Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 128 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 | C2×C3×C5×Q8 | C22 |
| hypercenter | C2×Q8 | D3×D5 |
| hypocenter | C3×C5 | #555 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #91836 | C2 | semidirect |
| 2. C5×#947 | C2 | semidirect |
| 3. C3×#4090 | C2 | semidirect |
| 4. #91420 | C2 | semidirect |
| 5. #91416 | C2 | semidirect |
| 6. #91405 | C2 | semidirect |
| 7. #91403 | C2 | semidirect |
| 8. #91400 | C2 | semidirect |
| 9. #91326 | C2 | semidirect |
| 35. #4090 | D3 | semidirect |
| 62. #947 | D5 | semidirect |
| 207. C3×C5 | #555 | semidirect |
| 247. C5 | #5734 | semidirect |
| 262. C3 | #66004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91836 | 2 |
| C5×#947 | 2 |
| C3×#4090 | 2 |
| #91420 | 2 |
| #91416 | 2 |
| #91405 | 2 |
| #91403 | 2 |
| #91400 | 2 |
| #91326 | 2 |
| #66004 | 3 |
| #5734 | 5 |