Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
808 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 315 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×#6029 | C2 | semidirect |
| 4. #11716699 | C2 | direct (N × H) |
| 8. C2×C52×D4 | C4 | semidirect |
| 13. C4⋊#1039 | C22 | semidirect |
| 15. C2×#6029 | C22 | semidirect |
| 24. C52×D4 | C2×C4 | semidirect |
| 51. C2×C5×D4 | Dic5 | semidirect |
| 61. C2×C52 | #102 | semidirect |
| 72. C5×D4 | C2×Dic5 | semidirect |
| 84. C52 | C2×#102 | semidirect |
| 100. C2×D4 | #1039 | semidirect |
| 109. C2×C5 | #3964 | semidirect |
| 120. D4 | C2×#1039 | semidirect |
| 128. C5 | C2×#3964 | semidirect |
| 142. C2 | #11716699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C4⋊#1039 | 2 |
| C22×#6029 | 2 |
| #11716699 | 2 |
| C2×#3964 | 5 |