Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
492 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 492 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×#5664 | C2 | semidirect |
| 2. C5×#5053 | C2 | semidirect |
| 4. C5×#4742 | C2 | semidirect |
| 5. C3×C5×#352 | C2 | semidirect |
| 6. C5×#4476 | C2 | semidirect |
| 7. C5×#4474 | C2 | semidirect |
| 28. #69140 | C5 | direct (N × H) |
| 35. C5×#352 | D3 | semidirect |
| 71. #5664 | C2×C5 | semidirect |
| 72. #5053 | C2×C5 | semidirect |
| 74. #4742 | C2×C5 | semidirect |
| 75. C3×#352 | C2×C5 | semidirect |
| 76. #4476 | C2×C5 | semidirect |
| 77. #4474 | C2×C5 | semidirect |
| 188. #352 | C5×D3 | semidirect |
| 384. C3×C5 | #2198 | semidirect |
| 447. C5 | #69140 | direct (N × H) |
| 468. C3 | C5×#2198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5664 | 2 |
| C5×#5053 | 2 |
| C5×#4747 | 2 |
| C5×#4742 | 2 |
| C3×C5×#352 | 2 |
| C5×#4476 | 2 |
| C5×#4474 | 2 |
| C5×#2198 | 3 |
| #69140 | 5 |