Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
308 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 308 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. #11717189 | C2 | semidirect |
| 4. C5×C4⋊#168 | C2 | semidirect |
| 5. #11716608 | C2 | semidirect |
| 40. C4⋊#168 | D5 | semidirect |
| 46. C4×C52 | SD16 | semidirect |
| 115. C52 | #461 | semidirect |
| 132. C4×C5 | #677 | semidirect |
| 133. C4×C5 | #687 | semidirect |
| 176. C5 | #65130 | semidirect |
| 177. C5 | #65308 | semidirect |
| 185. C4 | #87773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717189 | 2 |
| C4×C5×D20 | 2 |
| C2×#87773 | 2 |
| C5×C4⋊#168 | 2 |
| #11716608 | 2 |
| #65308 | 5 |
| #65130 | 5 |