Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
620 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 620 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 | C3×C42×C5 | C22 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #532 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6769 | C2 | semidirect |
| 2. #91763 | C2 | semidirect |
| 3. C42×C5×D3 | C2 | semidirect |
| 4. C3×#4015 | C2 | semidirect |
| 5. #91460 | C2 | semidirect |
| 6. #91428 | C2 | semidirect |
| 7. #91374 | C2 | semidirect |
| 29. #4015 | D3 | semidirect |
| 39. C4×C5×D3 | D4 | semidirect |
| 50. C42×D3 | D5 | semidirect |
| 71. C3×C4×C5 | #41 | semidirect |
| 126. C4×D3 | D20 | semidirect |
| 135. C4×C5 | #239 | semidirect |
| 150. C3×C5 | #532 | semidirect |
| 158. C3×C4 | #709 | semidirect |
| 183. C5 | #5725 | semidirect |
| 192. C4 | #6769 | semidirect |
| 194. C3 | #65811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6769 | 2 |
| #91763 | 2 |
| C42×C5×D3 | 2 |
| C3×#4015 | 2 |
| #91460 | 2 |
| #91428 | 2 |
| #91374 | 2 |
| #65811 | 3 |
| #5725 | 5 |