Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
288 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 94 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×C3×D40 | C2 | semidirect |
| 2. C2×C3×#677 | C2 | semidirect |
| 3. C3×#4021 | C2 | semidirect |
| 4. C3×#4020 | C2 | semidirect |
| 5. C3×C5×#97 | C2 | semidirect |
| 6. #65001 | C3 | direct (N × H) |
| 17. C2×D40 | C2×C3 | semidirect |
| 18. C2×#677 | C2×C3 | semidirect |
| 19. #4021 | C2×C3 | semidirect |
| 20. #4020 | C2×C3 | semidirect |
| 21. C5×#97 | C2×C3 | semidirect |
| 32. C3×C5×C8 | D4 | semidirect |
| 37. C3×#97 | D5 | semidirect |
| 75. C5×C8 | C3×D4 | semidirect |
| 80. #97 | C3×D5 | semidirect |
| 95. C3×C8 | D20 | semidirect |
| 113. C3×C5 | #496 | semidirect |
| 136. C8 | C3×D20 | semidirect |
| 141. C5 | C3×#496 | semidirect |
| 150. C3 | #65001 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D40 | 2 |
| C2×C3×#677 | 2 |
| C3×#4021 | 2 |
| C3×#4020 | 2 |
| C3×C5×#97 | 2 |
| #65001 | 3 |
| C3×#496 | 5 |