Finite Group Databasebeta

← C24×C4×C52×C9 #72192575

Subgroups — C24×C4×C52×C9 #72192575

Order 14400.

16344 conjugacy classes of subgroups.

The subgroup lattice has 135 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C52×C9C211yesmaximal, characteristic
2C23×C4×C52×C9C2130yesmaximal, direct product factor
3C24×C3×C4×C52C311yesmaximal, characteristic
4C24×C52×C9C4116yesdirect product factor
5C24×C52×C9C22115yes—
6C22×C4×C52×C9C221140yesdirect product factor
7C24×C4×C5×C9C516yesmaximal, direct product factor
8C25×C3×C52C2×C311yescharacteristic
9C23×C3×C4×C52C2×C3130yes—
10C23×C52×C9C2×C41120yesdirect product factor
11C23×C52×C9C23135yes—
12C2×C4×C52×C9C231120yesdirect product factor
13C24×C4×C52C911yescharacteristic, direct product factor, Hall
14C25×C5×C9C2×C516yes—
15C23×C4×C5×C9C2×C51180yesdirect product factor
16C24×C3×C52C3×C4116yes—
17C24×C3×C52C22×C3115yes—
18C22×C3×C4×C52C22×C31140yes—
19C24×C3×C4×C5C3×C516yes—
20C22×C52×C9C22×C41140yesdirect product factor
21C22×C52×C9C24115yes—
22C4×C52×C9C24116yesdirect product factor
23C25×C52C2×C911yescharacteristic
24C23×C4×C52C2×C9130yesdirect product factor
25C24×C5×C9C4×C5196yesdirect product factor
26C24×C5×C9C22×C5190yes—
27C22×C4×C5×C9C22×C51840yesdirect product factor
28C23×C3×C52C2×C3×C41120yes—
29C23×C3×C52C23×C3135yes—
30C2×C3×C4×C52C23×C31120yes—
31C24×C4×C9C5211yescharacteristic, direct product factor, Hall
32C25×C3×C5C2×C3×C516yes—
33C23×C3×C4×C5C2×C3×C51180yes—
34C2×C52×C9C23×C4130yesdirect product factor
35C2×C52×C9C2511yescharacteristic
36C24×C52C4×C9116yesdirect product factor
37C24×C52C22×C9115yes—
38C22×C4×C52C22×C91140yesdirect product factor
39C23×C5×C9C2×C4×C51720yesdirect product factor
40C23×C5×C9C23×C51210yes—
41C2×C4×C5×C9C23×C51720yesdirect product factor
42C24×C4×C5C5×C916yesdirect product factor
43C22×C3×C52C22×C3×C41140yes—
44C22×C3×C52C24×C3115yes—
45C3×C4×C52C24×C3116yes—
46C25×C9C2×C5211yescharacteristic
47C23×C4×C9C2×C52130yesdirect product factor
48C24×C3×C5C3×C4×C5196yes—
49C24×C3×C5C22×C3×C5190yes—
50C22×C3×C4×C5C22×C3×C51840yes—
51C52×C9C24×C411yescharacteristic, direct product factor, Hall
52C23×C52C2×C4×C91120yesdirect product factor
53C23×C52C23×C9135yes—
54C2×C4×C52C23×C91120yesdirect product factor
55C24×C3×C4C3×C5211yescharacteristic
56C22×C5×C9C22×C4×C51840yesdirect product factor
57C22×C5×C9C24×C5190yes—
58C4×C5×C9C24×C5196yesdirect product factor
59C25×C5C2×C5×C916yes—
60C23×C4×C5C2×C5×C91180yesdirect product factor
61C2×C3×C52C23×C3×C4130yes—
62C2×C3×C52C25×C311yescharacteristic
63C24×C9C4×C52116yesdirect product factor
64C24×C9C22×C52115yes—
65C22×C4×C9C22×C521140yesdirect product factor
66C23×C3×C5C2×C3×C4×C51720yes—
67C23×C3×C5C23×C3×C51210yes—
68C2×C3×C4×C5C23×C3×C51720yes—
69C22×C52C22×C4×C91140yesdirect product factor
70C22×C52C24×C9115yes—
71C4×C52C24×C9116yesdirect product factor
72C25×C3C2×C3×C5211yescharacteristic
73C23×C3×C4C2×C3×C52130yes—
74C2×C5×C9C23×C4×C51180yesdirect product factor
75C2×C5×C9C25×C516yes—
76C24×C5C4×C5×C9196yesdirect product factor
77C24×C5C22×C5×C9190yes—
78C22×C4×C5C22×C5×C91840yesdirect product factor
79C3×C52C24×C3×C411yescharacteristic
80C23×C9C2×C4×C521120yesdirect product factor
81C23×C9C23×C52135yes—
82C2×C4×C9C23×C521120yesdirect product factor
83C24×C4C52×C911yescharacteristic, direct product factor, Sylow
84C22×C3×C5C22×C3×C4×C51840yes—
85C22×C3×C5C24×C3×C5190yes—
86C3×C4×C5C24×C3×C5196yes—
87C2×C52C23×C4×C9130yesdirect product factor
88C2×C52C25×C911yescharacteristic
89C24×C3C3×C4×C52116yes—
90C24×C3C22×C3×C52115yes—
91C22×C3×C4C22×C3×C521140yes—
92C5×C9C24×C4×C516yesdirect product factor
93C23×C5C2×C4×C5×C91720yesdirect product factor
94C23×C5C23×C5×C91210yes—
