Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
171 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 2. C4⋊C4×D25 | C2 | semidirect |
| 3. C25×#102 | C2 | semidirect |
| 4. #11716381 | C2 | semidirect |
| 5. #11716368 | C2 | semidirect |
| 6. #11716366 | C2 | semidirect |
| 7. #11716356 | C2 | semidirect |
| 92. #102 | D25 | semidirect |
| 94. C25 | #481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716500 | 2 |
| C4⋊C4×D25 | 2 |
| C25×#102 | 2 |
| #11716381 | 2 |
| #11716368 | 2 |
| #11716366 | 2 |
| #11716356 | 2 |
| #65066 | 5 |