Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11717358 | C2 | semidirect |
| 3. #11716889 | C2 | semidirect |
| 4. C8×#1043 | C2 | semidirect |
| 5. #11716770 | C2 | semidirect |
| 13. C5×Dic20 | C4 | semidirect |
| 14. C5×D40 | C4 | semidirect |
| 15. #87772 | C4 | semidirect |
| 64. Dic20 | AGL(1,𝔽5) | semidirect |
| 65. D40 | AGL(1,𝔽5) | semidirect |
| 106. C52 | #443 | semidirect |
| 153. C5 | #65732 | semidirect |
| 154. C5 | #65740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717358 | 2 |
| #11716928 | 2 |
| #11716889 | 2 |
| C8×#1043 | 2 |
| #11716770 | 2 |
| #65740 | 5 |
| #65732 | 5 |