Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
420 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 155 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×Q8×D25 | C2 | semidirect |
| 2. C4×Q8×C25 | C2 | semidirect |
| 3. #11716459 | C2 | semidirect |
| 5. #11716431 | C2 | semidirect |
| 18. Q8×C25 | D4 | semidirect |
| 23. D100 | Q8 | direct (N × H) |
| 34. C2×D25 | C2×Q8 | semidirect |
| 37. C4×C25 | C2×Q8 | semidirect |
| 66. C4×Q8 | D25 | semidirect |
| 68. C25 | D4×Q8 | semidirect |
| 93. Q8 | D100 | direct (N × H) |
| 108. C4 | Q8×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D25 | 2 |
| C4×Q8×C25 | 2 |
| #11716459 | 2 |
| C4×D100 | 2 |
| #11716431 | 2 |
| Q8×D20 | 5 |