Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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. D4×Dic25 | C2 | semidirect |
| 3. #11716455 | C2 | semidirect |
| 4. C25×#102 | C2 | semidirect |
| 5. #11716369 | C2 | semidirect |
| 6. #11716364 | C2 | semidirect |
| 7. #11716356 | C2 | semidirect |
| 15. #87722 | C4 | semidirect |
| 24. D4×C25 | C2×C4 | semidirect |
| 32. D100 | C2×C4 | semidirect |
| 35. #6014 | C2×C4 | semidirect |
| 94. #102 | D25 | semidirect |
| 96. C25 | #442 | semidirect |
| 132. D4 | C4×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic25 | 2 |
| C2×#87722 | 2 |
| #11716455 | 2 |
| C25×#102 | 2 |
| #11716369 | 2 |
| #11716364 | 2 |
| #11716356 | 2 |
| #65074 | 5 |