Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
364 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 2. #11717271 | C2 | semidirect |
| 3. #11716979 | C2 | semidirect |
| 4. #11716949 | C2 | semidirect |
| 5. C5×#3969 | C2 | semidirect |
| 6. #11716610 | C2 | semidirect |
| 7. #11716599 | C2 | semidirect |
| 9. C2×#6045 | C22 | semidirect |
| 19. #87804 | C22 | semidirect |
| 20. C4×C5×Dic5 | C22 | semidirect |
| 21. C5×#681 | C22 | semidirect |
| 60. #3969 | D5 | semidirect |
| 108. C4×Dic5 | C2×D5 | semidirect |
| 112. #681 | C2×D5 | semidirect |
| 181. C52 | #455 | semidirect |
| 265. C5 | #65114 | semidirect |
| 266. C5 | #65531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4149 | 2 |
| #11717271 | 2 |
| #11716979 | 2 |
| #11716949 | 2 |
| C5×#3969 | 2 |
| #11716610 | 2 |
| #11716599 | 2 |
| #65531 | 5 |
| #65114 | 5 |