Finite Group Databasebeta

← C24×C34×C4×C5 #72203110

Subgroups — C24×C34×C4×C5 #72203110

Order 25920.

288744 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C34×C5C211yesmaximal, characteristic
2C23×C34×C4×C5C2130yesmaximal, direct product factor
3C24×C33×C4×C5C3140yesmaximal, direct product factor
4C24×C34×C5C4116yesdirect product factor
5C24×C34×C5C22115yes—
6C22×C34×C4×C5C221140yesdirect product factor
7C24×C34×C4C511yesmaximal, characteristic, direct product factor, Hall
8C25×C33×C5C2×C3140yes—
9C23×C33×C4×C5C2×C311200yesdirect product factor
10C23×C34×C5C2×C41120yesdirect product factor
11C23×C34×C5C23135yes—
12C2×C34×C4×C5C231120yesdirect product factor
13C24×C32×C4×C5C321130yesdirect product factor
14C25×C34C2×C511yescharacteristic
15C23×C34×C4C2×C5130yesdirect product factor
16C24×C33×C5C3×C41640yesdirect product factor
17C24×C33×C5C22×C31600yes—
18C22×C33×C4×C5C22×C315600yesdirect product factor
19C24×C33×C4C3×C5140yesdirect product factor
20C22×C34×C5C22×C41140yesdirect product factor
21C22×C34×C5C24115yes—
22C34×C4×C5C24116yesdirect product factor
23C25×C32×C5C2×C321130yes—
24C23×C32×C4×C5C2×C3213900yesdirect product factor
25C24×C34C4×C5116yesdirect product factor
26C24×C34C22×C5115yes—
27C22×C34×C4C22×C51140yesdirect product factor
28C23×C33×C5C2×C3×C414800yesdirect product factor
29C23×C33×C5C23×C311400yes—
30C2×C33×C4×C5C23×C314800yesdirect product factor
31C24×C3×C4×C5C33140yesdirect product factor
32C25×C33C2×C3×C5140yes—
33C23×C33×C4C2×C3×C511200yesdirect product factor
34C2×C34×C5C23×C4130yesdirect product factor
35C2×C34×C5C2511yescharacteristic
36C24×C32×C5C32×C412080yesdirect product factor
37C24×C32×C5C22×C3211950yes—
38C22×C32×C4×C5C22×C32118200yesdirect product factor
39C23×C34C2×C4×C51120yesdirect product factor
40C23×C34C23×C5135yes—
41C2×C34×C4C23×C51120yesdirect product factor
42C24×C32×C4C32×C51130yesdirect product factor
43C22×C33×C5C22×C3×C415600yesdirect product factor
44C22×C33×C5C24×C31600yes—
45C33×C4×C5C24×C31640yesdirect product factor
46C25×C3×C5C2×C33140yes—
47C23×C3×C4×C5C2×C3311200yesdirect product factor
48C24×C33C3×C4×C51640yesdirect product factor
49C24×C33C22×C3×C51600yes—
50C22×C33×C4C22×C3×C515600yesdirect product factor
51C34×C5C24×C411yescharacteristic, direct product factor, Hall
52C23×C32×C5C2×C32×C4115600yesdirect product factor
53C23×C32×C5C23×C3214550yes—
54C2×C32×C4×C5C23×C32115600yesdirect product factor
55C22×C34C22×C4×C51140yesdirect product factor
56C22×C34C24×C5115yes—
57C34×C4C24×C5116yesdirect product factor
58C24×C4×C5C3411yescharacteristic, direct product factor, Hall
59C25×C32C2×C32×C51130yes—
60C23×C32×C4C2×C32×C513900yesdirect product factor
61C2×C33×C5C23×C3×C411200yesdirect product factor
62C2×C33×C5C25×C3140yes—
63C24×C3×C5C33×C41640yesdirect product factor
64C24×C3×C5C22×C331600yes—
65C22×C3×C4×C5C22×C3315600yesdirect product factor
66C23×C33C2×C3×C4×C514800yesdirect product factor
67C23×C33C23×C3×C511400yes—
68C2×C33×C4C23×C3×C514800yesdirect product factor
69C24×C3×C4C33×C5140yesdirect product factor
70C22×C32×C5C22×C32×C4118200yesdirect product factor
71C22×C32×C5C24×C3211950yes—
72C32×C4×C5C24×C3212080yesdirect product factor
