Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 109 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×C5×#106 | C2 | semidirect |
| 3. C2×C8×Dic5 | C2 | semidirect |
| 5. #65263 | C2 | semidirect |
| 6. C2×#3942 | C2 | semidirect |
| 18. C2×#677 | C4 | semidirect |
| 58. C2×#106 | D5 | semidirect |
| 85. C2×Dic5 | SD16 | semidirect |
| 94. C5×C8 | C22⋊C4 | semidirect |
| 199. C8 | #685 | semidirect |
| 200. C5 | #1968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#677 | 2 |
| C2×C5×#106 | 2 |
| C2×C8×Dic5 | 2 |
| #65277 | 2 |
| #65263 | 2 |
| C2×#3942 | 2 |
| C2×#3941 | 2 |
| #1968 | 5 |