Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
186 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#87712 | C2 | semidirect |
| 2. C2×C8×D25 | C2 | semidirect |
| 4. C25×#97 | C2 | semidirect |
| 5. #11716368 | C2 | semidirect |
| 6. #11716368 | C2 | semidirect |
| 7. C4⋊#6014 | C2 | semidirect |
| 35. C8×C25 | D4 | semidirect |
| 51. C2×D25 | M16 | semidirect |
| 99. #97 | D25 | semidirect |
| 100. C25 | #435 | semidirect |
| 147. C8 | D100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87712 | 2 |
| C2×C8×D25 | 2 |
| C4×D100 | 2 |
| C25×#97 | 2 |
| #11716368 | 2 |
| C4⋊#6014 | 2 |
| #64995 | 5 |