Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
472 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 472 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×#5670 | C2 | semidirect |
| 2. C5×#5062 | C2 | semidirect |
| 3. C5×#4753 | C2 | semidirect |
| 4. C5×#4752 | C2 | semidirect |
| 5. C3×C5×#355 | C2 | semidirect |
| 6. C5×#4478 | C2 | semidirect |
| 7. C5×#4477 | C2 | semidirect |
| 28. #69161 | C5 | direct (N × H) |
| 35. C5×#355 | D3 | semidirect |
| 71. #5670 | C2×C5 | semidirect |
| 72. #5062 | C2×C5 | semidirect |
| 73. #4753 | C2×C5 | semidirect |
| 74. #4752 | C2×C5 | semidirect |
| 75. C3×#355 | C2×C5 | semidirect |
| 76. #4478 | C2×C5 | semidirect |
| 77. #4477 | C2×C5 | semidirect |
| 188. #355 | C5×D3 | semidirect |
| 375. C3×C5 | #2204 | semidirect |
| 432. C5 | #69161 | direct (N × H) |
| 449. C3 | C5×#2204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5670 | 2 |
| C5×#5062 | 2 |
| C5×#4753 | 2 |
| C5×#4752 | 2 |
| C3×C5×#355 | 2 |
| C5×#4478 | 2 |
| C5×#4477 | 2 |
| C5×#2204 | 3 |
| #69161 | 5 |