Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×#87768 | C2 | semidirect |
| 4. #11716681 | C2 | semidirect |
| 5. C5×#3952 | C2 | semidirect |
| 6. #11716597 | C2 | semidirect |
| 7. #11716594 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 44. C2×#676 | D5 | semidirect |
| 48. #3952 | D5 | semidirect |
| 64. #1039 | M16 | semidirect |
| 138. #168 | C22⋊D5 | semidirect |
| 146. C52 | #436 | semidirect |
| 221. C5 | #65018 | semidirect |
| 222. 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 |
| C2×#87768 | 2 |
| #11716681 | 2 |
| C5×#3952 | 2 |
| #11716597 | 2 |
| #11716594 | 2 |
| #65417 | 5 |
| #65018 | 5 |