95C2×C4×C5C23×C5×C91720yesdirect product factor
96C22×C9C22×C4×C521140yesdirect product factor
97C22×C9C24×C52115yes—
98C4×C9C24×C52116yesdirect product factor
99C25C2×C52×C911yescharacteristic
100C23×C4C2×C52×C9130yesdirect product factor
101C2×C3×C5C23×C3×C4×C51180yes—
102C2×C3×C5C25×C3×C516yes—
103C52C24×C4×C911yescharacteristic, direct product factor, Sylow
104C23×C3C2×C3×C4×C521120yes—
105C23×C3C23×C3×C52135yes—
106C2×C3×C4C23×C3×C521120yes—
107C22×C5C22×C4×C5×C91840yesdirect product factor
108C22×C5C24×C5×C9190yes—
109C4×C5C24×C5×C9196yesdirect product factor
110C2×C9C23×C4×C52130yesdirect product factor
111C2×C9C25×C5211yescharacteristic
112C24C4×C52×C9116yesdirect product factor
113C24C22×C52×C9115yes—
114C22×C4C22×C52×C91140yesdirect product factor
115C3×C5C24×C3×C4×C516yes—
116C22×C3C22×C3×C4×C521140yes—
117C22×C3C24×C3×C52115yes—
118C3×C4C24×C3×C52116yes—
119C2×C5C23×C4×C5×C91180yesdirect product factor
120C2×C5C25×C5×C916yes—
121C9C24×C4×C5211yescharacteristic, direct product factor, Sylow
122C23C2×C4×C52×C91120yesdirect product factor
123C23C23×C52×C9135yes—
124C2×C4C23×C52×C91120yesdirect product factor
125C2×C3C23×C3×C4×C52130yes—
126C2×C3C25×C3×C5211yescharacteristic
127C5C24×C4×C5×C916yesdirect product factor
128C22C22×C4×C52×C91140yesdirect product factor
129C22C24×C52×C9115yes—
130C4C24×C52×C9116yesdirect product factor
131C3C24×C3×C4×C5211yescharacteristic
132C2C23×C4×C52×C9130yesdirect product factor
133C2C25×C52×C911yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C25×C3×C52
socle, prime radicalC25×C3×C52C2×C3
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4×C52×C9C2direct (N × H)
4. C24×C52×C9C4direct (N × H)
6. C22×C4×C52×C9C22direct (N × H)
7. C24×C4×C5×C9C5direct (N × H)
10. C23×C52×C9C2×C4direct (N × H)
12. C2×C4×C52×C9C23direct (N × H)
13. C24×C4×C52C9direct (N × H)
15. C23×C4×C5×C9C2×C5direct (N × H)
20. C22×C52×C9C22×C4direct (N × H)
22. C4×C52×C9C24direct (N × H)
24. C23×C4×C52C2×C9direct (N × H)
25. C24×C5×C9C4×C5direct (N × H)
27. C22×C4×C5×C9C22×C5direct (N × H)
31. C24×C4×C9C52direct (N × H)
34. C2×C52×C9C23×C4direct (N × H)
36. C24×C52C4×C9direct (N × H)
38. C22×C4×C52C22×C9direct (N × H)
39. C23×C5×C9C2×C4×C5direct (N × H)
41. C2×C4×C5×C9C23×C5direct (N × H)
42. C24×C4×C5C5×C9direct (N × H)
47. C23×C4×C9C2×C52direct (N × H)
51. C52×C9C24×C4direct (N × H)
52. C23×C52C2×C4×C9direct (N × H)
54. C2×C4×C52C23×C9direct (N × H)
56. C22×C5×C9C22×C4×C5direct (N × H)
58. C4×C5×C9C24×C5direct (N × H)
60. C23×C4×C5C2×C5×C9direct (N × H)
63. C24×C9C4×C52direct (N × H)
65. C22×C4×C9C22×C52direct (N × H)
69. C22×C52C22×C4×C9direct (N × H)
71. C4×C52C24×C9direct (N × H)
74. C2×C5×C9C23×C4×C5direct (N × H)
76. C24×C5C4×C5×C9direct (N × H)
78. C22×C4×C5C22×C5×C9direct (N × H)
80. C23×C9C2×C4×C52direct (N × H)
82. C2×C4×C9C23×C52direct (N × H)
83. C24×C4C52×C9direct (N × H)
87. C2×C52C23×C4×C9direct (N × H)
92. C5×C9C24×C4×C5direct (N × H)
93. C23×C5C2×C4×C5×C9direct (N × H)
95. C2×C4×C5C23×C5×C9direct (N × H)
96. C22×C9C22×C4×C52direct (N × H)
98. C4×C9C24×C52direct (N × H)
100. C23×C4C2×C52×C9direct (N × H)
103. C52C24×C4×C9direct (N × H)
107. C22×C5C22×C4×C5×C9direct (N × H)
109. C4×C5C24×C5×C9direct (N × H)
110. C2×C9C23×C4×C52direct (N × H)
112. C24C4×C52×C9direct (N × H)
114. C22×C4C22×C52×C9direct (N × H)
119. C2×C5C23×C4×C5×C9direct (N × H)
121. C9C24×C4×C52direct (N × H)
122. C23C2×C4×C52×C9direct (N × H)
124. C2×C4C23×C52×C9direct (N × H)
127. C5C24×C4×C5×C9direct (N × H)
128. C22C22×C4×C52×C9direct (N × H)
130. C4C24×C52×C9direct (N × H)
132. C2C23×C4×C52×C9direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C52×C92
C23×C4×C52×C92
C24×C3×C4×C523
C24×C4×C5×C95