Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 76 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. C5×#4094 | C2 | semidirect |
| 3. #11716932 | C2 | semidirect |
| 4. #11716704 | C2 | semidirect |
| 5. #11716618 | C2 | semidirect |
| 6. #11716609 | C2 | semidirect |
| 7. #11716594 | C2 | semidirect |
| 12. C5×#689 | C4 | semidirect |
| 13. C5×#688 | C4 | semidirect |
| 14. C5×#687 | C4 | semidirect |
| 15. C5×#686 | C4 | semidirect |
| 45. #4094 | D5 | semidirect |
| 78. #689 | Dic5 | semidirect |
| 79. #688 | Dic5 | semidirect |
| 80. #687 | Dic5 | semidirect |
| 81. #686 | Dic5 | semidirect |
| 148. C52 | #443 | semidirect |
| 214. C5 | #65433 | semidirect |
| 215. C5 | #65485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4096 | 2 |
| C5×#4094 | 2 |
| #11716932 | 2 |
| #11716704 | 2 |
| #11716618 | 2 |
| #11716609 | 2 |
| #11716594 | 2 |
| #65485 | 5 |
| #65433 | 5 |