Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11717221 | C2 | semidirect |
| 2. C2×C5×D40 | C2 | semidirect |
| 3. #11716948 | C2 | semidirect |
| 4. C5×#3951 | C2 | semidirect |
| 5. #11716599 | C2 | semidirect |
| 34. C2×D40 | D5 | semidirect |
| 41. #3951 | D5 | semidirect |
| 118. C52 | #472 | semidirect |
| 173. C5 | #65186 | semidirect |
| 174. C5 | #65449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717221 | 2 |
| C2×C5×D40 | 2 |
| #11716948 | 2 |
| C5×#3951 | 2 |
| #11716599 | 2 |
| #65449 | 5 |
| #65186 | 5 |