Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 74 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. #11717268 | C2 | semidirect |
| 3. #11716933 | C2 | semidirect |
| 4. C5×#3969 | C2 | semidirect |
| 5. #11716618 | C2 | semidirect |
| 6. #11716610 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 14. C5×#689 | C4 | semidirect |
| 15. C5×#688 | C4 | semidirect |
| 16. C5×#687 | C4 | semidirect |
| 17. C5×#686 | C4 | semidirect |
| 50. #3969 | D5 | semidirect |
| 76. #689 | Dic5 | semidirect |
| 77. #688 | Dic5 | semidirect |
| 78. #687 | Dic5 | semidirect |
| 79. #686 | Dic5 | semidirect |
| 151. C52 | #444 | semidirect |
| 216. C5 | #65112 | semidirect |
| 217. C5 | #65486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717268 | 2 |
| C5×#4096 | 2 |
| #11716933 | 2 |
| C5×#3969 | 2 |
| #11716618 | 2 |
| #11716610 | 2 |
| #11716595 | 2 |
| #65486 | 5 |
| #65112 | 5 |