Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11717256 | C2 | semidirect |
| 3. C2×#87800 | C2 | semidirect |
| 4. #11717213 | C2 | semidirect |
| 5. C52×#102 | C2 | semidirect |
| 6. #11716681 | C2 | semidirect |
| 7. #11716677 | C2 | semidirect |
| 42. C5×#102 | D5 | semidirect |
| 99. #102 | C5⋊D5 | semidirect |
| 100. C52 | #463 | semidirect |
| 148. C5 | #65076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717256 | 2 |
| C2×#87809 | 2 |
| C2×#87800 | 2 |
| #11717213 | 2 |
| C52×#102 | 2 |
| #11716681 | 2 |
| #11716677 | 2 |
| #65076 | 5 |