Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C25×#97 | C2 | semidirect |
| 5. #11716364 | C2 | semidirect |
| 6. C8×Dic25 | C2 | semidirect |
| 7. C4×#6014 | C2 | semidirect |
| 17. #87712 | C4 | semidirect |
| 18. C8×D25 | C4 | semidirect |
| 76. #97 | D25 | semidirect |
| 79. C25 | #405 | 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 |
| #11716434 | 2 |
| C25×#97 | 2 |
| #11716364 | 2 |
| C8×Dic25 | 2 |
| C4×#6014 | 2 |
| #64997 | 5 |