Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
330 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 4. #11716691 | C2 | semidirect |
| 5. C5×#3956 | C2 | semidirect |
| 6. #11716602 | C2 | semidirect |
| 7. #11716601 | C2 | semidirect |
| 62. #3956 | D5 | direct (N × H) |
| 114. C5×D5 | #101 | semidirect |
| 170. C52 | C2×#101 | semidirect |
| 221. D5 | #3956 | direct (N × H) |
| 244. C5 | D5×#101 | semidirect |
| 245. C5 | C2×#3956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic10 | 2 |
| C5×D5×M16 | 2 |
| D5×#681 | 2 |
| #11716691 | 2 |
| C5×#3956 | 2 |
| #11716602 | 2 |
| #11716601 | 2 |
| C2×#3956 | 5 |
| D5×#101 | 5 |