Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
144 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×C8×A4 | C2 | semidirect |
| 3. C5×A4⋊C8 | C2 | semidirect |
| 9. #5400 | C5 | direct (N × H) |
| 11. C22×C5×C8 | D3 | semidirect |
| 23. C8×A4 | C2×C5 | semidirect |
| 24. A4⋊C8 | C2×C5 | semidirect |
| 40. C5×A4 | M16 | semidirect |
| 61. C5×C8 | S4 | semidirect |
| 63. C22×C8 | C5×D3 | semidirect |
| 81. C22×C5 | ΓL(1,𝔽25) | semidirect |
| 102. A4 | C5×M16 | semidirect |
| 123. C8 | C5×S4 | semidirect |
| 126. C5 | #5400 | direct (N × H) |
| 132. C22 | C5×ΓL(1,𝔽25) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×S4 | 2 |
| C5×C8×A4 | 2 |
| C5×A4⋊C8 | 2 |
| C5×#435 | 3 |
| C5×ΓL(1,𝔽25) | 4 |
| #5400 | 5 |