Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 144 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. C22×C5×#168 | C2 | semidirect |
| 4. #11716604 | C2 | direct (N × H) |
| 10. C2×C5×D20 | C4 | semidirect |
| 13. C4⋊#1039 | C22 | semidirect |
| 15. C2×C5×#168 | C22 | semidirect |
| 31. C5×D20 | C2×C4 | semidirect |
| 39. C22×#168 | D5 | semidirect |
| 68. C2×D20 | Dic5 | semidirect |
| 79. C2×#168 | C2×D5 | semidirect |
| 81. C2×C52 | #102 | semidirect |
| 120. D20 | C2×Dic5 | semidirect |
| 127. C52 | C2×#102 | semidirect |
| 176. C2×C5 | #3953 | semidirect |
| 177. C2×C5 | #3964 | semidirect |
| 201. C5 | C2×#3953 | semidirect |
| 202. C5 | C2×#3964 | semidirect |
| 216. C2 | #11716604 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C2×C4⋊#1039 | 2 |
| C22×C5×#168 | 2 |
| #11716604 | 2 |
| C2×#3964 | 5 |
| C2×#3953 | 5 |