Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
374 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#87874 | C2 | semidirect |
| 2. C2×C5×#677 | C2 | semidirect |
| 3. #11717026 | C2 | semidirect |
| 4. C2×#87771 | C2 | semidirect |
| 5. #11716688 | C2 | semidirect |
| 6. C5×#3952 | C2 | semidirect |
| 7. #11716607 | C2 | semidirect |
| 31. C4⋊(C5⋊D5) | D4 | semidirect |
| 39. C5×Dic10 | D4 | semidirect |
| 52. C2×#677 | D5 | semidirect |
| 58. #3952 | D5 | semidirect |
| 155. Dic10 | C22⋊D5 | semidirect |
| 168. C52 | #449 | semidirect |
| 258. C5 | #65023 | semidirect |
| 259. C5 | #65461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C2×C5×#677 | 2 |
| #11717026 | 2 |
| C2×#87771 | 2 |
| #11716688 | 2 |
| C5×#3952 | 2 |
| #11716607 | 2 |
| #65461 | 5 |
| #65023 | 5 |