Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
624 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 120 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×C4×#1039 | C2 | semidirect |
| 3. C2×C5×#685 | C2 | semidirect |
| 4. C2×#87781 | C2 | semidirect |
| 5. C2×#87778 | C2 | semidirect |
| 13. C2×#6037 | C4 | semidirect |
| 29. C2×C4×C52 | D4 | semidirect |
| 35. C2×#1039 | D4 | semidirect |
| 44. C2×#685 | D5 | semidirect |
| 64. #1039 | C22⋊C4 | semidirect |
| 119. C2×C4×C5 | C22⋊D5 | semidirect |
| 141. C52 | #390 | semidirect |
| 226. C2×C4 | #6037 | semidirect |
| 228. C5 | #65246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6037 | 2 |
| C2×C4×#1039 | 2 |
| C2×C5×#685 | 2 |
| C2×#87781 | 2 |
| C2×#87778 | 2 |
| #65246 | 5 |