Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 460 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×#5684 | C2 | semidirect |
| 2. C5×#5058 | C2 | semidirect |
| 3. C5×#4713 | C2 | semidirect |
| 4. C5×#4712 | C2 | semidirect |
| 5. C3×C5×#329 | C2 | semidirect |
| 6. C5×#4465 | C2 | semidirect |
| 7. C5×#4464 | C2 | semidirect |
| 28. #68351 | C5 | direct (N × H) |
| 35. C5×#329 | D3 | semidirect |
| 67. #5684 | C2×C5 | semidirect |
| 68. #5058 | C2×C5 | semidirect |
| 69. #4713 | C2×C5 | semidirect |
| 70. #4712 | C2×C5 | semidirect |
| 71. C3×#329 | C2×C5 | semidirect |
| 72. #4465 | C2×C5 | semidirect |
| 73. #4464 | C2×C5 | semidirect |
| 176. #329 | C5×D3 | semidirect |
| 350. C3×C5 | #1656 | semidirect |
| 406. C5 | #68351 | direct (N × H) |
| 424. C3 | C5×#1656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5684 | 2 |
| C5×#5058 | 2 |
| C5×#4713 | 2 |
| C5×#4712 | 2 |
| C3×C5×#329 | 2 |
| C5×#4465 | 2 |
| C5×#4464 | 2 |
| C5×#1656 | 3 |
| #68351 | 5 |