Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 92 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×C8×C5⋊D5 | C2 | semidirect |
| 2. C2×C5×C8×D5 | C2 | semidirect |
| 4. C5×C8×Dic5 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 6. #11716598 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 34. #6038 | C8 | direct (N × H) |
| 35. C52×C8 | D4 | semidirect |
| 44. C2×C8×D5 | D5 | semidirect |
| 52. C8×Dic5 | D5 | semidirect |
| 57. C2×C5⋊D5 | C2×C8 | semidirect |
| 60. C2×C5×D5 | C2×C8 | semidirect |
| 66. C5×Dic5 | C2×C8 | semidirect |
| 135. C5×C8 | D20 | semidirect |
| 136. C5×C8 | C22⋊D5 | semidirect |
| 149. C52 | C8×D4 | semidirect |
| 167. C2×D5 | C8×D5 | semidirect |
| 182. Dic5 | C8×D5 | semidirect |
| 225. C8 | #6038 | direct (N × H) |
| 227. C5 | C8×D20 | semidirect |
| 228. C5 | C8×C22⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C5⋊D5 | 2 |
| C2×C5×C8×D5 | 2 |
| C4×#6038 | 2 |
| C5×C8×Dic5 | 2 |
| #11716612 | 2 |
| #11716598 | 2 |
| #11716597 | 2 |
| C8×C22⋊D5 | 5 |
| C8×D20 | 5 |