Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11717195 | C2 | semidirect |
| 2. C4×C5×D20 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 5. C5×C4⋊#168 | C2 | semidirect |
| 6. #11716608 | C2 | semidirect |
| 7. #11716605 | C2 | semidirect |
| 47. C4×D20 | D5 | semidirect |
| 53. C4⋊#168 | D5 | semidirect |
| 152. C52 | #463 | semidirect |
| 232. C5 | #65133 | semidirect |
| 233. C5 | #65305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717195 | 2 |
| C4×C5×D20 | 2 |
| C2×#87773 | 2 |
| C2×#87771 | 2 |
| C5×C4⋊#168 | 2 |
| #11716608 | 2 |
| #11716605 | 2 |
| #65305 | 5 |
| #65133 | 5 |