Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 59 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. C2×#87721 | C2 | semidirect |
| 3. C2×#87713 | C2 | semidirect |
| 4. #11716459 | C2 | semidirect |
| 5. C25×#102 | C2 | semidirect |
| 6. #11716368 | C2 | semidirect |
| 7. #11716358 | C2 | semidirect |
| 15. C2×Dic50 | C22 | semidirect |
| 16. C2×C8×C25 | C22 | semidirect |
| 17. C4⋊C4×C25 | C22 | semidirect |
| 21. C2×#6014 | C22 | semidirect |
| 62. C2×D25 | SD16 | semidirect |
| 116. #102 | D25 | semidirect |
| 118. C25 | #450 | semidirect |
| 146. C2×C8 | C2×D25 | semidirect |
| 148. C4⋊C4 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D25 | 2 |
| C2×#87721 | 2 |
| C2×#87713 | 2 |
| #11716459 | 2 |
| C25×#102 | 2 |
| #11716368 | 2 |
| #11716358 | 2 |
| #65065 | 5 |