73C2×C34C23×C4×C5130yesdirect product factor
74C2×C34C25×C511yescharacteristic
75C25×C5C2×C3411yescharacteristic
76C23×C4×C5C2×C34130yesdirect product factor
77C24×C32C32×C4×C512080yesdirect product factor
78C24×C32C22×C32×C511950yes—
79C22×C32×C4C22×C32×C5118200yesdirect product factor
80C33×C5C24×C3×C4140yesdirect product factor
81C23×C3×C5C2×C33×C414800yesdirect product factor
82C23×C3×C5C23×C3311400yes—
83C2×C3×C4×C5C23×C3314800yesdirect product factor
84C22×C33C22×C3×C4×C515600yesdirect product factor
85C22×C33C24×C3×C51600yes—
86C33×C4C24×C3×C51640yesdirect product factor
87C25×C3C2×C33×C5140yes—
88C23×C3×C4C2×C33×C511200yesdirect product factor
89C2×C32×C5C23×C32×C413900yesdirect product factor
90C2×C32×C5C25×C321130yes—
91C34C24×C4×C511yescharacteristic, direct product factor, Sylow
92C24×C5C34×C4116yesdirect product factor
93C24×C5C22×C34115yes—
94C22×C4×C5C22×C341140yesdirect product factor
95C23×C32C2×C32×C4×C5115600yesdirect product factor
96C23×C32C23×C32×C514550yes—
97C2×C32×C4C23×C32×C5115600yesdirect product factor
98C24×C4C34×C511yescharacteristic, direct product factor, Sylow
99C22×C3×C5C22×C33×C415600yesdirect product factor
100C22×C3×C5C24×C331600yes—
101C3×C4×C5C24×C331640yesdirect product factor
102C2×C33C23×C3×C4×C511200yesdirect product factor
103C2×C33C25×C3×C5140yes—
104C24×C3C33×C4×C51640yesdirect product factor
105C24×C3C22×C33×C51600yes—
106C22×C3×C4C22×C33×C515600yesdirect product factor
107C32×C5C24×C32×C41130yesdirect product factor
108C23×C5C2×C34×C41120yesdirect product factor
109C23×C5C23×C34135yes—
110C2×C4×C5C23×C341120yesdirect product factor
111C22×C32C22×C32×C4×C5118200yesdirect product factor
112C22×C32C24×C32×C511950yes—
113C32×C4C24×C32×C512080yesdirect product factor
114C25C2×C34×C511yescharacteristic
115C23×C4C2×C34×C5130yesdirect product factor
116C2×C3×C5C23×C33×C411200yesdirect product factor
117C2×C3×C5C25×C33140yes—
118C33C24×C3×C4×C5140yesdirect product factor
119C23×C3C2×C33×C4×C514800yesdirect product factor
120C23×C3C23×C33×C511400yes—
121C2×C3×C4C23×C33×C514800yesdirect product factor
122C22×C5C22×C34×C41140yesdirect product factor
123C22×C5C24×C34115yes—
124C4×C5C24×C34116yesdirect product factor
125C2×C32C23×C32×C4×C513900yesdirect product factor
126C2×C32C25×C32×C51130yes—
127C24C34×C4×C5116yesdirect product factor
128C24C22×C34×C5115yes—
129C22×C4C22×C34×C51140yesdirect product factor
130C3×C5C24×C33×C4140yesdirect product factor
131C22×C3C22×C33×C4×C515600yesdirect product factor
132C22×C3C24×C33×C51600yes—
133C3×C4C24×C33×C51640yesdirect product factor
134C2×C5C23×C34×C4130yesdirect product factor
135C2×C5C25×C3411yescharacteristic
136C32C24×C32×C4×C51130yesdirect product factor
137C23C2×C34×C4×C51120yesdirect product factor
138C23C23×C34×C5135yes—
139C2×C4C23×C34×C51120yesdirect product factor
140C2×C3C23×C33×C4×C511200yesdirect product factor
141C2×C3C25×C33×C5140yes—
142C5C24×C34×C411yescharacteristic, direct product factor, Sylow
143C22C22×C34×C4×C51140yesdirect product factor
144C22C24×C34×C5115yes—
145C4C24×C34×C5116yesdirect product factor
146C3C24×C33×C4×C5140yesdirect product factor
147C2C23×C34×C4×C5130yesdirect product factor
