Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 72 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×#87800 | C2 | semidirect |
| 2. C2×C5×#677 | C2 | semidirect |
| 3. #11716982 | C2 | semidirect |
| 4. #11716979 | C2 | semidirect |
| 5. C2×#87776 | C2 | semidirect |
| 7. C5×C8×Dic5 | C2 | semidirect |
| 49. C2×#677 | D5 | semidirect |
| 53. C8×Dic5 | D5 | semidirect |
| 146. C52 | #495 | semidirect |
| 214. C5 | #64985 | semidirect |
| 215. C5 | #65457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87800 | 2 |
| C2×C5×#677 | 2 |
| #11716982 | 2 |
| #11716979 | 2 |
| C2×#87776 | 2 |
| C2×#87771 | 2 |
| C5×C8×Dic5 | 2 |
| #65457 | 5 |
| #64985 | 5 |