Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #4083 |
| commutator, cosocle | C22×C4×C5 | C23 |
| Frattini | C22×C4 | C22×D5 |
| Fitting | C5×#418 | C2 |
| socle | C22×C5 | #120 |
| hypercenter | #418 | D5 |
| hypocenter | C5 | #2002 |
| LCS | G ▷ C22×C4×C5 ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #418 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4086 | C2 | semidirect |
| 2. C2×#4078 | C2 | semidirect |
| 3. #65859 | C2 | semidirect |
| 4. C5×#418 | C2 | semidirect |
| 5. C2×#3957 | C2 | semidirect |
| 6. C2×#3955 | C2 | semidirect |
| 7. #64752 | C2 | semidirect |
| 37. C2×C5×D4 | D4 | semidirect |
| 54. C2×D20 | D4 | semidirect |
| 56. C2×Dic10 | D4 | semidirect |
| 60. C5×C4⋊C4 | D4 | semidirect |
| 67. C4×Dic5 | D4 | semidirect |
| 69. #681 | D4 | semidirect |
| 75. #418 | D5 | semidirect |
| 183. C2×D4 | D20 | semidirect |
| 195. C4⋊C4 | C22⋊D5 | semidirect |
| 248. C5 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4086 | 2 |
| C2×#4078 | 2 |
| #65859 | 2 |
| C5×#418 | 2 |
| C2×#3957 | 2 |
| C2×#3955 | 2 |
| #64752 | 2 |
| #2002 | 5 |