Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 114 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. C3×C4×C5×Q16 | C2 | semidirect |
| 2. C2×C5×#828 | C2 | semidirect |
| 4. C5×#4491 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊C16) | C2 | semidirect |
| 17. #70914 | C5 | direct (N × H) |
| 20. C4×C5×Q16 | D3 | semidirect |
| 28. C3×C5×Q16 | D4 | semidirect |
| 39. C3×C4×Q16 | C2×C5 | semidirect |
| 40. C2×#828 | C2×C5 | semidirect |
| 42. #4491 | C2×C5 | semidirect |
| 43. C4⋊(C3⋊C16) | C2×C5 | semidirect |
| 85. C5×Q16 | D12 | semidirect |
| 98. C4×Q16 | C5×D3 | semidirect |
| 108. C3×C4×C5 | SD32 | semidirect |
| 116. C3×Q16 | C5×D4 | semidirect |
| 178. C4×C5 | #828 | semidirect |
| 186. Q16 | C5×D12 | semidirect |
| 197. C3×C5 | #2207 | semidirect |
| 205. C3×C4 | C5×SD32 | semidirect |
| 231. C5 | #70914 | direct (N × H) |
| 239. C4 | C5×#828 | semidirect |
| 242. C3 | C5×#2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q16 | 2 |
| C2×C5×#828 | 2 |
| C5×#4695 | 2 |
| C5×#4491 | 2 |
| C5×C4⋊(C3⋊C16) | 2 |
| C5×#2207 | 3 |
| #70914 | 5 |