Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
297 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 63 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×D100 | C2 | semidirect |
| 2. C25×#121 | C2 | semidirect |
| 3. C2×#87722 | C2 | semidirect |
| 4. C22⋊#6014 | C2 | semidirect |
| 5. #11716358 | C2 | semidirect |
| 8. C2×D4×C25 | C22 | semidirect |
| 13. C4⋊C4×C25 | C22 | semidirect |
| 16. C2×#6014 | C22 | semidirect |
| 32. D100 | D4 | semidirect |
| 44. C22×C25 | D8 | semidirect |
| 89. #121 | D25 | semidirect |
| 92. C25 | #447 | semidirect |
| 112. C2×D4 | C2×D25 | semidirect |
| 116. C4⋊C4 | C2×D25 | semidirect |
| 150. C22 | #87722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D100 | 2 |
| C25×#121 | 2 |
| C2×#87722 | 2 |
| C22⋊#6014 | 2 |
| #11716358 | 2 |
| #65325 | 5 |