Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
315 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 85 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×C22⋊C4×C25 | C2 | semidirect |
| 3. C2×C22⋊Dic25 | C2 | semidirect |
| 4. #11716354 | C2 | direct (N × H) |
| 6. C23×D25 | C4 | semidirect |
| 12. C2×C22⋊D25 | C4 | semidirect |
| 15. C22×Dic25 | C4 | semidirect |
| 17. C22⋊C4×C25 | C22 | semidirect |
| 19. C22⋊Dic25 | C22 | semidirect |
| 32. C22×D25 | C2×C4 | semidirect |
| 43. C2×Dic25 | C2×C4 | semidirect |
| 91. C2×C25 | #99 | semidirect |
| 119. C2×C22⋊C4 | D25 | semidirect |
| 121. C25 | C2×#99 | semidirect |
| 157. C22⋊C4 | C2×D25 | semidirect |
| 219. C2 | #11716354 | 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 |
| C2×C22⋊C4×C25 | 2 |
| C2×C22⋊Dic25 | 2 |
| #11716354 | 2 |
| C2×#3938 | 5 |