Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
338 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. C4×C5×Dic10 | C2 | semidirect |
| 4. C4×C5×#168 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 19. #87774 | C4 | direct (N × H) |
| 33. C5×Dic10 | C2×C4 | semidirect |
| 35. C5×#168 | C2×C4 | semidirect |
| 42. C4×Dic10 | D5 | semidirect |
| 50. C4×#168 | D5 | semidirect |
| 56. C4×C52 | SD16 | semidirect |
| 127. Dic10 | C4×D5 | semidirect |
| 131. #168 | C4×D5 | semidirect |
| 139. C52 | C4×SD16 | semidirect |
| 160. C4×C5 | #677 | semidirect |
| 161. C4×C5 | #688 | semidirect |
| 210. C5 | C4×#677 | semidirect |
| 211. C5 | C4×#688 | semidirect |
| 220. C4 | #87774 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C5⋊D5) | 2 |
| C4×C5×Dic10 | 2 |
| C2×#87774 | 2 |
| C4×C5×#168 | 2 |
| #11716614 | 2 |
| #11716607 | 2 |
| #11716605 | 2 |
| C4×#688 | 5 |
| C4×#677 | 5 |