Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
374 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 374 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. C2×C5×#676 | C2 | semidirect |
| 3. D5×C4⋊Dic5 | C2 | semidirect |
| 4. #11716688 | C2 | semidirect |
| 5. C5×#3948 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 7. #11716605 | C2 | semidirect |
| 15. #87874 | C4 | semidirect |
| 29. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 36. C5×Dic10 | C2×C4 | semidirect |
| 46. C2×#676 | D5 | semidirect |
| 55. #3948 | D5 | semidirect |
| 143. Dic10 | C4×D5 | semidirect |
| 156. C52 | #417 | semidirect |
| 237. C5 | #65092 | semidirect |
| 238. C5 | #65422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C2×C5×#676 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11716688 | 2 |
| C5×#3948 | 2 |
| #11716607 | 2 |
| #11716605 | 2 |
| #65422 | 5 |
| #65092 | 5 |