Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#87800 | C2 | semidirect |
| 2. C2×#87799 | C2 | semidirect |
| 3. #11717217 | C2 | semidirect |
| 5. C52×#107 | C2 | semidirect |
| 6. #11716677 | C2 | semidirect |
| 7. #11716676 | C2 | semidirect |
| 36. C52×C8 | D4 | semidirect |
| 42. C5×#107 | D5 | semidirect |
| 91. C5×C8 | D20 | semidirect |
| 97. #107 | C5⋊D5 | semidirect |
| 100. C52 | #468 | semidirect |
| 147. C8 | C4⋊(C5⋊D5) | semidirect |
| 148. C5 | #65175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87800 | 2 |
| C2×#87799 | 2 |
| #11717217 | 2 |
| #11717215 | 2 |
| C52×#107 | 2 |
| #11716677 | 2 |
| #11716676 | 2 |
| #65175 | 5 |