Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
624 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C42×C5 | C22 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #550 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6772 | C2 | semidirect |
| 2. C4×Dic30 | C2 | semidirect |
| 3. C5×#874 | C2 | semidirect |
| 4. C3×C4×D20 | C2 | semidirect |
| 5. #91463 | C2 | semidirect |
| 6. #91453 | C2 | semidirect |
| 7. #91449 | C2 | semidirect |
| 8. #91435 | C2 | semidirect |
| 34. C4×D20 | D3 | semidirect |
| 43. Dic30 | D4 | semidirect |
| 59. #874 | D5 | semidirect |
| 88. C3×C4×C5 | #41 | semidirect |
| 164. C4×C5 | #235 | semidirect |
| 186. C3×C5 | #550 | semidirect |
| 197. C3×C4 | #711 | semidirect |
| 227. C5 | #5553 | semidirect |
| 239. C4 | #6772 | 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×#6772 | 2 |
| C4×Dic30 | 2 |
| C5×#874 | 2 |
| C3×C4×D20 | 2 |
| #91463 | 2 |
| #91453 | 2 |
| #91449 | 2 |
| #91435 | 2 |
| #66052 | 3 |
| #5553 | 5 |