Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 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. #91833 | C2 | semidirect |
| 2. C5×#947 | C2 | semidirect |
| 3. C3×#4093 | C2 | semidirect |
| 4. #91462 | C2 | semidirect |
| 5. #91453 | C2 | semidirect |
| 6. #91442 | C2 | semidirect |
| 7. #91408 | C2 | semidirect |
| 8. #91398 | C2 | semidirect |
| 9. #91393 | C2 | semidirect |
| 34. #4093 | D3 | semidirect |
| 60. #947 | D5 | semidirect |
| 207. C3×C5 | #555 | semidirect |
| 247. C5 | #5670 | semidirect |
| 262. C3 | #66004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91833 | 2 |
| C5×#947 | 2 |
| C3×#4093 | 2 |
| #91462 | 2 |
| #91453 | 2 |
| #91442 | 2 |
| #91408 | 2 |
| #91398 | 2 |
| #91393 | 2 |
| #66004 | 3 |
| #5670 | 5 |