Finite Group Databasebeta

← C25×C4×C5×C29 #72196370

Subgroups — C25×C4×C5×C29 #72196370

Order 18560.

21104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×C5×C29C2162yesmaximal, direct product factor
2C26×C5×C29C211yesmaximal, characteristic
3C23×C4×C5×C29C221620yesdirect product factor
4C25×C5×C29C4132yesdirect product factor
5C25×C5×C29C22131yes—
6C24×C5×C29C2×C41496yesdirect product factor
7C24×C5×C29C231155yes—
8C22×C4×C5×C29C2311240yesdirect product factor
9C25×C4×C29C511yesmaximal, characteristic, direct product factor, Hall
10C26×C29C2×C511yescharacteristic
11C24×C4×C29C2×C5162yesdirect product factor
12C23×C5×C29C22×C411240yesdirect product factor
13C23×C5×C29C241155yes—
14C2×C4×C5×C29C241496yesdirect product factor
15C25×C29C4×C5132yesdirect product factor
16C25×C29C22×C5131yes—
17C23×C4×C29C22×C51620yesdirect product factor
18C25×C4×C5C2911yesmaximal, characteristic, direct product factor, Hall
19C22×C5×C29C23×C41620yesdirect product factor
20C22×C5×C29C25131yes—
21C4×C5×C29C25132yesdirect product factor
22C24×C29C2×C4×C51496yesdirect product factor
23C24×C29C23×C51155yes—
24C22×C4×C29C23×C511240yesdirect product factor
25C26×C5C2×C2911yescharacteristic
26C24×C4×C5C2×C29162yesdirect product factor
27C2×C5×C29C24×C4162yesdirect product factor
28C2×C5×C29C2611yescharacteristic
29C23×C29C22×C4×C511240yesdirect product factor
30C23×C29C24×C51155yes—
31C2×C4×C29C24×C51496yesdirect product factor
32C25×C5C4×C29132yesdirect product factor
33C25×C5C22×C29131yes—
34C23×C4×C5C22×C291620yesdirect product factor
35C5×C29C25×C411yescharacteristic, direct product factor, Hall
36C25×C4C5×C2911yescharacteristic, direct product factor, Sylow
37C22×C29C23×C4×C51620yesdirect product factor
38C22×C29C25×C5131yes—
39C4×C29C25×C5132yesdirect product factor
40C24×C5C2×C4×C291496yesdirect product factor
41C24×C5C23×C291155yes—
42C22×C4×C5C23×C2911240yesdirect product factor
43C26C2×C5×C2911yescharacteristic
44C24×C4C2×C5×C29162yesdirect product factor
45C2×C29C24×C4×C5162yesdirect product factor
46C2×C29C26×C511yescharacteristic
47C23×C5C22×C4×C2911240yesdirect product factor
48C23×C5C24×C291155yes—
49C2×C4×C5C24×C291496yesdirect product factor
50C25C4×C5×C29132yesdirect product factor
51C25C22×C5×C29131yes—
52C23×C4C22×C5×C291620yesdirect product factor
53C29C25×C4×C511yescharacteristic, direct product factor, Sylow
54C22×C5C23×C4×C291620yesdirect product factor
55C22×C5C25×C29131yes—
56C4×C5C25×C29132yesdirect product factor
57C24C2×C4×C5×C291496yesdirect product factor
58C24C23×C5×C291155yes—
59C22×C4C23×C5×C2911240yesdirect product factor
60C2×C5C24×C4×C29162yesdirect product factor
61C2×C5C26×C2911yescharacteristic
62C23C22×C4×C5×C2911240yesdirect product factor
63C23C24×C5×C291155yes—
64C2×C4C24×C5×C291496yesdirect product factor
65C5C25×C4×C2911yescharacteristic, direct product factor, Sylow
66C22C25×C5×C29131yes—
67C22C23×C4×C5×C291620yesdirect product factor
68C4C25×C5×C29132yesdirect product factor
69C2C26×C5×C2911yescharacteristic
70C2C24×C4×C5×C29162yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C26×C5×C29
socle, prime radicalC26×C5×C29C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×C4×C5×C29C2direct (N × H)
3. C23×C4×C5×C29C22direct (N × H)
4. C25×C5×C29C4direct (N × H)
6. C24×C5×C29C2×C4direct (N × H)
8. C22×C4×C5×C29C23direct (N × H)
9. C25×C4×C29C5direct (N × H)
11. C24×C4×C29C2×C5direct (N × H)
12. C23×C5×C29C22×C4direct (N × H)
14. C2×C4×C5×C29C24direct (N × H)
15. C25×C29C4×C5direct (N × H)
17. C23×C4×C29C22×C5direct (N × H)
18. C25×C4×C5C29direct (N × H)
19. C22×C5×C29C23×C4direct (N × H)
21. C4×C5×C29C25direct (N × H)
22. C24×C29C2×C4×C5direct (N × H)
24. C22×C4×C29C23×C5direct (N × H)
26. C24×C4×C5C2×C29direct (N × H)
27. C2×C5×C29C24×C4direct (N × H)
29. C23×C29C22×C4×C5direct (N × H)
31. C2×C4×C29C24×C5direct (N × H)
32. C25×C5C4×C29direct (N × H)
34. C23×C4×C5C22×C29direct (N × H)
35. C5×C29C25×C4direct (N × H)
36. C25×C4C5×C29direct (N × H)
37. C22×C29C23×C4×C5direct (N × H)
39. C4×C29C25×C5direct (N × H)
40. C24×C5C2×C4×C29direct (N × H)
42. C22×C4×C5C23×C29direct (N × H)
44. C24×C4C2×C5×C29direct (N × H)
45. C2×C29C24×C4×C5direct (N × H)
47. C23×C5C22×C4×C29direct (N × H)
49. C2×C4×C5C24×C29direct (N × H)
50. C25C4×C5×C29direct (N × H)
52. C23×C4C22×C5×C29direct (N × H)
53. C29C25×C4×C5direct (N × H)
54. C22×C5C23×C4×C29direct (N × H)
56. C4×C5C25×C29direct (N × H)
57. C24C2×C4×C5×C29direct (N × H)
59. C22×C4C23×C5×C29direct (N × H)
60. C2×C5C24×C4×C29direct (N × H)
62. C23C22×C4×C5×C29direct (N × H)
64. C2×C4C24×C5×C29direct (N × H)
65. C5C25×C4×C29direct (N × H)
67. C22C23×C4×C5×C29direct (N × H)
68. C4C25×C5×C29direct (N × H)
70. C2C24×C4×C5×C29direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×C5×C292
C26×C5×C292
C25×C4×C295
C25×C4×C529