Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1600 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1600 conjugacy classes of subgroups — too many to draw. Only its 271 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×C5×H(5,𝔽2) | C2 | semidirect |
| 2. #11756563 | C2 | semidirect |
| 3. #11751345 | C2 | semidirect |
| 4. #11751344 | C2 | semidirect |
| 5. C2×#91118 | C2 | semidirect |
| 12. C22×#1220 | C22 | semidirect |
| 14. C2×#6719 | C22 | semidirect |
| 16. #91826 | C22 | semidirect |
| 17. #91824 | C22 | semidirect |
| 19. #91118 | C22 | semidirect |
| 21. C2×C5×H(5,𝔽2) | D3 | semidirect |
| 27. C24×C3×C5 | D4 | semidirect |
| 29. C23×D15 | C23 | semidirect |
| 38. C2×C3×C5×D4 | D4 | semidirect |
| 41. C22×C3×C4×C5 | D4 | semidirect |
| 46. C22×Dic15 | C23 | semidirect |
| 49. #6719 | C23 | semidirect |
| 52. C2×C3×H(5,𝔽2) | D5 | semidirect |
| 111. C24×C5 | #67 | semidirect |
| 122. C2×C5×D4 | #67 | semidirect |
| 125. C22×C4×C5 | #67 | semidirect |
| 136. C2×H(5,𝔽2) | D15 | semidirect |
| 158. C24×C3 | C22⋊D5 | semidirect |
| 169. C2×C3×D4 | C22⋊D5 | semidirect |
| 172. C22×C3×C4 | C22⋊D5 | semidirect |
| 272. C24 | #1220 | semidirect |
| 285. C2×D4 | #1220 | semidirect |
| 290. C22×C4 | #1220 | semidirect |
| 296. C3×C5 | #3026 | semidirect |
| 351. C5 | #84110 | semidirect |
| 368. C3 | #10615841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×H(5,𝔽2) | 2 |
| #11756563 | 2 |
| #11751345 | 2 |
| #11751344 | 2 |
| C2×#91118 | 2 |
| #10615841 | 3 |
| #84110 | 5 |