Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Frattini | C22 | C22×D3×D5 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #532 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6817 | C2 | semidirect |
| 2. C2×C5×#235 | C2 | semidirect |
| 3. C2×C3×C4×Dic5 | C2 | semidirect |
| 4. #91566 | C2 | semidirect |
| 5. #91451 | C2 | semidirect |
| 6. C4×#1203 | C2 | semidirect |
| 7. #91376 | C2 | semidirect |
| 8. #91375 | C2 | semidirect |
| 9. #91373 | C2 | semidirect |
| 39. C2×C4×Dic5 | D3 | semidirect |
| 43. C2×C3×C4×C5 | D4 | semidirect |
| 61. C2×#235 | D5 | semidirect |
| 100. C3×Dic5 | #41 | semidirect |
| 129. C2×C4×C5 | D12 | semidirect |
| 161. C2×C3×C4 | C22⋊D5 | semidirect |
| 187. Dic5 | #235 | semidirect |
| 207. C3×C5 | #532 | semidirect |
| 243. C2×C4 | #1203 | semidirect |
| 251. C5 | #5477 | semidirect |
| 265. C3 | #66166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C2×C5×#235 | 2 |
| C2×C3×C4×Dic5 | 2 |
| #91566 | 2 |
| #91451 | 2 |
| C4×#1203 | 2 |
| #91376 | 2 |
| #91375 | 2 |
| #91373 | 2 |
| #66166 | 3 |
| #5477 | 5 |