Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5699 | C2 | semidirect |
| 2. C3×C5×#490 | C2 | semidirect |
| 4. C5×#5071 | C2 | semidirect |
| 5. C5×#4543 | C2 | semidirect |
| 6. C5×#4465 | C2 | semidirect |
| 7. C5×#4464 | C2 | semidirect |
| 28. #71249 | C5 | direct (N × H) |
| 32. C5×#490 | D3 | semidirect |
| 65. #5699 | C2×C5 | semidirect |
| 66. C3×#490 | C2×C5 | semidirect |
| 68. #5071 | C2×C5 | semidirect |
| 69. #4543 | C2×C5 | semidirect |
| 70. #4465 | C2×C5 | semidirect |
| 71. #4464 | C2×C5 | semidirect |
| 164. #490 | C5×D3 | semidirect |
| 322. C3×C5 | #1657 | semidirect |
| 369. C5 | #71249 | direct (N × H) |
| 385. C3 | C5×#1657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5699 | 2 |
| C3×C5×#490 | 2 |
| C5×#5074 | 2 |
| C5×#5071 | 2 |
| C5×#4543 | 2 |
| C5×#4465 | 2 |
| C5×#4464 | 2 |
| C5×#1657 | 3 |
| #71249 | 5 |