Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 77 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×C8×D25 | C2 | semidirect |
| 3. C4⋊C4×D25 | C2 | semidirect |
| 4. C25×#102 | C2 | semidirect |
| 5. #11716381 | C2 | semidirect |
| 6. #11716369 | C2 | semidirect |
| 7. #11716358 | C2 | semidirect |
| 12. D4×D25 | C4 | semidirect |
| 16. C2×C8×C25 | C22 | semidirect |
| 17. C4⋊C4×C25 | C22 | semidirect |
| 18. C4⋊Dic25 | C22 | semidirect |
| 20. C2×#6014 | C22 | semidirect |
| 30. D4×C25 | C2×C4 | semidirect |
| 37. D100 | C2×C4 | semidirect |
| 86. D25 | #102 | direct (N × H) |
| 113. #102 | D25 | direct (N × H) |
| 114. C25 | C2×#102 | semidirect |
| 141. C2×C8 | C2×D25 | semidirect |
| 144. C4⋊C4 | C2×D25 | semidirect |
| 161. D4 | C4×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×C8×D25 | 2 |
| C4⋊C4×D25 | 2 |
| C25×#102 | 2 |
| #11716381 | 2 |
| #11716369 | 2 |
| #11716358 | 2 |
| D5×#102 | 5 |