Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
432 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 127 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. #11717208 | C2 | semidirect |
| 5. #11716685 | C2 | semidirect |
| 6. #11716681 | C2 | semidirect |
| 7. #11716674 | C2 | semidirect |
| 22. C52×D4 | Q8 | semidirect |
| 69. C5×D4 | Dic10 | semidirect |
| 87. C52 | #474 | semidirect |
| 117. D4 | #6045 | semidirect |
| 127. C5 | #65048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1039 | 2 |
| #11717208 | 2 |
| C52×#102 | 2 |
| #11716699 | 2 |
| #11716685 | 2 |
| #11716681 | 2 |
| #11716674 | 2 |
| #65048 | 5 |