Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 64 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. #91460 | C2 | semidirect |
| 3. #91456 | C2 | semidirect |
| 4. C2×#6653 | C2 | semidirect |
| 5. #91105 | C2 | semidirect |
| 6. C3×#3953 | C2 | semidirect |
| 7. #90987 | C2 | semidirect |
| 28. #3953 | D3 | semidirect |
| 46. C5×C3⋊C8 | D4 | semidirect |
| 49. C2×ΓL(1,𝔽25) | D5 | semidirect |
| 142. C3⋊C8 | C22⋊D5 | semidirect |
| 171. C3×C5 | #469 | semidirect |
| 216. C5 | #4782 | semidirect |
| 232. C3 | #65424 | 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 |
| #91460 | 2 |
| #91456 | 2 |
| C2×#6653 | 2 |
| #91105 | 2 |
| C3×#3953 | 2 |
| #90987 | 2 |
| #65424 | 3 |
| #4782 | 5 |