Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. C4×Q8×C25 | C2 | semidirect |
| 4. #11716384 | C2 | semidirect |
| 6. #11716355 | C2 | semidirect |
| 7. #11716351 | C2 | semidirect |
| 15. #87724 | C4 | semidirect |
| 23. Q8×C25 | C2×C4 | semidirect |
| 34. #6014 | C2×C4 | semidirect |
| 85. C4×Q8 | D25 | semidirect |
| 91. C25 | #440 | semidirect |
| 121. Q8 | C4×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C25 | 2 |
| C2×#87724 | 2 |
| C4×D100 | 2 |
| #11716384 | 2 |
| #11716358 | 2 |
| #11716355 | 2 |
| #11716351 | 2 |
| #65315 | 5 |