Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
439 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 439 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#87853 | C2 | semidirect |
| 3. C2×C5×#704 | C2 | semidirect |
| 4. #11716757 | C2 | direct (N × H) |
| 15. #87853 | C22 | semidirect |
| 18. C5×#704 | C22 | semidirect |
| 46. C2×#704 | D5 | semidirect |
| 89. #704 | C2×D5 | semidirect |
| 101. C2×C52 | #100 | semidirect |
| 156. C52 | C2×#100 | semidirect |
| 221. C2×C5 | #3955 | semidirect |
| 222. C2×C5 | #4013 | semidirect |
| 251. C5 | C2×#3955 | semidirect |
| 252. C5 | C2×#4013 | semidirect |
| 273. C2 | #11716757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6038 | 2 |
| C2×#87853 | 2 |
| C2×C5×#704 | 2 |
| #11716757 | 2 |
| C2×#4013 | 5 |
| C2×#3955 | 5 |