Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
410 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 410 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×C3×D60 | C2 | semidirect |
| 2. C2×#67156 | C2 | semidirect |
| 3. C2×#67156 | C2 | semidirect |
| 4. C2×#67154 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 6. C3×#6712 | C2 | semidirect |
| 7. #10623829 | C2 | semidirect |
| 22. C2×D60 | D3 | semidirect |
| 30. #6712 | D3 | semidirect |
| 46. C2×C3×D15 | D4 | semidirect |
| 50. C3×Dic15 | D4 | semidirect |
| 56. #3752 | D5 | semidirect |
| 118. C2×D15 | #67 | semidirect |
| 138. Dic15 | D12 | semidirect |
| 159. C32×C5 | #121 | semidirect |
| 255. C3×C5 | #895 | semidirect |
| 256. C3×C5 | #939 | semidirect |
| 297. C32 | #4030 | semidirect |
| 325. C5 | #63886 | semidirect |
| 341. C3 | #91408 | semidirect |
| 342. C3 | #91420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×#67156 | 2 |
| C2×#67154 | 2 |
| C5×#3752 | 2 |
| C3×#6712 | 2 |
| #10623829 | 2 |
| #91420 | 3 |
| #91408 | 3 |
| #63886 | 5 |