Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
366 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 366 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. C5×D5×C4⋊C4 | C2 | semidirect |
| 3. C2×#87768 | C2 | semidirect |
| 4. #11716677 | C2 | semidirect |
| 5. C5×#3941 | C2 | semidirect |
| 6. #11716608 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 15. #87870 | C4 | semidirect |
| 30. #6045 | C2×C4 | semidirect |
| 34. C5×D20 | C2×C4 | semidirect |
| 47. D5×C4⋊C4 | D5 | semidirect |
| 56. #3941 | D5 | semidirect |
| 133. D20 | C4×D5 | semidirect |
| 156. C52 | #417 | semidirect |
| 234. C5 | #65060 | semidirect |
| 235. C5 | #65255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| C5×D5×C4⋊C4 | 2 |
| C2×#87768 | 2 |
| #11716677 | 2 |
| C5×#3941 | 2 |
| #11716608 | 2 |
| #11716603 | 2 |
| #65255 | 5 |
| #65060 | 5 |