Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 616 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. C2×#87804 | C2 | semidirect |
| 4. #11716704 | C2 | semidirect |
| 7. C52×#41 | C4 | semidirect |
| 9. C2×C52×Q8 | C4 | semidirect |
| 11. C2×C52×D4 | C4 | semidirect |
| 16. C4×#1039 | C22 | semidirect |
| 18. #87804 | C22 | semidirect |
| 58. C5×#41 | Dic5 | semidirect |
| 60. C2×C5×Q8 | Dic5 | semidirect |
| 62. C2×C5×D4 | Dic5 | semidirect |
| 100. C52 | #421 | semidirect |
| 115. #41 | #1039 | semidirect |
| 117. C2×Q8 | #1039 | semidirect |
| 119. C2×D4 | #1039 | semidirect |
| 152. C5 | #65525 | 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 |
| C2×#87804 | 2 |
| #11716704 | 2 |
| #65525 | 5 |