Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 55 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×#121 | C2 | semidirect |
| 2. C2×#87722 | C2 | semidirect |
| 3. #11716492 | C2 | semidirect |
| 4. C2×#87716 | C2 | semidirect |
| 5. #11716381 | C2 | semidirect |
| 6. #11716358 | C2 | semidirect |
| 7. #11716356 | C2 | semidirect |
| 38. #6014 | D4 | semidirect |
| 101. #121 | D25 | semidirect |
| 105. C25 | #469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#121 | 2 |
| C2×#87722 | 2 |
| #11716492 | 2 |
| C2×#87716 | 2 |
| #11716381 | 2 |
| #11716358 | 2 |
| #11716356 | 2 |
| #65328 | 5 |