Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
630 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 74 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C22⋊C4 | C23×C5 |
| LCS | G ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C5 ◁ C23×C5 ◁ C2×C5×C22⋊C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2812 | C2 | semidirect |
| 2. C5×#2021 | C2 | semidirect |
| 3. C5×#1607 | C2 | semidirect |
| 4. C5×#1595 | C2 | semidirect |
| 5. C5×#1344 | C2 | semidirect |
| 6. C5×#1343 | C2 | semidirect |
| 7. C5×#1316 | C2 | semidirect |
| 27. #12093 | C5 | direct (N × H) |
| 34. C22×C5×D4 | D4 | semidirect |
| 45. C2×C5×C4⋊C4 | D4 | semidirect |
| 66. C5×#95 | D4 | semidirect |
| 67. C5×#95 | D4 | semidirect |
| 68. #2812 | C2×C5 | semidirect |
| 69. #2021 | C2×C5 | semidirect |
| 70. #1607 | C2×C5 | semidirect |
| 71. #1595 | C2×C5 | semidirect |
| 72. #1344 | C2×C5 | semidirect |
| 73. #1343 | C2×C5 | semidirect |
| 74. #1316 | C2×C5 | semidirect |
| 83. C24×C5 | D8 | semidirect |
| 236. C22×D4 | C5×D4 | semidirect |
| 247. C2×C4⋊C4 | C5×D4 | semidirect |
| 268. #95 | C5×D4 | semidirect |
| 269. #95 | C5×D4 | semidirect |
| 321. C24 | C5×D8 | semidirect |
| 459. C5 | #12093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2812 | 2 |
| C5×#2021 | 2 |
| C5×#1607 | 2 |
| C5×#1595 | 2 |
| C5×#1344 | 2 |
| C5×#1343 | 2 |
| C5×#1316 | 2 |
| #12093 | 5 |