Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 1. #11717017 | C2 | semidirect |
| 3. C8×#1039 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. #11716617 | C2 | semidirect |
| 13. #87770 | C4 | semidirect |
| 21. C5×D20 | C2×C4 | semidirect |
| 24. #6029 | C2×C4 | semidirect |
| 29. #3953 | D5 | semidirect |
| 40. #1039 | D8 | semidirect |
| 76. D20 | C4×D5 | semidirect |
| 87. C52 | C4×D8 | semidirect |
| 133. C5 | #65045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717017 | 2 |
| C2×#87770 | 2 |
| C8×#1039 | 2 |
| C5×#3953 | 2 |
| #11716617 | 2 |
| #65045 | 5 |