Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
198 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 49 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×#1035 | C2 | semidirect |
| 3. #11716424 | C2 | semidirect |
| 4. #11716411 | C2 | semidirect |
| 5. #11716410 | C2 | semidirect |
| 12. D8×C25 | C4 | semidirect |
| 13. #87722 | C4 | semidirect |
| 14. D200 | C4 | semidirect |
| 21. D4×C25 | C2×C4 | semidirect |
| 23. D100 | C2×C4 | semidirect |
| 26. C8×C25 | C2×C4 | semidirect |
| 27. #6014 | C2×C4 | semidirect |
| 73. C25 | #442 | semidirect |
| 87. D8 | #1035 | semidirect |
| 100. D4 | C2×#1035 | semidirect |
| 107. C8 | C2×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1035 | 2 |
| D8×D25 | 2 |
| #11716424 | 2 |
| #11716411 | 2 |
| #11716410 | 2 |
| #65731 | 5 |