Finite Group Databasebeta

← C24×C32×C4×C25 #72192576

Subgroups — C24×C32×C4×C25 #72192576

Order 14400.

12258 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×C32×C25C211yesmaximal, characteristic
2C23×C32×C4×C25C2130yesmaximal, direct product factor
3C24×C3×C4×C25C314yesmaximal, direct product factor
4C24×C32×C25C4116yesdirect product factor
5C24×C32×C25C22115yes—
6C22×C32×C4×C25C221140yesdirect product factor
7C24×C32×C4×C5C511yesmaximal, characteristic
8C25×C3×C25C2×C314yes—
9C23×C3×C4×C25C2×C31120yesdirect product factor
10C23×C32×C25C2×C41120yesdirect product factor
11C23×C32×C25C23135yes—
12C2×C32×C4×C25C231120yesdirect product factor
13C24×C4×C25C3211yescharacteristic, direct product factor, Hall
14C25×C32×C5C2×C511yescharacteristic
15C23×C32×C4×C5C2×C5130yes—
16C24×C3×C25C3×C4164yesdirect product factor
17C24×C3×C25C22×C3160yes—
18C22×C3×C4×C25C22×C31560yesdirect product factor
19C24×C3×C4×C5C3×C514yes—
20C22×C32×C25C22×C41140yesdirect product factor
21C22×C32×C25C24115yes—
22C32×C4×C25C24116yesdirect product factor
23C25×C25C2×C3211yescharacteristic
24C23×C4×C25C2×C32130yesdirect product factor
25C24×C32×C5C4×C5116yes—
26C24×C32×C5C22×C5115yes—
27C22×C32×C4×C5C22×C51140yes—
28C23×C3×C25C2×C3×C41480yesdirect product factor
29C23×C3×C25C23×C31140yes—
30C2×C3×C4×C25C23×C31480yesdirect product factor
31C24×C32×C4C2511yescharacteristic, direct product factor, Hall
32C25×C3×C5C2×C3×C514yes—
33C23×C3×C4×C5C2×C3×C51120yes—
34C2×C32×C25C23×C4130yesdirect product factor
35C2×C32×C25C2511yescharacteristic
36C24×C25C32×C4116yesdirect product factor
37C24×C25C22×C32115yes—
38C22×C4×C25C22×C321140yesdirect product factor
39C23×C32×C5C2×C4×C51120yes—
40C23×C32×C5C23×C5135yes—
41C2×C32×C4×C5C23×C51120yes—
42C24×C4×C5C32×C511yescharacteristic
43C22×C3×C25C22×C3×C41560yesdirect product factor
44C22×C3×C25C24×C3160yes—
45C3×C4×C25C24×C3164yesdirect product factor
46C25×C32C2×C2511yescharacteristic
47C23×C32×C4C2×C25130yesdirect product factor
48C24×C3×C5C3×C4×C5164yes—
49C24×C3×C5C22×C3×C5160yes—
50C22×C3×C4×C5C22×C3×C51560yes—
51C32×C25C24×C411yescharacteristic, direct product factor, Hall
52C23×C25C2×C32×C41120yesdirect product factor
53C23×C25C23×C32135yes—
54C2×C4×C25C23×C321120yesdirect product factor
55C24×C3×C4C3×C2514yesdirect product factor
56C22×C32×C5C22×C4×C51140yes—
57C22×C32×C5C24×C5115yes—
58C32×C4×C5C24×C5116yes—
59C25×C5C2×C32×C511yescharacteristic
60C23×C4×C5C2×C32×C5130yes—
61C2×C3×C25C23×C3×C41120yesdirect product factor
62C2×C3×C25C25×C314yes—
63C24×C32C4×C25116yesdirect product factor
64C24×C32C22×C25115yes—
65C22×C32×C4C22×C251140yesdirect product factor
66C23×C3×C5C2×C3×C4×C51480yes—
67C23×C3×C5C23×C3×C51140yes—
68C2×C3×C4×C5C23×C3×C51480yes—
69C22×C25C22×C32×C41140yesdirect product factor
70C22×C25C24×C32115yes—
71C4×C25C24×C32116yesdirect product factor
72C25×C3C2×C3×C2514yes—
73C23×C3×C4C2×C3×C251120yesdirect product factor
74C2×C32×C5C23×C4×C5130yes—
75C2×C32×C5C25×C511yescharacteristic
76C24×C5C32×C4×C5116yes—
77C24×C5C22×C32×C5115yes—
78C22×C4×C5C22×C32×C51140yes—
79C3×C25C24×C3×C414yesdirect product factor
80C23×C32C2×C4×C251120yesdirect product factor
81C23×C32C23×C25135yes—
82C2×C32×C4C23×C251120yesdirect product factor
83C24×C4C32×C2511yescharacteristic, direct product factor, Sylow
84C22×C3×C5C22×C3×C4×C51560yes—
85C22×C3×C5C24×C3×C5160yes—
86C3×C4×C5C24×C3×C5164yes—
87C2×C25C23×C32×C4130yesdirect product factor
88C2×C25C25×C3211yescharacteristic
89C24×C3C3×C4×C25164yesdirect product factor
90C24×C3C22×C3×C25160yes—
91C22×C3×C4C22×C3×C251560yesdirect product factor
92C32×C5C24×C4×C511yescharacteristic
93C23×C5C2×C32×C4×C51120yes—
94C23×C5C23×C32×C5135yes—
95C2×C4×C5C23×C32×C51120yes—
96C22×C32C22×C4×C251140yesdirect product factor
