Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×C5×ΓL(1,𝔽25) | C2 | semidirect |
| 2. C2×C3×C8×D5 | C2 | semidirect |
| 4. #91099 | C2 | semidirect |
| 5. #90983 | C2 | semidirect |
| 6. (C2×D3)⋊#168 | C2 | semidirect |
| 7. #90955 | C2 | semidirect |
| 25. C2×C8×D5 | D3 | semidirect |
| 42. C3×C5×C8 | D4 | semidirect |
| 48. C2×ΓL(1,𝔽25) | D5 | semidirect |
| 73. C2×C3×D5 | M16 | semidirect |
| 106. C5×C8 | #67 | semidirect |
| 134. C3×C8 | C22⋊D5 | semidirect |
| 143. C2×D5 | ΓL(1,𝔽25) | semidirect |
| 163. C3×C5 | #435 | semidirect |
| 197. C8 | #1201 | semidirect |
| 203. C5 | #5111 | 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×C5×ΓL(1,𝔽25) | 2 |
| C2×C3×C8×D5 | 2 |
| C4×#1201 | 2 |
| #91099 | 2 |
| #90983 | 2 |
| (C2×D3)⋊#168 | 2 |
| #90955 | 2 |
| #65416 | 3 |
| #5111 | 5 |