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×C4×C5×D4 | C2 |
| hypercenter | C4×D4 | D15 |
| hypocenter | C3×C5 | #550 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6817 | C2 | semidirect |
| 2. C3×C4×C5×D4 | C2 | semidirect |
| 3. #91829 | C2 | semidirect |
| 4. #91819 | C2 | semidirect |
| 5. #91782 | C2 | semidirect |
| 6. #91773 | C2 | semidirect |
| 7. #91763 | C2 | semidirect |
| 8. C4×Dic30 | C2 | semidirect |
| 29. C4×C5×D4 | D3 | semidirect |
| 52. Dic30 | D4 | semidirect |
| 54. C3×C4×D4 | D5 | semidirect |
| 89. C3×C4×C5 | #41 | semidirect |
| 133. C4×D4 | D15 | semidirect |
| 165. C4×C5 | #235 | semidirect |
| 186. C3×C5 | #550 | semidirect |
| 196. C3×C4 | #709 | semidirect |
| 227. C5 | #5553 | semidirect |
| 239. C4 | #6817 | semidirect |
| 241. C3 | #65887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C3×C4×C5×D4 | 2 |
| #91829 | 2 |
| #91819 | 2 |
| #91782 | 2 |
| #91773 | 2 |
| #91763 | 2 |
| C4×Dic30 | 2 |
| #65887 | 3 |
| #5553 | 5 |