Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 144 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×D4 | C22 |
| hypercenter | C2×D4 | D3×D5 |
| hypocenter | C3×C5 | #532 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6819 | C2 | semidirect |
| 2. C2×#6766 | C2 | semidirect |
| 3. C5×#936 | C2 | semidirect |
| 4. C3×#4086 | C2 | semidirect |
| 5. #91559 | C2 | semidirect |
| 6. #91533 | C2 | semidirect |
| 7. C4×#1200 | C2 | semidirect |
| 8. #91376 | C2 | semidirect |
| 9. #91364 | C2 | semidirect |
| 35. #4086 | D3 | semidirect |
| 49. C4×D15 | D4 | semidirect |
| 65. #936 | D5 | semidirect |
| 99. C3×Dic5 | #41 | semidirect |
| 187. Dic5 | #237 | semidirect |
| 207. C3×C5 | #532 | semidirect |
| 251. C5 | #5716 | semidirect |
| 265. C3 | #66002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6819 | 2 |
| C2×#6766 | 2 |
| C5×#936 | 2 |
| C3×#4086 | 2 |
| #91559 | 2 |
| #91533 | 2 |
| C4×#1200 | 2 |
| #91376 | 2 |
| #91364 | 2 |
| #66002 | 3 |
| #5716 | 5 |