Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 79 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×(C3⋊D3)⋊D5 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C4×C5 | C22 |
| hypercenter | C2×C4 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | #121 |
| 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×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×#67156 | C2 | semidirect |
| 3. C2×#67156 | C2 | semidirect |
| 4. C2×#67155 | C2 | semidirect |
| 5. C3×#6714 | C2 | semidirect |
| 6. C3×#6712 | C2 | semidirect |
| 7. #10623830 | C2 | semidirect |
| 31. #6714 | D3 | semidirect |
| 32. #6712 | D3 | semidirect |
| 43. C2×C5×C3⋊D3 | D4 | semidirect |
| 50. C3×Dic15 | D4 | semidirect |
| 52. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 143. Dic15 | D12 | semidirect |
| 162. C32×C5 | #121 | semidirect |
| 180. C2×C3⋊D3 | C22⋊D5 | semidirect |
| 260. C3×C5 | #884 | semidirect |
| 261. C3×C5 | #895 | semidirect |
| 304. C32 | #4085 | semidirect |
| 333. C5 | #63910 | semidirect |
| 349. C3 | #91416 | semidirect |
| 350. C3 | #91453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×#67156 | 2 |
| C2×#67155 | 2 |
| C3×#6714 | 2 |
| C3×#6712 | 2 |
| #10623830 | 2 |
| #91453 | 3 |
| #91416 | 3 |
| #63910 | 5 |