Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
696 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 136 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×#87904 | C2 | semidirect |
| 2. C2×#87871 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. #11717068 | C2 | direct (N × H) |
| 6. C2×#87774 | C2 | semidirect |
| 7. C2×#87771 | C2 | semidirect |
| 8. C2×#87767 | C2 | semidirect |
| 11. #87904 | C22 | semidirect |
| 21. #87871 | C22 | semidirect |
| 22. C5×#689 | C22 | semidirect |
| 23. C5×#688 | C22 | semidirect |
| 26. #87774 | C22 | semidirect |
| 27. #87771 | C22 | semidirect |
| 28. #87767 | C22 | semidirect |
| 61. C2×#689 | D5 | semidirect |
| 63. C2×#688 | D5 | semidirect |
| 120. #689 | C2×D5 | semidirect |
| 122. #688 | C2×D5 | semidirect |
| 131. C2×C52 | #135 | semidirect |
| 203. C52 | C2×#135 | semidirect |
| 260. C2×C5 | #4062 | semidirect |
| 261. C2×C5 | #4065 | semidirect |
| 295. C5 | C2×#4062 | semidirect |
| 296. C5 | C2×#4065 | semidirect |
| 312. C2 | #11717068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| C2×#87871 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#688 | 2 |
| #11717068 | 2 |
| C2×#87774 | 2 |
| C2×#87771 | 2 |
| C2×#87767 | 2 |
| C2×#4065 | 5 |
| C2×#4062 | 5 |