Finite Group DatabasebetaFinite Group DatabasebetaOrder 46080.
174 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D11520 |
| commutator, cosocle | C5×C9×C256 | C22 |
| Frattini | C3×C256 | C2×D15 |
| Fitting | C5×C9×C512 | C2 |
| socle | C2×C3×C5 | D768 |
| hypercenter | C512 | D45 |
| hypocenter | C5×C9 | D512 |
| LCS | G ▷ C5×C9×C256 ▷ C5×C9×C128 ▷ C5×C9×C64 ▷ C5×C9×C32 ▷ C5×C9×C16 ▷ C5×C8×C9 ▷ C4×C5×C9 ▷ C2×C5×C9 ▷ C5×C9 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ C64 ◁ C128 ◁ C256 ◁ C512 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D11520 | C2 | semidirect |
| 16. C5×C9×C512 | C2 | semidirect |
| 20. C9×C512 | D5 | semidirect |
| 23. C5×C512 | D9 | semidirect |
| 45. C512 | D45 | semidirect |
| 86. C5×C9 | D512 | semidirect |
| 108. C9 | D2560 | semidirect |
| 113. C5 | D4608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D11520 | 2 |
| D7680 | 3 |
| D4608 | 5 |
| C5×C9×C512 | 2 |