Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
464 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 166 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. D4×#170 | C2 | semidirect |
| 3. #65756 | C2 | semidirect |
| 4. C2×#4003 | C2 | semidirect |
| 5. #65705 | C2 | semidirect |
| 6. #65693 | C2 | semidirect |
| 7. #65683 | C2 | semidirect |
| 8. #65680 | C2 | semidirect |
| 11. C22×#170 | C22 | semidirect |
| 12. C2×#700 | C22 | semidirect |
| 22. C22⋊#170 | C22 | semidirect |
| 26. #4003 | C22 | semidirect |
| 27. #4002 | C22 | semidirect |
| 28. C4⋊#170 | C22 | semidirect |
| 29. C4⋊#170 | C22 | semidirect |
| 30. C4×#170 | C22 | semidirect |
| 76. C5×D4 | M16 | semidirect |
| 183. D4 | #700 | semidirect |
| 203. C5 | #2974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D5 | 2 |
| D4×#170 | 2 |
| #65756 | 2 |
| C2×#4003 | 2 |
| #65705 | 2 |
| #65693 | 2 |
| #65683 | 2 |
| #65680 | 2 |
| #2974 | 5 |