Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
366 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#87870 | C2 | semidirect |
| 2. C5×#4041 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 4. C2×#87770 | C2 | semidirect |
| 5. #11716677 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 32. #6045 | D4 | semidirect |
| 38. C5×D20 | D4 | semidirect |
| 52. #4041 | D5 | semidirect |
| 59. #3941 | D5 | semidirect |
| 146. D20 | D20 | semidirect |
| 168. C52 | #449 | semidirect |
| 255. C5 | #65070 | semidirect |
| 256. C5 | #65326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| C5×#4041 | 2 |
| C2×#87773 | 2 |
| C2×#87770 | 2 |
| #11716677 | 2 |
| C5×#3941 | 2 |
| #11716597 | 2 |
| #65326 | 5 |
| #65070 | 5 |