Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 285 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. C22×#6032 | C2 | semidirect |
| 2. C2×D5⋊#168 | C2 | semidirect |
| 4. C22⋊#6032 | C2 | semidirect |
| 5. #11716847 | C2 | semidirect |
| 6. #11716846 | C2 | semidirect |
| 7. C4×#6032 | C2 | semidirect |
| 27. C5×C22⋊D5 | C8 | semidirect |
| 38. #6032 | D4 | semidirect |
| 55. C22×C52 | C2×C8 | semidirect |
| 59. C2×C5×D5 | C2×C8 | semidirect |
| 63. C5×Dic5 | C2×C8 | semidirect |
| 118. C22⋊D5 | #168 | semidirect |
| 141. C52 | C8×D4 | semidirect |
| 153. C22×C5 | C2×#168 | semidirect |
| 154. C22×C5 | D5⋊C8 | semidirect |
| 159. C2×D5 | C2×#168 | semidirect |
| 171. Dic5 | C2×#168 | semidirect |
| 218. C5 | D4×#168 | semidirect |
| 219. C5 | #65692 | semidirect |
| 225. C22 | D5⋊#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6032 | 2 |
| C2×D5⋊#168 | 2 |
| C5×#4027 | 2 |
| C22⋊#6032 | 2 |
| #11716847 | 2 |
| #11716846 | 2 |
| C4×#6032 | 2 |
| #65692 | 5 |
| D4×#168 | 5 |