Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
639 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×C22⋊D25 | C2 | semidirect |
| 2. C22×C22⋊D25 | C2 | semidirect |
| 3. C22×D100 | C2 | semidirect |
| 4. C22×C4×D25 | C2 | semidirect |
| 5. C2×C22⋊C4×C25 | C2 | semidirect |
| 6. C2×#87720 | C2 | semidirect |
| 7. C2×#87718 | C2 | semidirect |
| 8. #11716446 | C2 | direct (N × H) |
| 16. C2×C22⋊D25 | C22 | semidirect |
| 17. C2×C22⋊D25 | C22 | semidirect |
| 21. C2×D100 | C22 | semidirect |
| 23. C2×C4×D25 | C22 | semidirect |
| 24. C22⋊C4×C25 | C22 | semidirect |
| 25. #87720 | C22 | semidirect |
| 26. #87718 | C22 | semidirect |
| 38. C22×D25 | D4 | semidirect |
| 48. C2×Dic25 | D4 | semidirect |
| 76. C2×D25 | C2×D4 | semidirect |
| 80. Dic25 | C2×D4 | semidirect |
| 101. C2×C25 | #121 | semidirect |
| 139. C2×C22⋊C4 | D25 | semidirect |
| 140. C25 | C2×#121 | semidirect |
| 178. C22⋊C4 | C2×D25 | semidirect |
| 235. C2 | #11716446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D25 | 2 |
| C22×D100 | 2 |
| C22×C4×D25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×#87720 | 2 |
| C2×#87718 | 2 |
| #11716446 | 2 |
| C2×#4030 | 5 |