Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 486 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D15 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | D3×D15 |
| hypocenter | C32×C5 | #127 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊(C3⋊D15) | C2 | semidirect |
| 2. C2×C3×D60 | C2 | semidirect |
| 3. C2×#67151 | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 19. C2×D60 | D3 | semidirect |
| 23. C4×C5×Dic3 | D3 | semidirect |
| 29. C32×C4×C5 | D4 | semidirect |
| 30. C3×C5×Dic3 | D4 | semidirect |
| 35. C3×C4×Dic3 | D5 | semidirect |
| 85. C3×C4×C5 | D12 | semidirect |
| 86. C3×C4×C5 | #67 | semidirect |
| 87. C5×Dic3 | D12 | semidirect |
| 96. C4×Dic3 | D15 | semidirect |
| 97. C32×C5 | #127 | semidirect |
| 110. C32×C4 | D20 | semidirect |
| 111. C3×Dic3 | D20 | semidirect |
| 147. C4×C5 | #626 | semidirect |
| 157. C3×C5 | #874 | semidirect |
| 158. C3×C5 | #940 | semidirect |
| 174. C3×C4 | #1202 | semidirect |
| 175. C3×C4 | D60 | semidirect |
| 176. Dic3 | D60 | semidirect |
| 181. C32 | #4020 | semidirect |
| 200. C5 | #63911 | semidirect |
| 207. C4 | #67151 | semidirect |
| 209. C3 | #91458 | semidirect |
| 210. C3 | #91763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D15) | 2 |
| C2×C3×D60 | 2 |
| C2×#67151 | 2 |
| C3×C4×C5×Dic3 | 2 |
| #91763 | 3 |
| #91458 | 3 |
| #63911 | 5 |