Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×C5×#124 | C2 | semidirect |
| 2. C2×#4088 | C2 | semidirect |
| 4. #65514 | C2 | semidirect |
| 5. C2×#3965 | C2 | semidirect |
| 6. C2×#3937 | C2 | semidirect |
| 7. #64743 | C2 | semidirect |
| 36. C2×C5×Q8 | D4 | semidirect |
| 57. C42×C5 | D4 | semidirect |
| 67. #681 | D4 | semidirect |
| 72. C2×#124 | D5 | semidirect |
| 165. C2×Q8 | C22⋊D5 | semidirect |
| 193. C42 | C22⋊D5 | semidirect |
| 238. C5 | #2004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#124 | 2 |
| C2×#4088 | 2 |
| #66139 | 2 |
| #65514 | 2 |
| C2×#3965 | 2 |
| C2×#3937 | 2 |
| #64743 | 2 |
| #2004 | 5 |