Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 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×C5×#676 | C2 | semidirect |
| 3. C8×#1039 | C2 | semidirect |
| 4. #11716613 | C2 | semidirect |
| 5. #11716597 | C2 | semidirect |
| 24. C52×C8 | D4 | semidirect |
| 29. C2×#676 | D5 | semidirect |
| 42. #1039 | M16 | semidirect |
| 82. C5×C8 | C22⋊D5 | semidirect |
| 91. C52 | #436 | semidirect |
| 137. C8 | #6037 | semidirect |
| 139. C5 | #65417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#676 | 2 |
| C4×#6037 | 2 |
| C8×#1039 | 2 |
| #11716613 | 2 |
| #11716597 | 2 |
| #65417 | 5 |