Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#1010 | C2 | semidirect |
| 2. C5×#949 | C2 | semidirect |
| 3. C5×#908 | C2 | semidirect |
| 4. C5×#875 | C2 | semidirect |
| 5. C3×C5×#104 | C2 | semidirect |
| 6. C5×#824 | C2 | semidirect |
| 7. C5×#805 | C2 | semidirect |
| 26. #4827 | C5 | direct (N × H) |
| 32. C5×#104 | D3 | semidirect |
| 56. #1010 | C2×C5 | semidirect |
| 57. #949 | C2×C5 | semidirect |
| 58. #908 | C2×C5 | semidirect |
| 59. #875 | C2×C5 | semidirect |
| 60. C3×#104 | C2×C5 | semidirect |
| 61. #824 | C2×C5 | semidirect |
| 62. #805 | C2×C5 | semidirect |
| 136. #104 | C5×D3 | semidirect |
| 193. C3×C5 | #454 | semidirect |
| 237. C5 | #4827 | direct (N × H) |
| 249. C3 | C5×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1010 | 2 |
| C5×#949 | 2 |
| C5×#908 | 2 |
| C5×#875 | 2 |
| C3×C5×#104 | 2 |
| C5×#824 | 2 |
| C5×#805 | 2 |
| C5×#454 | 3 |
| #4827 | 5 |