Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11717262 | C2 | semidirect |
| 2. C2×#87811 | C2 | semidirect |
| 4. #11717227 | C2 | semidirect |
| 5. C52×#101 | C2 | semidirect |
| 6. #11716690 | C2 | semidirect |
| 7. #11716689 | C2 | semidirect |
| 44. C5×#101 | D5 | semidirect |
| 96. #101 | C5⋊D5 | semidirect |
| 98. C52 | #471 | semidirect |
| 142. C5 | #65043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717262 | 2 |
| C2×#87811 | 2 |
| #11717228 | 2 |
| #11717227 | 2 |
| C52×#101 | 2 |
| #11716690 | 2 |
| #11716689 | 2 |
| #65043 | 5 |