Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
430 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×A4 |
| commutator, socle, cosocle | C23×C5 | C23×C3 |
| Fitting | C22×C5×Q8 | C2×C3 |
| hypercenter | Q8 | D5×A4 |
| hypocenter | C22×C5 | C3×#41 |
| LCS | G ▷ C23×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×Q8×A4 | C2 | semidirect |
| 2. A4×D20 | C2 | semidirect |
| 3. C4×D5×A4 | C2 | semidirect |
| 4. C22×#713 | C3 | semidirect |
| 10. C22×C5×Q8 | C2×C3 | semidirect |
| 15. C22×D20 | C2×C3 | semidirect |
| 16. C22×C4×D5 | C2×C3 | semidirect |
| 22. Q8×A4 | D5 | semidirect |
| 36. #713 | A4 | direct (N × H) |
| 46. C5×A4 | #41 | semidirect |
| 60. C5×Q8 | C2×A4 | semidirect |
| 68. D20 | C2×A4 | semidirect |
| 73. C4×D5 | C2×A4 | semidirect |
| 78. C22×Q8 | C3×D5 | semidirect |
| 90. C22×C5 | C3×#41 | semidirect |
| 122. A4 | #713 | direct (N × H) |
| 137. Q8 | D5×A4 | semidirect |
| 153. C5 | A4×#41 | semidirect |
| 162. C22 | C3×#713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×A4 | 2 |
| A4×D20 | 2 |
| C4×D5×A4 | 2 |
| C22×#713 | 3 |
| C3×#713 | 4 |
| A4×#41 | 5 |