Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
598 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×C42 | C23×C5 |
| prime radical | C5×#3213 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#3152 | C2 | semidirect |
| 3. C5×#2640 | C2 | semidirect |
| 4. C5×#1558 | C2 | semidirect |
| 5. C5×#1527 | C2 | semidirect |
| 6. C5×#1505 | C2 | semidirect |
| 7. C5×#1300 | C2 | semidirect |
| 31. #10090 | C5 | direct (N × H) |
| 78. #3152 | C2×C5 | semidirect |
| 79. #2640 | C2×C5 | semidirect |
| 80. #1558 | C2×C5 | semidirect |
| 81. #1527 | C2×C5 | semidirect |
| 82. #1505 | C2×C5 | semidirect |
| 83. #1300 | C2×C5 | semidirect |
| 353. C5 | #10090 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3213 | 2 |
| C5×#3152 | 2 |
| C5×#2640 | 2 |
| C5×#1558 | 2 |
| C5×#1527 | 2 |
| C5×#1505 | 2 |
| C5×#1300 | 2 |
| #10090 | 5 |