Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 91 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. C22×C3×C5×C8 | C2 | semidirect |
| 3. C2×#6705 | C2 | semidirect |
| 4. #91114 | C2 | semidirect |
| 5. #91104 | C2 | semidirect |
| 6. #91099 | C2 | semidirect |
| 7. #91098 | C2 | semidirect |
| 23. C22×C5×C8 | D3 | semidirect |
| 43. C3×C5×C8 | D4 | semidirect |
| 46. C22×C3×C8 | D5 | semidirect |
| 69. C22×C3×C5 | M16 | semidirect |
| 106. C5×C8 | #67 | semidirect |
| 110. C22×C8 | D15 | semidirect |
| 134. C3×C8 | C22⋊D5 | semidirect |
| 139. C22×C5 | ΓL(1,𝔽25) | semidirect |
| 163. C3×C5 | #435 | semidirect |
| 166. C22×C3 | #676 | semidirect |
| 197. C8 | #1220 | semidirect |
| 203. C5 | #5111 | semidirect |
| 209. C22 | #6705 | semidirect |
| 217. C3 | #65400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×C8 | 2 |
| C4×#1220 | 2 |
| C2×#6705 | 2 |
| #91114 | 2 |
| #91104 | 2 |
| #91099 | 2 |
| #91098 | 2 |
| #65400 | 3 |
| #5111 | 5 |