Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 432 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×#5735 | C2 | semidirect |
| 2. C5×#5095 | C2 | semidirect |
| 4. C5×#4752 | C2 | semidirect |
| 5. C3×C5×#356 | C2 | semidirect |
| 6. C5×#4478 | C2 | semidirect |
| 7. C5×#4477 | C2 | semidirect |
| 28. #69167 | C5 | direct (N × H) |
| 34. C5×#356 | D3 | semidirect |
| 71. #5735 | C2×C5 | semidirect |
| 72. #5095 | C2×C5 | semidirect |
| 74. #4752 | C2×C5 | semidirect |
| 75. C3×#356 | C2×C5 | semidirect |
| 76. #4478 | C2×C5 | semidirect |
| 77. #4477 | C2×C5 | semidirect |
| 184. #356 | C5×D3 | semidirect |
| 359. C3×C5 | #2203 | semidirect |
| 408. C5 | #69167 | direct (N × H) |
| 422. C3 | C5×#2203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5735 | 2 |
| C5×#5095 | 2 |
| C5×#4753 | 2 |
| C5×#4752 | 2 |
| C3×C5×#356 | 2 |
| C5×#4478 | 2 |
| C5×#4477 | 2 |
| C5×#2203 | 3 |
| #69167 | 5 |