Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 122 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. C22×C3×C5×Q16 | C2 | semidirect |
| 2. C2×C5×#828 | C2 | semidirect |
| 4. C5×#4564 | C2 | semidirect |
| 5. C5×#4549 | C2 | semidirect |
| 18. #72063 | C5 | direct (N × H) |
| 19. C22×C5×Q16 | D3 | semidirect |
| 34. C3×C5×Q16 | D4 | semidirect |
| 42. C22×C3×Q16 | C2×C5 | semidirect |
| 43. C2×#828 | C2×C5 | semidirect |
| 45. #4564 | C2×C5 | semidirect |
| 46. #4549 | C2×C5 | semidirect |
| 97. C5×Q16 | #67 | semidirect |
| 105. C22×Q16 | C5×D3 | semidirect |
| 112. C22×C3×C5 | SD32 | semidirect |
| 132. C3×Q16 | C5×D4 | semidirect |
| 195. C22×C5 | #828 | semidirect |
| 212. Q16 | C5×#67 | semidirect |
| 220. C3×C5 | #2185 | semidirect |
| 223. C22×C3 | C5×SD32 | semidirect |
| 260. C5 | #72063 | direct (N × H) |
| 266. C22 | C5×#828 | semidirect |
| 273. C3 | C5×#2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q16 | 2 |
| C2×C5×#828 | 2 |
| C5×#5115 | 2 |
| C5×#4564 | 2 |
| C5×#4549 | 2 |
| C5×#2185 | 3 |
| #72063 | 5 |