Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
576 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 144 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×C5×Q8×D5 | C2 | semidirect |
| 3. C2×#87812 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. #11717064 | C2 | direct (N × H) |
| 6. C2×#87776 | C2 | semidirect |
| 7. C2×#87772 | C2 | semidirect |
| 8. C2×#87768 | C2 | semidirect |
| 12. C5×Q8×D5 | C22 | semidirect |
| 22. #87812 | C22 | semidirect |
| 24. C5×#688 | C22 | semidirect |
| 26. #87776 | C22 | semidirect |
| 27. #87772 | C22 | semidirect |
| 28. #87768 | C22 | semidirect |
| 55. C2×Q8×D5 | D5 | semidirect |
| 65. C2×#688 | D5 | semidirect |
| 96. Q8×D5 | C2×D5 | semidirect |
| 117. #688 | C2×D5 | semidirect |
| 127. C2×C52 | #137 | semidirect |
| 193. C52 | C2×#137 | semidirect |
| 245. C2×C5 | #4061 | semidirect |
| 246. C2×C5 | #4088 | semidirect |
| 275. C5 | C2×#4061 | semidirect |
| 276. C5 | C2×#4088 | semidirect |
| 290. C2 | #11717064 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×#87870 | 2 |
| C2×#87812 | 2 |
| C2×C5×#688 | 2 |
| #11717064 | 2 |
| C2×#87776 | 2 |
| C2×#87772 | 2 |
| C2×#87768 | 2 |
| C2×#4088 | 5 |
| C2×#4061 | 5 |