Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 1. C2×C52×SD16 | C2 | semidirect |
| 2. Q8×#1039 | C2 | semidirect |
| 3. C2×#87811 | C2 | semidirect |
| 5. #11716699 | C2 | semidirect |
| 6. #11716688 | C2 | semidirect |
| 7. #11716681 | C2 | semidirect |
| 25. C52×Q8 | D4 | semidirect |
| 39. C2×C5×SD16 | D5 | semidirect |
| 58. #1039 | SD16 | semidirect |
| 81. C5×Q8 | C22⋊D5 | semidirect |
| 96. C2×SD16 | C5⋊D5 | semidirect |
| 102. C52 | #460 | semidirect |
| 137. Q8 | C22⋊(C5⋊D5) | semidirect |
| 151. C5 | #65452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| Q8×#1039 | 2 |
| C2×#87811 | 2 |
| #11717260 | 2 |
| #11716699 | 2 |
| #11716688 | 2 |
| #11716681 | 2 |
| #65452 | 5 |