Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
284 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 284 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×C52×Q16 | C2 | semidirect |
| 3. C5×Q8×Dic5 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 7. C5×#3946 | C2 | semidirect |
| 22. #65474 | C5 | direct (N × H) |
| 39. C2×C5×Q16 | D5 | semidirect |
| 40. C2×C5×Q16 | C2×C5 | semidirect |
| 45. Q8×Dic5 | C2×C5 | semidirect |
| 50. #3967 | C2×C5 | semidirect |
| 52. #3946 | C2×C5 | semidirect |
| 137. C2×Q16 | C5×D5 | semidirect |
| 144. C52 | #464 | semidirect |
| 212. C5 | #65474 | direct (N × H) |
| 213. C5 | C5×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C5×#4093 | 2 |
| C5×Q8×Dic5 | 2 |
| C2×C5×#688 | 2 |
| C5×#3967 | 2 |
| C5×#3953 | 2 |
| C5×#3946 | 2 |
| C5×#464 | 5 |
| #65474 | 5 |