Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
520 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 82 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. C5×#5666 | C2 | semidirect |
| 2. C5×#5053 | C2 | semidirect |
| 3. C5×#4747 | C2 | semidirect |
| 4. C5×#4741 | C2 | semidirect |
| 5. C3×C5×#352 | C2 | semidirect |
| 6. C5×#4475 | C2 | semidirect |
| 7. C5×#4474 | C2 | semidirect |
| 28. #69139 | C5 | direct (N × H) |
| 34. C5×#352 | D3 | semidirect |
| 38. C22×C3×C4×C5 | D4 | semidirect |
| 50. C2×C5×D12 | D4 | semidirect |
| 56. C3×C5×C22⋊C4 | D4 | semidirect |
| 68. C4×C5×Dic3 | D4 | semidirect |
| 71. #5666 | C2×C5 | semidirect |
| 72. #5053 | C2×C5 | semidirect |
| 73. #4747 | C2×C5 | semidirect |
| 74. #4741 | C2×C5 | semidirect |
| 75. C3×#352 | C2×C5 | semidirect |
| 76. #4475 | C2×C5 | semidirect |
| 77. #4474 | C2×C5 | semidirect |
| 166. C22×C4×C5 | D12 | semidirect |
| 184. C5×C22⋊C4 | D12 | semidirect |
| 191. #352 | C5×D3 | semidirect |
| 219. C22×C3×C4 | C5×D4 | semidirect |
| 231. C2×D12 | C5×D4 | semidirect |
| 237. C3×C22⋊C4 | C5×D4 | semidirect |
| 249. C4×Dic3 | C5×D4 | semidirect |
| 385. C22×C4 | C5×D12 | semidirect |
| 403. C22⋊C4 | C5×D12 | semidirect |
| 405. C3×C5 | #2200 | semidirect |
| 478. C5 | #69139 | direct (N × H) |
| 503. C3 | C5×#2200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5666 | 2 |
| C5×#5053 | 2 |
| C5×#4747 | 2 |
| C5×#4741 | 2 |
| C3×C5×#352 | 2 |
| C5×#4475 | 2 |
| C5×#4474 | 2 |
| C5×#2200 | 3 |
| #69139 | 5 |