Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
156 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 53 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×#131 | C2 | semidirect |
| 3. #11716511 | C2 | semidirect |
| 4. C2×#87713 | C2 | semidirect |
| 5. #11716372 | C2 | semidirect |
| 6. #11716371 | C2 | semidirect |
| 7. #11716361 | C2 | semidirect |
| 94. #131 | D25 | semidirect |
| 98. C25 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#131 | 2 |
| #11716512 | 2 |
| #11716511 | 2 |
| C2×#87713 | 2 |
| #11716372 | 2 |
| #11716371 | 2 |
| #11716361 | 2 |
| #65430 | 5 |