Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#4033 | C2 | semidirect |
| 5. C5×#3940 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 19. #87774 | C4 | semidirect |
| 32. C5×Dic10 | C2×C4 | semidirect |
| 35. C5×#168 | C2×C4 | semidirect |
| 40. #4033 | D5 | semidirect |
| 49. #3940 | D5 | semidirect |
| 61. C5×Dic5 | SD16 | semidirect |
| 122. Dic10 | C4×D5 | semidirect |
| 127. #168 | C4×D5 | semidirect |
| 135. C52 | C4×SD16 | semidirect |
| 164. Dic5 | #688 | semidirect |
| 204. C5 | #65141 | semidirect |
| 205. C5 | C4×#688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4033 | 2 |
| #11717013 | 2 |
| C2×#87774 | 2 |
| #11716676 | 2 |
| C5×#3940 | 2 |
| #11716606 | 2 |
| Dic5×#168 | 2 |
| C4×#688 | 5 |
| #65141 | 5 |