Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
404 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C5 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#3204 | C2 | semidirect |
| 2. C5×#2191 | C2 | semidirect |
| 3. C5×#2190 | C2 | semidirect |
| 4. C5×#2017 | C2 | semidirect |
| 5. C5×#1342 | C2 | semidirect |
| 6. C5×#1341 | C2 | semidirect |
| 7. C5×#1321 | C2 | semidirect |
| 27. #12119 | C5 | direct (N × H) |
| 71. #3204 | C2×C5 | semidirect |
| 72. #2191 | C2×C5 | semidirect |
| 73. #2190 | C2×C5 | semidirect |
| 74. #2017 | C2×C5 | semidirect |
| 75. #1342 | C2×C5 | semidirect |
| 76. #1341 | C2×C5 | semidirect |
| 77. #1321 | C2×C5 | semidirect |
| 355. C5 | #12119 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3204 | 2 |
| C5×#2191 | 2 |
| C5×#2190 | 2 |
| C5×#2017 | 2 |
| C5×#1342 | 2 |
| C5×#1341 | 2 |
| C5×#1321 | 2 |
| #12119 | 5 |