Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 152 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 | #532 |
| 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. C2×C5×#239 | C2 | semidirect |
| 2. C2×#6769 | C2 | semidirect |
| 3. #91836 | C2 | semidirect |
| 4. C3×#4090 | C2 | semidirect |
| 5. #91451 | C2 | semidirect |
| 6. #91446 | C2 | semidirect |
| 7. #91416 | C2 | semidirect |
| 8. C4×D3×Dic5 | C2 | semidirect |
| 9. #91370 | C2 | semidirect |
| 34. #4090 | D3 | semidirect |
| 52. C4×C5×D3 | D4 | semidirect |
| 61. C2×#239 | D5 | semidirect |
| 100. C3×Dic5 | #41 | semidirect |
| 174. C4×D3 | C22⋊D5 | semidirect |
| 187. Dic5 | #239 | semidirect |
| 207. C3×C5 | #532 | semidirect |
| 251. C5 | #5725 | 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×C5×#239 | 2 |
| C2×#6769 | 2 |
| #91836 | 2 |
| C3×#4090 | 2 |
| #91451 | 2 |
| #91446 | 2 |
| #91416 | 2 |
| C4×D3×Dic5 | 2 |
| #91370 | 2 |
| #66166 | 3 |
| #5725 | 5 |