Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 532 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×D8 | C2 | semidirect |
| 2. C2×C5×#826 | C2 | semidirect |
| 3. C5×#5115 | C2 | semidirect |
| 4. C5×#4562 | C2 | semidirect |
| 5. C5×#4549 | C2 | semidirect |
| 13. C2×C5×D24 | C22 | semidirect |
| 16. C5×#818 | C22 | semidirect |
| 17. C2×C5×C3⋊C16 | C22 | semidirect |
| 18. #72035 | C5 | direct (N × H) |
| 19. C22×C5×D8 | D3 | semidirect |
| 34. C3×C5×D8 | D4 | semidirect |
| 42. C22×C3×D8 | C2×C5 | semidirect |
| 43. C2×#826 | C2×C5 | semidirect |
| 44. #5115 | C2×C5 | semidirect |
| 45. #4562 | C2×C5 | semidirect |
| 46. #4549 | C2×C5 | semidirect |
| 84. C2×D24 | C22×C5 | semidirect |
| 87. #818 | C22×C5 | semidirect |
| 88. C2×C3⋊C16 | C22×C5 | semidirect |
| 100. C5×D8 | #67 | semidirect |
| 107. C22×D8 | C5×D3 | semidirect |
| 118. C22×C3×C5 | D16 | semidirect |
| 137. C3×D8 | C5×D4 | semidirect |
| 209. C22×C5 | #826 | semidirect |
| 226. D8 | C5×#67 | semidirect |
| 233. C3×C5 | #2184 | semidirect |
| 240. C22×C3 | C5×D16 | semidirect |
| 280. C5 | #72035 | direct (N × H) |
| 290. C22 | C5×#826 | semidirect |
| 296. C3 | C5×#2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×D8 | 2 |
| C2×C5×#826 | 2 |
| C5×#5115 | 2 |
| C5×#4562 | 2 |
| C5×#4549 | 2 |
| C5×#2184 | 3 |
| #72035 | 5 |