Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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×Q8×D25 | C2 | semidirect |
| 2. C22×Dic50 | C2 | semidirect |
| 3. C25×C22⋊Q8 | C2 | semidirect |
| 4. #11716506 | C2 | semidirect |
| 6. #11716459 | C2 | semidirect |
| 7. #11716458 | C2 | semidirect |
| 8. #11716450 | C2 | semidirect |
| 9. #11716449 | C2 | semidirect |
| 11. #11716440 | C2 | semidirect |
| 46. C22⋊D25 | Q8 | semidirect |
| 58. Dic50 | D4 | semidirect |
| 72. C22×C25 | C2×Q8 | semidirect |
| 76. C2×D25 | C2×Q8 | semidirect |
| 85. Dic25 | C2×Q8 | semidirect |
| 145. C22⋊Q8 | D25 | semidirect |
| 149. C25 | D4×Q8 | semidirect |
| 223. C22 | Q8×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D25 | 2 |
| C22×Dic50 | 2 |
| C25×C22⋊Q8 | 2 |
| #11716506 | 2 |
| C4×C22⋊D25 | 2 |
| #11716459 | 2 |
| #11716458 | 2 |
| #11716450 | 2 |
| #11716449 | 2 |
| #11716443 | 2 |
| #11716440 | 2 |
| #65966 | 5 |