter | C23 | D3×D15 |
| hypocenter | C32×C5 | #121 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#67184 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×#67152 | C2 | semidirect |
| 4. C2×#67149 | C2 | semidirect |
| 5. C3×#6719 | C2 | semidirect |
| 6. Dic3⋊Dic15 | C2 | semidirect |
| 7. (C2×D3)⋊Dic15 | C2 | semidirect |
| 28. C2×C5×#67 | D3 | semidirect |
| 32. #6719 | D3 | semidirect |
| 43. C2×C3⋊D15 | D4 | semidirect |
| 50. C3×C5×Dic3 | D4 | semidirect |
| 53. C2×C3×#67 | D5 | semidirect |
| 146. C5×Dic3 | #67 | semidirect |
| 152. C2×#67 | D15 | semidirect |
| 162. C32×C5 | #121 | semidirect |
| 187. C3×Dic3 | C22⋊D5 | semidirect |
| 260. C3×C5 | #884 | semidirect |
| 261. C3×C5 | #938 | semidirect |
| 297. Dic3 | #1220 | semidirect |
| 304. C32 | #4084 | semidirect |
| 333. C5 | #63958 | semidirect |
| 349. C3 | #91557 | semidirect |
| 350. C3 | #91827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67184 | 2 |
| C2×C3×C5×#67 | 2 |
| C2×#67152 | 2 |
| C2×#67149 | 2 |
| C3×#6719 | 2 |
| Dic3⋊Dic15 | 2 |
| (C2×D3)⋊Dic15 | 2 |
| #91827 | 3 |
| #91557 | 3 |
| #63958 | 5 |