Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
560 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11717260 | C2 | semidirect |
| 2. C2×#87809 | C2 | semidirect |
| 3. C2×#87801 | C2 | semidirect |
| 4. #11717213 | C2 | semidirect |
| 5. C52×#102 | C2 | semidirect |
| 6. #11716681 | C2 | semidirect |
| 7. #11716676 | C2 | semidirect |
| 36. C4⋊(C5⋊D5) | D4 | semidirect |
| 44. C5×#102 | D5 | semidirect |
| 61. #1039 | D8 | semidirect |
| 106. #102 | C5⋊D5 | semidirect |
| 107. C52 | #459 | semidirect |
| 160. C5 | #65075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717260 | 2 |
| C2×#87809 | 2 |
| C2×#87801 | 2 |
| #11717213 | 2 |
| C52×#102 | 2 |
| #11716681 | 2 |
| #11716676 | 2 |
| #65075 | 5 |