Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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. C25×#135 | C2 | semidirect |
| 2. #11716467 | C2 | semidirect |
| 3. #11716377 | C2 | semidirect |
| 4. #11716376 | C2 | semidirect |
| 5. #11716375 | C2 | semidirect |
| 6. #11716374 | C2 | semidirect |
| 7. C2×#87707 | C2 | semidirect |
| 73. #135 | D25 | semidirect |
| 79. C25 | #508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#135 | 2 |
| #11716467 | 2 |
| #11716377 | 2 |
| #11716376 | 2 |
| #11716375 | 2 |
| #11716374 | 2 |
| C2×#87707 | 2 |
| #65483 | 5 |