Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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×#87834 | C2 | semidirect |
| 2. C2×D5⋊#170 | C2 | semidirect |
| 4. #11716895 | C2 | semidirect |
| 5. #11716872 | C2 | semidirect |
| 6. #11716779 | C2 | semidirect |
| 7. #11716779 | C2 | semidirect |
| 36. #6034 | D4 | semidirect |
| 60. C2×C5×D5 | M16 | semidirect |
| 146. C52 | #435 | semidirect |
| 161. C2×D5 | #704 | semidirect |
| 221. C5 | #65704 | semidirect |
| 222. C5 | #65773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87834 | 2 |
| C2×D5⋊#170 | 2 |
| #11717017 | 2 |
| #11716895 | 2 |
| #11716872 | 2 |
| #11716779 | 2 |
| #65773 | 5 |
| #65704 | 5 |