Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
281 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 281 conjugacy classes of subgroups — too many to draw. Only its 99 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×D5⋊#168 | C2 | semidirect |
| 3. #11716846 | C2 | semidirect |
| 4. C4⋊#6032 | C2 | semidirect |
| 5. C4×#6032 | C2 | semidirect |
| 22. C5×D20 | C8 | semidirect |
| 27. #6032 | D4 | semidirect |
| 41. C2×C5×D5 | C2×C8 | semidirect |
| 43. C4×C52 | C2×C8 | semidirect |
| 86. D20 | #168 | semidirect |
| 100. C52 | C8×D4 | semidirect |
| 109. C2×D5 | C2×#168 | semidirect |
| 117. C4×C5 | C2×#168 | semidirect |
| 118. C4×C5 | D5⋊C8 | semidirect |
| 154. C5 | D4×#168 | semidirect |
| 155. C5 | #65702 | semidirect |
| 164. C4 | D5⋊#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊#168 | 2 |
| C5×#4039 | 2 |
| #11716846 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| #65702 | 5 |
| D4×#168 | 5 |