Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊Dic25 | C2 | semidirect |
| 3. C22×#6014 | C2 | semidirect |
| 4. #11716381 | C2 | direct (N × H) |
| 8. C2×D4×C25 | C4 | semidirect |
| 13. C4⋊Dic25 | C22 | semidirect |
| 15. C2×#6014 | C22 | semidirect |
| 24. D4×C25 | C2×C4 | semidirect |
| 61. C2×C25 | #102 | semidirect |
| 84. C25 | C2×#102 | semidirect |
| 100. C2×D4 | Dic25 | semidirect |
| 120. D4 | C2×Dic25 | semidirect |
| 142. C2 | #11716381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C25 | 2 |
| C2×C4⋊Dic25 | 2 |
| C22×#6014 | 2 |
| #11716381 | 2 |
| C2×#3964 | 5 |