Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
764 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C5×#3006 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3007 | C2 | semidirect |
| 3. C5×#2816 | C2 | semidirect |
| 4. C5×#1782 | C2 | semidirect |
| 5. C5×#1511 | C2 | semidirect |
| 6. C5×#1510 | C2 | semidirect |
| 7. C5×#1306 | C2 | semidirect |
| 33. #9981 | C5 | direct (N × H) |
| 87. #3007 | C2×C5 | semidirect |
| 89. #2816 | C2×C5 | semidirect |
| 90. #1782 | C2×C5 | semidirect |
| 91. #1511 | C2×C5 | semidirect |
| 92. #1510 | C2×C5 | semidirect |
| 93. #1306 | C2×C5 | semidirect |
| 472. C5 | #9981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3007 | 2 |
| C5×#3006 | 2 |
| C5×#2816 | 2 |
| C5×#1782 | 2 |
| C5×#1511 | 2 |
| C5×#1510 | 2 |
| C5×#1306 | 2 |
| #9981 | 5 |