Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 107 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. C52×#135 | C2 | semidirect |
| 2. #11717224 | C2 | semidirect |
| 3. #11716696 | C2 | semidirect |
| 4. #11716695 | C2 | semidirect |
| 5. #11716694 | C2 | semidirect |
| 6. #11716693 | C2 | semidirect |
| 7. C2×#87756 | C2 | semidirect |
| 31. C5×#135 | D5 | semidirect |
| 73. #135 | C5⋊D5 | semidirect |
| 79. C52 | #508 | semidirect |
| 113. C5 | #65483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#135 | 2 |
| #11717224 | 2 |
| #11716696 | 2 |
| #11716695 | 2 |
| #11716694 | 2 |
| #11716693 | 2 |
| C2×#87756 | 2 |
| #65483 | 5 |