Finite Group Databasebeta

← C26×C5×C92 #72203113

Subgroups — C26×C5×C92 #72203113

Order 25920.

129950 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C5×C92C2163yesmaximal, direct product factor
2C26×C3×C5×C9C314yesmaximal
3C24×C5×C92C221651yesdirect product factor
4C26×C92C511yesmaximal, characteristic, direct product factor, Hall
5C25×C3×C5×C9C2×C31252yes—
6C23×C5×C92C2311395yesdirect product factor
7C26×C5×C9C9112yesdirect product factor
8C26×C32×C5C3211yescharacteristic
9C25×C92C2×C5163yesdirect product factor
10C24×C3×C5×C9C22×C312604yes—
11C26×C3×C9C3×C514yes—
12C22×C5×C92C241651yesdirect product factor
13C25×C32×C5C2×C32163yes—
14C25×C5×C9C2×C91756yesdirect product factor
15C24×C92C22×C51651yesdirect product factor
16C23×C3×C5×C9C23×C315580yes—
17C26×C3×C5C3×C914yes—
18C25×C3×C9C2×C3×C51252yes—
19C2×C5×C92C25163yesdirect product factor
20C24×C32×C5C22×C321651yes—
21C24×C5×C9C22×C917812yesdirect product factor
22C23×C92C23×C511395yesdirect product factor
23C26×C32C32×C511yescharacteristic
24C26×C9C5×C9112yesdirect product factor
25C22×C3×C5×C9C24×C312604yes—
26C25×C3×C5C2×C3×C91252yes—
27C24×C3×C9C22×C3×C512604yes—
28C5×C92C2611yescharacteristic, direct product factor, Hall
29C23×C32×C5C23×C3211395yes—
30C23×C5×C9C23×C9116740yesdirect product factor
31C22×C92C24×C51651yesdirect product factor
32C26×C5C9211yescharacteristic, direct product factor, Hall
33C25×C32C2×C32×C5163yes—
34C25×C9C2×C5×C91756yesdirect product factor
35C2×C3×C5×C9C25×C31252yes—
36C24×C3×C5C22×C3×C912604yes—
37C23×C3×C9C23×C3×C515580yes—
38C26×C3C3×C5×C914yes—
39C22×C32×C5C24×C321651yes—
40C22×C5×C9C24×C917812yesdirect product factor
41C2×C92C25×C5163yesdirect product factor
42C25×C5C2×C92163yesdirect product factor
43C24×C32C22×C32×C51651yes—
44C24×C9C22×C5×C917812yesdirect product factor
45C3×C5×C9C26×C314yes—
46C23×C3×C5C23×C3×C915580yes—
47C22×C3×C9C24×C3×C512604yes—
48C25×C3C2×C3×C5×C91252yes—
49C2×C32×C5C25×C32163yes—
50C2×C5×C9C25×C91756yesdirect product factor
51C92C26×C511yescharacteristic, direct product factor, Sylow
52C24×C5C22×C921651yesdirect product factor
53C23×C32C23×C32×C511395yes—
54C23×C9C23×C5×C9116740yesdirect product factor
55C26C5×C9211yescharacteristic, direct product factor, Sylow
56C22×C3×C5C24×C3×C912604yes—
57C2×C3×C9C25×C3×C51252yes—
58C24×C3C22×C3×C5×C912604yes—
59C32×C5C26×C3211yescharacteristic
60C5×C9C26×C9112yesdirect product factor
61C23×C5C23×C9211395yesdirect product factor
62C22×C32C24×C32×C51651yes—
63C22×C9C24×C5×C917812yesdirect product factor
64C25C2×C5×C92163yesdirect product factor
65C2×C3×C5C25×C3×C91252yes—
66C3×C9C26×C3×C514yes—
67C23×C3C23×C3×C5×C915580yes—
68C22×C5C24×C921651yesdirect product factor
69C2×C32C25×C32×C5163yes—
70C2×C9C25×C5×C91756yesdirect product factor
71C24C22×C5×C921651yesdirect product factor
72C3×C5C26×C3×C914yes—
73C22×C3C24×C3×C5×C912604yes—
74C2×C5C25×C92163yesdirect product factor
75C32C26×C32×C511yescharacteristic
76C9C26×C5×C9112yesdirect product factor
77C23C23×C5×C9211395yesdirect product factor
78C2×C3C25×C3×C5×C91252yes—
79C5C26×C9211yescharacteristic, direct product factor, Sylow
80C22C24×C5×C921651yesdirect product factor
81C3C26×C3×C5×C914yes—
82C2C25×C5×C92163yesdirect product factor
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC32C26×C32×C5
socle, prime radicalC26×C32×C5C32
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C25×C5×C92C2direct (N × H)
3. C24×C5×C92C22direct (N × H)
4. C26×C92C5direct (N × H)
6. C23×C5×C92C23direct (N × H)
7. C26×C5×C9C9direct (N × H)
9. C25×C92C2×C5direct (N × H)
12. C22×C5×C92C24direct (N × H)
14. C25×C5×C9C2×C9direct (N × H)
15. C24×C92C22×C5direct (N × H)
19. C2×C5×C92C25direct (N × H)
21. C24×C5×C9C22×C9direct (N × H)
22. C23×C92C23×C5direct (N × H)
24. C26×C9C5×C9direct (N × H)
28. C5×C92C26direct (N × H)
30. C23×C5×C9C23×C9direct (N × H)
31. C22×C92C24×C5direct (N × H)
32. C26×C5C92direct (N × H)
34. C25×C9C2×C5×C9direct (N × H)
40. C22×C5×C9C24×C9direct (N × H)
41. C2×C92C25×C5direct (N × H)
42. C25×C5C2×C92direct (N × H)
44. C24×C9C22×C5×C9direct (N × H)
50. C2×C5×C9C25×C9direct (N × H)
51. C92C26×C5direct (N × H)
52. C24×C5C22×C92direct (N × H)
54. C23×C9C23×C5×C9direct (N × H)
55. C26C5×C92direct (N × H)
60. C5×C9C26×C9direct (N × H)
61. C23×C5C23×C92direct (N × H)
63. C22×C9C24×C5×C9direct (N × H)
64. C25C2×C5×C92direct (N × H)
68. C22×C5C24×C92direct (N × H)
70. C2×C9C25×C5×C9direct (N × H)
71. C24C22×C5×C92direct (N × H)
74. C2×C5C25×C92direct (N × H)
76. C9C26×C5×C9direct (N × H)
77. C23C23×C5×C92direct (N × H)
79. C5C26×C92direct (N × H)
80. C22C24×C5×C92direct (N × H)
82. C2C25×C5×C92direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C5×C922
C26×C3×C5×C93
C26×C925