Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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×#4090 | C2 | semidirect |
| 4. C2×C5×#689 | C2 | semidirect |
| 7. C5×#3947 | C2 | semidirect |
| 22. #65479 | C5 | direct (N × H) |
| 41. C2×C5×Q16 | D5 | semidirect |
| 42. C2×C5×Q16 | C2×C5 | semidirect |
| 48. #4090 | C2×C5 | semidirect |
| 49. C2×#689 | C2×C5 | semidirect |
| 53. #3947 | C2×C5 | semidirect |
| 138. C2×Q16 | C5×D5 | semidirect |
| 144. C52 | #497 | semidirect |
| 206. C5 | #65479 | direct (N × H) |
| 207. C5 | C5×#497 | 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×#4090 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#688 | 2 |
| C2×C5×#677 | 2 |
| C5×#3947 | 2 |
| C5×#497 | 5 |
| #65479 | 5 |