Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
588 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 160 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 | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #537 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#235 | C2 | semidirect |
| 2. C2×C3×#709 | C2 | semidirect |
| 3. C2×C4⋊Dic15 | C2 | semidirect |
| 4. #91571 | C2 | semidirect |
| 5. #91456 | C2 | semidirect |
| 6. #91449 | C2 | semidirect |
| 7. #91369 | C2 | semidirect |
| 8. #91359 | C2 | semidirect |
| 30. C2×#709 | D3 | semidirect |
| 40. C2×C3×C4×C5 | D4 | semidirect |
| 57. C2×#235 | D5 | semidirect |
| 124. C2×C4×C5 | #67 | semidirect |
| 157. C2×C3×C4 | C22⋊D5 | semidirect |
| 201. C3×C5 | #537 | semidirect |
| 239. C2×C4 | #1201 | semidirect |
| 248. C5 | #5833 | semidirect |
| 264. C3 | #66167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#235 | 2 |
| C2×C3×#709 | 2 |
| C2×C4⋊Dic15 | 2 |
| #91571 | 2 |
| #91456 | 2 |
| #91449 | 2 |
| #91369 | 2 |
| #91359 | 2 |
| #66167 | 3 |
| #5833 | 5 |