Finite Group Databasebeta

← C26×C3×C53 #72201294

Subgroups — C26×C3×C53 #72201294

Order 24000.

361600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C3×C53C2163yesmaximal, direct product factor
2C26×C53C311yesmaximal, characteristic, direct product factor, Hall
3C24×C3×C53C221651yesdirect product factor
4C26×C3×C52C5131yesmaximal, direct product factor
5C25×C53C2×C3163yesdirect product factor
6C23×C3×C53C2311395yesdirect product factor
7C25×C3×C52C2×C511953yesdirect product factor
8C24×C53C22×C31651yesdirect product factor
9C26×C52C3×C5131yesdirect product factor
10C22×C3×C53C241651yesdirect product factor
11C24×C3×C52C22×C5120181yesdirect product factor
12C23×C53C23×C311395yesdirect product factor
13C26×C3×C5C52131yesdirect product factor
14C25×C52C2×C3×C511953yesdirect product factor
15C2×C3×C53C25163yesdirect product factor
16C23×C3×C52C23×C5143245yesdirect product factor
17C22×C53C24×C31651yesdirect product factor
18C25×C3×C5C2×C5211953yesdirect product factor
19C24×C52C22×C3×C5120181yesdirect product factor
20C3×C53C2611yescharacteristic, direct product factor, Hall
21C26×C5C3×C52131yesdirect product factor
22C22×C3×C52C24×C5120181yesdirect product factor
23C2×C53C25×C3163yesdirect product factor
24C24×C3×C5C22×C52120181yesdirect product factor
25C23×C52C23×C3×C5143245yesdirect product factor
26C26×C3C5311yescharacteristic, direct product factor, Hall
27C25×C5C2×C3×C5211953yesdirect product factor
28C2×C3×C52C25×C511953yesdirect product factor
29C53C26×C311yescharacteristic, direct product factor, Sylow
30C23×C3×C5C23×C52143245yesdirect product factor
31C22×C52C24×C3×C5120181yesdirect product factor
32C25×C3C2×C53163yesdirect product factor
33C24×C5C22×C3×C52120181yesdirect product factor
34C3×C52C26×C5131yesdirect product factor
35C26C3×C5311yescharacteristic, direct product factor, Sylow
36C22×C3×C5C24×C52120181yesdirect product factor
37C2×C52C25×C3×C511953yesdirect product factor
38C24×C3C22×C531651yesdirect product factor
39C23×C5C23×C3×C52143245yesdirect product factor
40C25C2×C3×C53163yesdirect product factor
41C2×C3×C5C25×C5211953yesdirect product factor
42C52C26×C3×C5131yesdirect product factor
43C23×C3C23×C5311395yesdirect product factor
44C22×C5C24×C3×C52120181yesdirect product factor
45C24C22×C3×C531651yesdirect product factor
46C3×C5C26×C52131yesdirect product factor
47C22×C3C24×C531651yesdirect product factor
48C2×C5C25×C3×C5211953yesdirect product factor
49C23C23×C3×C5311395yesdirect product factor
50C2×C3C25×C53163yesdirect product factor
51C5C26×C3×C52131yesdirect product factor
52C22C24×C3×C531651yesdirect product factor
53C3C26×C5311yescharacteristic, direct product factor, Sylow
54C2C25×C3×C53163yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C25×C3×C53C2direct (N × H)
2. C26×C53C3direct (N × H)
3. C24×C3×C53C22direct (N × H)
4. C26×C3×C52C5direct (N × H)
5. C25×C53C2×C3direct (N × H)
6. C23×C3×C53C23direct (N × H)
7. C25×C3×C52C2×C5direct (N × H)
8. C24×C53C22×C3direct (N × H)
9. C26×C52C3×C5direct (N × H)
10. C22×C3×C53C24direct (N × H)
11. C24×C3×C52C22×C5direct (N × H)
12. C23×C53C23×C3direct (N × H)
13. C26×C3×C5C52direct (N × H)
14. C25×C52C2×C3×C5direct (N × H)
15. C2×C3×C53C25direct (N × H)
16. C23×C3×C52C23×C5direct (N × H)
17. C22×C53C24×C3direct (N × H)
18. C25×C3×C5C2×C52direct (N × H)
19. C24×C52C22×C3×C5direct (N × H)
20. C3×C53C26direct (N × H)
21. C26×C5C3×C52direct (N × H)
22. C22×C3×C52C24×C5direct (N × H)
23. C2×C53C25×C3direct (N × H)
24. C24×C3×C5C22×C52direct (N × H)
25. C23×C52C23×C3×C5direct (N × H)
26. C26×C3C53direct (N × H)
27. C25×C5C2×C3×C52direct (N × H)
28. C2×C3×C52C25×C5direct (N × H)
29. C53C26×C3direct (N × H)
30. C23×C3×C5C23×C52direct (N × H)
31. C22×C52C24×C3×C5direct (N × H)
32. C25×C3C2×C53direct (N × H)
33. C24×C5C22×C3×C52direct (N × H)
34. C3×C52C26×C5direct (N × H)
35. C26C3×C53direct (N × H)
36. C22×C3×C5C24×C52direct (N × H)
37. C2×C52C25×C3×C5direct (N × H)
38. C24×C3C22×C53direct (N × H)
39. C23×C5C23×C3×C52direct (N × H)
40. C25C2×C3×C53direct (N × H)
41. C2×C3×C5C25×C52direct (N × H)
42. C52C26×C3×C5direct (N × H)
43. C23×C3C23×C53direct (N × H)
44. C22×C5C24×C3×C52direct (N × H)
45. C24C22×C3×C53direct (N × H)
46. C3×C5C26×C52direct (N × H)
47. C22×C3C24×C53direct (N × H)
48. C2×C5C25×C3×C52direct (N × H)
49. C23C23×C3×C53direct (N × H)
50. C2×C3C25×C53direct (N × H)
51. C5C26×C3×C52direct (N × H)
52. C22C24×C3×C53direct (N × H)
53. C3C26×C53direct (N × H)
54. C2C25×C3×C53direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C25×C3×C532
C26×C533
C26×C3×C525