Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
438 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D45 |
| commutator, cosocle | C2×C5×C9 | C24 |
| Frattini | C2×C3 | C23×D15 |
| Fitting | C2×C5×Q8×C9 | C2 |
| socle | C2×C3×C5 | C23×D3 |
| hypercenter | C2×Q8 | D45 |
| hypocenter | C5×C9 | 2−1+4 |
| LCS | G ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×Q8×C9 | C2 | semidirect |
| 2. #10623713 | C2 | semidirect |
| 3. Q8×D45 | C2 | semidirect |
| 4. #10623709 | C2 | semidirect |
| 22. C2×Q8×C9 | D5 | semidirect |
| 36. C2×C5×Q8 | D9 | semidirect |
| 54. C5×C9 | 2−1+4 | semidirect |
| 85. C2×Q8 | D45 | semidirect |
| 94. C9 | #4147 | semidirect |
| 104. C5 | #63713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×C9 | 2 |
| #10623713 | 2 |
| Q8×D45 | 2 |
| #10623709 | 2 |
| #92098 | 3 |
| #63713 | 5 |