Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C5 |
| prime radical | C25×C5 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#397 | C2 | semidirect |
| 2. C5×#393 | C2 | semidirect |
| 3. C5×#388 | C2 | semidirect |
| 6. C22×C5×Q8 | C22 | semidirect |
| 7. C2×C5×C4⋊C4 | C22 | semidirect |
| 12. C2×C42×C5 | C22 | semidirect |
| 13. C5×#95 | C22 | semidirect |
| 14. C5×#95 | C22 | semidirect |
| 15. C5×#95 | C22 | semidirect |
| 16. #2736 | C5 | direct (N × H) |
| 31. #397 | C2×C5 | semidirect |
| 32. #393 | C2×C5 | semidirect |
| 33. #388 | C2×C5 | semidirect |
| 53. C22×Q8 | C22×C5 | semidirect |
| 54. C2×C4⋊C4 | C22×C5 | semidirect |
| 59. C2×C42 | C22×C5 | semidirect |
| 60. #95 | C22×C5 | semidirect |
| 61. #95 | C22×C5 | semidirect |
| 62. #95 | C22×C5 | semidirect |
| 110. C5 | #2736 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#397 | 2 |
| C5×#393 | 2 |
| C5×#388 | 2 |
| C5×#379 | 2 |
| #2736 | 5 |