Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. D5⋊#681 | C2 | semidirect |
| 3. C5×D5⋊M16 | C2 | semidirect |
| 4. #11716758 | C2 | semidirect |
| 5. #11716757 | C2 | semidirect |
| 53. D5⋊M16 | D5 | semidirect |
| 176. C52 | #413 | semidirect |
| 269. C5 | #65421 | semidirect |
| 270. C5 | #65761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87873 | 2 |
| D5⋊#681 | 2 |
| C5×D5⋊M16 | 2 |
| #11716758 | 2 |
| #11716757 | 2 |
| #65761 | 5 |
| #65421 | 5 |