Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C2×C8×D15 | C2 | semidirect |
| 2. C2×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 4. C3×#3947 | C2 | semidirect |
| 5. #90982 | C2 | semidirect |
| 6. #90957 | C2 | semidirect |
| 7. (C2×D3)⋊#168 | C2 | semidirect |
| 28. #3947 | D3 | semidirect |
| 42. C3×C5×C8 | D4 | semidirect |
| 46. C2×ΓL(1,𝔽25) | D5 | semidirect |
| 70. C2×D15 | M16 | semidirect |
| 106. C5×C8 | D12 | semidirect |
| 134. C3×C8 | C22⋊D5 | semidirect |
| 163. C3×C5 | #435 | semidirect |
| 197. C8 | #1203 | semidirect |
| 203. C5 | #4706 | semidirect |
| 217. C3 | #65416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D15 | 2 |
| C2×C5×ΓL(1,𝔽25) | 2 |
| C4×#1203 | 2 |
| C3×#3947 | 2 |
| #90982 | 2 |
| #90957 | 2 |
| (C2×D3)⋊#168 | 2 |
| #65416 | 3 |
| #4706 | 5 |