Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
278 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 64 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×D5×C4⋊C4 | C2 | semidirect |
| 3. #11716676 | C2 | semidirect |
| 4. C5×#3940 | C2 | semidirect |
| 5. #11716615 | C2 | semidirect |
| 6. #11716605 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 39. D5×C4⋊C4 | D5 | semidirect |
| 50. #3940 | D5 | semidirect |
| 138. C52 | #481 | semidirect |
| 213. C5 | #65152 | semidirect |
| 214. C5 | #65257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×C4⋊C4 | 2 |
| #11717027 | 2 |
| #11716676 | 2 |
| C5×#3940 | 2 |
| #11716615 | 2 |
| #11716605 | 2 |
| #11716597 | 2 |
| #65257 | 5 |
| #65152 | 5 |