Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 66 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. C4×#6045 | C2 | semidirect |
| 3. C2×#87776 | C2 | semidirect |
| 5. C5×C4⋊#168 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 52. C4⋊#168 | D5 | semidirect |
| 144. C52 | #464 | semidirect |
| 214. C5 | #65134 | semidirect |
| 215. C5 | #65343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C5×#4021 | 2 |
| C2×#87776 | 2 |
| C2×#87773 | 2 |
| C5×C4⋊#168 | 2 |
| #11716607 | 2 |
| #11716604 | 2 |
| #65343 | 5 |
| #65134 | 5 |