Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D5×#625 |
| commutator, Fitting, cosocle | C32×C4×C5 | C23 |
| Frattini, hypercenter | C4 | D32×D5 |
| socle | C2×C32×C5 | C2×D4 |
| hypocenter | C32×C5 | AGL(1,ℤ/8) |
| LCS | G ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×D5×D12 | C2 | semidirect |
| 2. C3×#6772 | C2 | semidirect |
| 3. #10623825 | C2 | semidirect |
| 4. #10623802 | C2 | semidirect |
| 5. #10623798 | C2 | semidirect |
| 6. C5×#3713 | C2 | semidirect |
| 7. #10623754 | C2 | semidirect |
| 12. C3×Dic30 | C22 | semidirect |
| 14. C3×C5×D12 | C22 | semidirect |
| 19. C3⋊(C3⋊#168) | C22 | semidirect |
| 20. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 24. D5×D12 | D3 | semidirect |
| 25. #6772 | D3 | semidirect |
| 52. #3713 | D5 | semidirect |
| 58. Dic30 | C2×D3 | semidirect |
| 60. C5×D12 | C2×D3 | semidirect |
| 98. C3×D12 | C2×D5 | semidirect |
| 102. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 186. D12 | D3×D5 | semidirect |
| 216. C3×C5 | #932 | semidirect |
| 217. C3×C5 | #949 | semidirect |
| 242. C32 | #4057 | semidirect |
| 266. C5 | #63823 | semidirect |
| 276. C3 | #91478 | semidirect |
| 277. C3 | #91489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×D12 | 2 |
| C3×#6772 | 2 |
| #10623825 | 2 |
| #10623802 | 2 |
| #10623798 | 2 |
| C5×#3713 | 2 |
| #10623754 | 2 |
| #91489 | 3 |
| #91478 | 3 |
| #63823 | 5 |