Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
135 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 47 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. C25×#135 | C2 | semidirect |
| 2. C2×D200 | C2 | semidirect |
| 3. #11716376 | C2 | semidirect |
| 4. #11716374 | C2 | semidirect |
| 5. #11716360 | C2 | semidirect |
| 8. Q16×C25 | C22 | semidirect |
| 10. D8×C25 | C22 | semidirect |
| 14. #87707 | C22 | semidirect |
| 62. #135 | D25 | semidirect |
| 67. C25 | #509 | semidirect |
| 77. Q16 | C2×D25 | semidirect |
| 81. D8 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#135 | 2 |
| C2×D200 | 2 |
| #11716376 | 2 |
| #11716374 | 2 |
| #11716360 | 2 |
| #65482 | 5 |