Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
624 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 155 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 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C5×#127 | C2 |
| hypercenter | #127 | D15 |
| hypocenter | C3×C5 | #550 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6819 | C2 | semidirect |
| 2. C3×C5×#127 | C2 | semidirect |
| 3. #91829 | C2 | semidirect |
| 4. #91828 | C2 | semidirect |
| 5. #91827 | C2 | semidirect |
| 6. D4×Dic15 | C2 | semidirect |
| 7. C4×D60 | C2 | semidirect |
| 8. C4×Dic30 | C2 | semidirect |
| 29. C5×#127 | D3 | semidirect |
| 52. Dic30 | D4 | semidirect |
| 54. C3×#127 | D5 | semidirect |
| 88. C3×C4×C5 | #41 | semidirect |
| 128. #127 | D15 | semidirect |
| 165. C4×C5 | #237 | semidirect |
| 186. C3×C5 | #550 | semidirect |
| 196. C3×C4 | #711 | semidirect |
| 227. C5 | #5718 | semidirect |
| 240. C4 | #6819 | semidirect |
| 241. C3 | #66052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6819 | 2 |
| C3×C5×#127 | 2 |
| #91829 | 2 |
| #91828 | 2 |
| #91827 | 2 |
| D4×Dic15 | 2 |
| C4×D60 | 2 |
| C4×Dic30 | 2 |
| #66052 | 3 |
| #5718 | 5 |