Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
278 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 76 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. C5×#4015 | C2 | semidirect |
| 4. C4⋊#6029 | C2 | semidirect |
| 5. #11716606 | C2 | semidirect |
| 35. #4015 | D5 | semidirect |
| 46. C4×C52 | SD16 | semidirect |
| 111. C52 | #461 | semidirect |
| 129. C4×C5 | #687 | semidirect |
| 130. C4×C5 | #688 | semidirect |
| 171. C5 | #65308 | semidirect |
| 172. C5 | #65372 | semidirect |
| 180. C4 | #87772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D20 | 2 |
| C5×#4015 | 2 |
| C2×#87772 | 2 |
| C4⋊#6029 | 2 |
| #11716606 | 2 |
| #65372 | 5 |
| #65308 | 5 |