Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
380 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×#4130 | C2 | semidirect |
| 3. C3×D5⋊M16 | C2 | semidirect |
| 4. C3×#4007 | C2 | semidirect |
| 5. #65767 | C3 | direct (N × H) |
| 7. C2×C3×C5×D4 | C4 | semidirect |
| 11. C3×D4×D5 | C4 | semidirect |
| 13. C2×C3×D20 | C4 | semidirect |
| 17. C3×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 20. C3×D5⋊C8 | C22 | semidirect |
| 23. #4130 | C2×C3 | semidirect |
| 24. D5⋊M16 | C2×C3 | semidirect |
| 25. #4007 | C2×C3 | semidirect |
| 51. C2×C5×D4 | C3×C4 | semidirect |
| 55. D4×D5 | C3×C4 | semidirect |
| 57. C2×D20 | C3×C4 | semidirect |
| 61. C4⋊AGL(1,𝔽5) | C22×C3 | semidirect |
| 64. D5⋊C8 | C22×C3 | semidirect |
| 88. C2×C3×D4 | AGL(1,𝔽5) | semidirect |
| 168. C2×D4 | C3×AGL(1,𝔽5) | semidirect |
| 176. C3×C5 | #418 | semidirect |
| 224. C5 | C3×#418 | semidirect |
| 240. C3 | #65767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D5 | 2 |
| C3×#4130 | 2 |
| C3×D5⋊M16 | 2 |
| C3×#4007 | 2 |
| #65767 | 3 |
| C3×#418 | 5 |