Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
3376 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 3376 conjugacy classes of subgroups — too many to draw. Only its 395 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11717517 | C2 | semidirect |
| 2. C2×#11717260 | C2 | semidirect |
| 3. C2×#11717228 | C2 | semidirect |
| 4. C2×C52×#100 | C2 | semidirect |
| 5. C2×#11716692 | C2 | semidirect |
| 6. #13102610 | C2 | direct (N × H) |
| 12. #11717517 | C22 | semidirect |
| 16. C22×C4⋊(C5⋊D5) | C22 | semidirect |
| 17. C2×C52×M16 | C22 | semidirect |
| 19. #11717260 | C22 | semidirect |
| 20. C2×C4×#1039 | C22 | semidirect |
| 22. #11717228 | C22 | semidirect |
| 25. C52×#100 | C22 | semidirect |
| 26. #11716692 | C22 | semidirect |
| 50. #87900 | D4 | semidirect |
| 55. C2×C4⋊(C5⋊D5) | D4 | semidirect |
| 56. C2×C4⋊(C5⋊D5) | C23 | semidirect |
| 58. C2×#6045 | D4 | semidirect |
| 60. C52×M16 | C23 | semidirect |
| 63. C4×#1039 | C23 | semidirect |
| 69. C2×C5×#100 | D5 | semidirect |
| 101. C4⋊(C5⋊D5) | C2×D4 | semidirect |
| 105. #6045 | C2×D4 | semidirect |
| 117. C2×C5×M16 | C2×D5 | semidirect |
| 125. C5×#100 | C2×D5 | semidirect |
| 179. C5×M16 | C22×D5 | semidirect |
| 190. C2×#100 | C5⋊D5 | semidirect |
| 194. C2×C52 | #453 | semidirect |
| 247. C2×M16 | C2×C5⋊D5 | semidirect |
| 252. #100 | C2×C5⋊D5 | semidirect |
| 253. C52 | C2×#453 | semidirect |
| 307. M16 | C22×C5⋊D5 | semidirect |
| 314. C2×C5 | #65036 | semidirect |
| 353. C5 | C2×#65036 | semidirect |
| 378. C2 | #13102610 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717517 | 2 |
| C2×#11717260 | 2 |
| C2×#11717228 | 2 |
| C2×C52×#100 | 2 |
| C2×#11716692 | 2 |
| #13102610 | 2 |
| C2×#65036 | 5 |