Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 2. C5×#951 | C2 | semidirect |
| 3. C5×#909 | C2 | semidirect |
| 4. C5×#875 | C2 | semidirect |
| 5. C3×C5×#104 | C2 | semidirect |
| 6. C5×#823 | C2 | semidirect |
| 7. C5×#805 | C2 | semidirect |
| 17. C2×C5×Dic6 | C22 | semidirect |
| 18. C3×C5×M16 | C22 | semidirect |
| 19. C3×C42×C5 | C22 | semidirect |
| 23. C5×#208 | C22 | semidirect |
| 26. #4825 | C5 | direct (N × H) |
| 32. C5×#104 | D3 | semidirect |
| 57. #951 | C2×C5 | semidirect |
| 58. #909 | C2×C5 | semidirect |
| 59. #875 | C2×C5 | semidirect |
| 60. C3×#104 | C2×C5 | semidirect |
| 61. #823 | C2×C5 | semidirect |
| 62. #805 | C2×C5 | semidirect |
| 77. C5×M16 | C2×D3 | semidirect |
| 79. C42×C5 | C2×D3 | semidirect |
| 101. C2×Dic6 | C22×C5 | semidirect |
| 102. C3×M16 | C22×C5 | semidirect |
| 103. C3×C42 | C22×C5 | semidirect |
| 107. #208 | C22×C5 | semidirect |
| 137. #104 | C5×D3 | semidirect |
| 192. M16 | C2×C5×D3 | semidirect |
| 194. C42 | C2×C5×D3 | semidirect |
| 195. C3×C5 | #455 | semidirect |
| 240. C5 | #4825 | direct (N × H) |
| 253. C3 | C5×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1009 | 2 |
| C5×#951 | 2 |
| C5×#909 | 2 |
| C5×#875 | 2 |
| C3×C5×#104 | 2 |
| C5×#823 | 2 |
| C5×#805 | 2 |
| C5×#455 | 3 |
| #4825 | 5 |