97C22×C32C24×C25115yes—
98C32×C4C24×C25116yesdirect product factor
99C25C2×C32×C2511yescharacteristic
100C23×C4C2×C32×C25130yesdirect product factor
101C2×C3×C5C23×C3×C4×C51120yes—
102C2×C3×C5C25×C3×C514yes—
103C25C24×C32×C411yescharacteristic, direct product factor, Sylow
104C23×C3C2×C3×C4×C251480yesdirect product factor
105C23×C3C23×C3×C251140yes—
106C2×C3×C4C23×C3×C251480yesdirect product factor
107C22×C5C22×C32×C4×C51140yes—
108C22×C5C24×C32×C5115yes—
109C4×C5C24×C32×C5116yes—
110C2×C32C23×C4×C25130yesdirect product factor
111C2×C32C25×C2511yescharacteristic
112C24C32×C4×C25116yesdirect product factor
113C24C22×C32×C25115yes—
114C22×C4C22×C32×C251140yesdirect product factor
115C3×C5C24×C3×C4×C514yes—
116C22×C3C22×C3×C4×C251560yesdirect product factor
117C22×C3C24×C3×C25160yes—
118C3×C4C24×C3×C25164yesdirect product factor
119C2×C5C23×C32×C4×C5130yes—
120C2×C5C25×C32×C511yescharacteristic
121C32C24×C4×C2511yescharacteristic, direct product factor, Sylow
122C23C2×C32×C4×C251120yesdirect product factor
123C23C23×C32×C25135yes—
124C2×C4C23×C32×C251120yesdirect product factor
125C2×C3C23×C3×C4×C251120yesdirect product factor
126C2×C3C25×C3×C2514yes—
127C5C24×C32×C4×C511yescharacteristic
128C22C22×C32×C4×C251140yesdirect product factor
129C22C24×C32×C25115yes—
130C4C24×C32×C25116yesdirect product factor
131C3C24×C3×C4×C2514yesdirect product factor
132C2C23×C32×C4×C25130yesdirect product factor
133C2C25×C32×C2511yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5C25×C32×C5
socle, prime radicalC25×C32×C5C2×C5
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C32×C4×C25C2direct (N × H)
3. C24×C3×C4×C25C3direct (N × H)
4. C24×C32×C25C4direct (N × H)
6. C22×C32×C4×C25C22direct (N × H)
9. C23×C3×C4×C25C2×C3direct (N × H)
10. C23×C32×C25C2×C4direct (N × H)
12. C2×C32×C4×C25C23direct (N × H)
13. C24×C4×C25C32direct (N × H)
16. C24×C3×C25C3×C4direct (N × H)
18. C22×C3×C4×C25C22×C3direct (N × H)
20. C22×C32×C25C22×C4direct (N × H)
22. C32×C4×C25C24direct (N × H)
24. C23×C4×C25C2×C32direct (N × H)
28. C23×C3×C25C2×C3×C4direct (N × H)
30. C2×C3×C4×C25C23×C3direct (N × H)
31. C24×C32×C4C25direct (N × H)
34. C2×C32×C25C23×C4direct (N × H)
36. C24×C25C32×C4direct (N × H)
38. C22×C4×C25C22×C32direct (N × H)
43. C22×C3×C25C22×C3×C4direct (N × H)
45. C3×C4×C25C24×C3direct (N × H)
47. C23×C32×C4C2×C25direct (N × H)
51. C32×C25C24×C4direct (N × H)
52. C23×C25C2×C32×C4direct (N × H)
54. C2×C4×C25C23×C32direct (N × H)
55. C24×C3×C4C3×C25direct (N × H)
61. C2×C3×C25C23×C3×C4direct (N × H)
63. C24×C32C4×C25direct (N × H)
65. C22×C32×C4C22×C25direct (N × H)
69. C22×C25C22×C32×C4direct (N × H)
71. C4×C25C24×C32direct (N × H)
73. C23×C3×C4C2×C3×C25direct (N × H)
79. C3×C25C24×C3×C4direct (N × H)
80. C23×C32C2×C4×C25direct (N × H)
82. C2×C32×C4C23×C25direct (N × H)
83. C24×C4C32×C25direct (N × H)
87. C2×C25C23×C32×C4direct (N × H)
89. C24×C3C3×C4×C25direct (N × H)
91. C22×C3×C4C22×C3×C25direct (N × H)
96. C22×C32C22×C4×C25direct (N × H)
98. C32×C4C24×C25direct (N × H)
100. C23×C4C2×C32×C25direct (N × H)
103. C25C24×C32×C4direct (N × H)
104. C23×C3C2×C3×C4×C25direct (N × H)
106. C2×C3×C4C23×C3×C25direct (N × H)
110. C2×C32C23×C4×C25direct (N × H)
112. C24C32×C4×C25direct (N × H)
114. C22×C4C22×C32×C25direct (N × H)
116. C22×C3C22×C3×C4×C25direct (N × H)
118. C3×C4C24×C3×C25direct (N × H)
121. C32C24×C4×C25direct (N × H)
122. C23C2×C32×C4×C25direct (N × H)
124. C2×C4C23×C32×C25direct (N × H)
125. C2×C3C23×C3×C4×C25direct (N × H)
128. C22C22×C32×C4×C25direct (N × H)
130. C4C24×C32×C25direct (N × H)
131. C3C24×C3×C4×C25direct (N × H)
132. C2C23×C32×C4×C25direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C32×C252
C23×C32×C4×C252
C24×C3×C4×C253
C24×C32×C4×C55