Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
388 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11717260 | C2 | semidirect |
| 2. C2×C5×#686 | C2 | semidirect |
| 3. #11717017 | C2 | semidirect |
| 4. C2×#87771 | C2 | semidirect |
| 5. C5×#3964 | C2 | semidirect |
| 6. #11716613 | C2 | semidirect |
| 7. #11716605 | C2 | semidirect |
| 37. C5×D20 | D4 | semidirect |
| 47. C2×#686 | D5 | semidirect |
| 51. #3964 | D5 | semidirect |
| 69. #1039 | D8 | semidirect |
| 150. D20 | C22⋊D5 | semidirect |
| 163. C52 | #459 | semidirect |
| 254. C5 | #65075 | semidirect |
| 255. C5 | #65439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717260 | 2 |
| C2×C5×#686 | 2 |
| #11717017 | 2 |
| C2×#87771 | 2 |
| C5×#3964 | 2 |
| #11716613 | 2 |
| #11716605 | 2 |
| #65439 | 5 |
| #65075 | 5 |