Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 235 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. #11717246 | C2 | semidirect |
| 3. #11716701 | C2 | semidirect |
| 6. C2×C52×Q8 | C4 | semidirect |
| 7. C2×C52×D4 | C4 | semidirect |
| 9. C22×C4×C52 | C4 | semidirect |
| 43. C2×C5×Q8 | Dic5 | semidirect |
| 44. C2×C5×D4 | Dic5 | semidirect |
| 46. C22×C4×C5 | Dic5 | semidirect |
| 72. C52 | #410 | semidirect |
| 85. C2×Q8 | #1039 | semidirect |
| 86. C2×D4 | #1039 | semidirect |
| 88. C22×C4 | #1039 | semidirect |
| 110. C5 | #65529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| #11717246 | 2 |
| #11716701 | 2 |
| #65529 | 5 |