Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
580 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 226 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×#713 | C2 | semidirect |
| 2. C2×C3×Q8×D5 | C2 | semidirect |
| 3. C3×C4×C5×Q8 | C2 | semidirect |
| 4. C3×#4043 | C2 | semidirect |
| 5. C3×#4041 | C2 | semidirect |
| 6. C3×#4021 | C2 | semidirect |
| 7. C3×C4×D20 | C2 | semidirect |
| 8. #65910 | C3 | direct (N × H) |
| 24. C2×#713 | C2×C3 | semidirect |
| 25. C2×Q8×D5 | C2×C3 | semidirect |
| 26. C4×C5×Q8 | C2×C3 | semidirect |
| 27. #4043 | C2×C3 | semidirect |
| 28. #4041 | C2×C3 | semidirect |
| 29. #4021 | C2×C3 | semidirect |
| 30. C4×D20 | C2×C3 | semidirect |
| 33. C3×C5×Q8 | D4 | semidirect |
| 49. C3×C4×Q8 | D5 | semidirect |
| 72. C2×C3×D5 | #41 | semidirect |
| 94. C5×Q8 | C3×D4 | semidirect |
| 110. C4×Q8 | C3×D5 | semidirect |
| 120. C3×Q8 | D20 | semidirect |
| 136. C2×D5 | C3×#41 | semidirect |
| 156. C3×C5 | #548 | semidirect |
| 177. Q8 | C3×D20 | semidirect |
| 192. C5 | C3×#548 | semidirect |
| 205. C3 | #65910 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| C2×C3×Q8×D5 | 2 |
| C3×C4×C5×Q8 | 2 |
| C3×#4043 | 2 |
| C3×#4041 | 2 |
| C3×#4021 | 2 |
| C3×C4×D20 | 2 |
| #65910 | 3 |
| C3×#548 | 5 |