Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D5 |
| commutator, cosocle | C2×C4×C5 | C24 |
| Frattini | C2×C4 | C23×D5 |
| Fitting | C5×#466 | C2 |
| socle | C22×C5 | C22×D4 |
| hypercenter | #466 | D5 |
| hypocenter | C5 | #3334 |
| LCS | G ▷ C2×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #466 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #65945 | C2 | semidirect |
| 2. C5×#466 | C2 | semidirect |
| 3. #65446 | C2 | semidirect |
| 4. D8×Dic5 | C2 | semidirect |
| 5. C8×C22⋊D5 | C2 | semidirect |
| 6. C2×#3950 | C2 | semidirect |
| 7. #65322 | C2 | semidirect |
| 8. D5×#107 | C2 | semidirect |
| 9. #65163 | C2 | semidirect |
| 10. #65063 | C2 | semidirect |
| 11. #65048 | C2 | semidirect |
| 77. #466 | D5 | semidirect |
| 94. C22⋊D5 | D8 | semidirect |
| 107. C5×C8 | #41 | semidirect |
| 220. C8 | #711 | semidirect |
| 221. C5 | #3334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65945 | 2 |
| C5×#466 | 2 |
| #65446 | 2 |
| D8×Dic5 | 2 |
| C8×C22⋊D5 | 2 |
| C2×#3950 | 2 |
| #65322 | 2 |
| D5×#107 | 2 |
| #65163 | 2 |
| #65063 | 2 |
| #65048 | 2 |
| #3334 | 5 |