Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
312 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 82 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×#87799 | C2 | semidirect |
| 2. C2×C5×#676 | C2 | semidirect |
| 4. C5×C8×Dic5 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 6. #11716598 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 35. C52×C8 | D4 | semidirect |
| 44. C2×#676 | D5 | semidirect |
| 52. C8×Dic5 | D5 | semidirect |
| 66. C5×Dic5 | M16 | semidirect |
| 135. C5×C8 | D20 | semidirect |
| 136. C5×C8 | C22⋊D5 | semidirect |
| 149. C52 | #436 | semidirect |
| 182. Dic5 | #676 | semidirect |
| 225. C8 | #6038 | semidirect |
| 227. C5 | #64977 | semidirect |
| 228. C5 | #65417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87799 | 2 |
| C2×C5×#676 | 2 |
| C4×#6038 | 2 |
| C5×C8×Dic5 | 2 |
| #11716612 | 2 |
| #11716598 | 2 |
| #11716597 | 2 |
| #65417 | 5 |
| #64977 | 5 |