Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
374 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 68 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. D4×#1039 | C2 | semidirect |
| 2. C2×C5×#686 | C2 | semidirect |
| 3. #11717032 | C2 | semidirect |
| 4. #11716613 | C2 | semidirect |
| 5. #11716604 | C2 | semidirect |
| 20. C52×D4 | D4 | semidirect |
| 35. C2×#686 | D5 | semidirect |
| 50. #1039 | D8 | semidirect |
| 84. C5×D4 | C22⋊D5 | semidirect |
| 106. C52 | #459 | semidirect |
| 158. D4 | #6037 | semidirect |
| 166. C5 | #65439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1039 | 2 |
| C2×C5×#686 | 2 |
| #11717032 | 2 |
| #11716613 | 2 |
| #11716604 | 2 |
| #65439 | 5 |