148C2C25×C34×C511yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C34×C5
socle, prime radicalC25×C34×C5C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C34×C4×C5C2direct (N × H)
3. C24×C33×C4×C5C3direct (N × H)
4. C24×C34×C5C4direct (N × H)
6. C22×C34×C4×C5C22direct (N × H)
7. C24×C34×C4C5direct (N × H)
9. C23×C33×C4×C5C2×C3direct (N × H)
10. C23×C34×C5C2×C4direct (N × H)
12. C2×C34×C4×C5C23direct (N × H)
13. C24×C32×C4×C5C32direct (N × H)
15. C23×C34×C4C2×C5direct (N × H)
16. C24×C33×C5C3×C4direct (N × H)
18. C22×C33×C4×C5C22×C3direct (N × H)
19. C24×C33×C4C3×C5direct (N × H)
20. C22×C34×C5C22×C4direct (N × H)
22. C34×C4×C5C24direct (N × H)
24. C23×C32×C4×C5C2×C32direct (N × H)
25. C24×C34C4×C5direct (N × H)
27. C22×C34×C4C22×C5direct (N × H)
28. C23×C33×C5C2×C3×C4direct (N × H)
30. C2×C33×C4×C5C23×C3direct (N × H)
31. C24×C3×C4×C5C33direct (N × H)
33. C23×C33×C4C2×C3×C5direct (N × H)
34. C2×C34×C5C23×C4direct (N × H)
36. C24×C32×C5C32×C4direct (N × H)
38. C22×C32×C4×C5C22×C32direct (N × H)
39. C23×C34C2×C4×C5direct (N × H)
41. C2×C34×C4C23×C5direct (N × H)
42. C24×C32×C4C32×C5direct (N × H)
43. C22×C33×C5C22×C3×C4direct (N × H)
45. C33×C4×C5C24×C3direct (N × H)
47. C23×C3×C4×C5C2×C33direct (N × H)
48. C24×C33C3×C4×C5direct (N × H)
50. C22×C33×C4C22×C3×C5direct (N × H)
51. C34×C5C24×C4direct (N × H)
52. C23×C32×C5C2×C32×C4direct (N × H)
54. C2×C32×C4×C5C23×C32direct (N × H)
55. C22×C34C22×C4×C5direct (N × H)
57. C34×C4C24×C5direct (N × H)
58. C24×C4×C5C34direct (N × H)
60. C23×C32×C4C2×C32×C5direct (N × H)
61. C2×C33×C5C23×C3×C4direct (N × H)
63. C24×C3×C5C33×C4direct (N × H)
65. C22×C3×C4×C5C22×C33direct (N × H)
66. C23×C33C2×C3×C4×C5direct (N × H)
68. C2×C33×C4C23×C3×C5direct (N × H)
69. C24×C3×C4C33×C5direct (N × H)
70. C22×C32×C5C22×C32×C4direct (N × H)
72. C32×C4×C5C24×C32direct (N × H)
73. C2×C34C23×C4×C5direct (N × H)
76. C23×C4×C5C2×C34direct (N × H)
77. C24×C32C32×C4×C5direct (N × H)
79. C22×C32×C4C22×C32×C5direct (N × H)
80. C33×C5C24×C3×C4direct (N × H)
81. C23×C3×C5C2×C33×C4direct (N × H)
83. C2×C3×C4×C5C23×C33direct (N × H)
84. C22×C33C22×C3×C4×C5direct (N × H)
86. C33×C4C24×C3×C5direct (N × H)
88. C23×C3×C4C2×C33×C5direct (N × H)
89. C2×C32×C5C23×C32×C4direct (N × H)
91. C34C24×C4×C5direct (N × H)
92. C24×C5C34×C4direct (N × H)
94. C22×C4×C5C22×C34direct (N × H)
95. C23×C32C2×C32×C4×C5direct (N × H)
97. C2×C32×C4C23×C32×C5direct (N × H)
98. C24×C4C34×C5direct (N × H)
99. C22×C3×C5C22×C33×C4direct (N × H)
101. C3×C4×C5C24×C33direct (N × H)
102. C2×C33C23×C3×C4×C5direct (N × H)
104. C24×C3C33×C4×C5direct (N × H)
106. C22×C3×C4C22×C33×C5direct (N × H)
107. C32×C5C24×C32×C4direct (N × H)
108. C23×C5C2×C34×C4direct (N × H)
110. C2×C4×C5C23×C34direct (N × H)
111. C22×C32C22×C32×C4×C5direct (N × H)
113. C32×C4C24×C32×C5direct (N × H)
115. C23×C4C2×C34×C5direct (N × H)
116. C2×C3×C5C23×C33×C4direct (N × H)
118. C33C24×C3×C4×C5direct (N × H)
119. C23×C3C2×C33×C4×C5direct (N × H)
121. C2×C3×C4C23×C33×C5direct (N × H)
122. C22×C5C22×C34×C4direct (N × H)
124. C4×C5C24×C34direct (N × H)
125. C2×C32C23×C32×C4×C5direct (N × H)
127. C24C34×C4×C5direct (N × H)
129. C22×C4C22×C34×C5direct (N × H)
130. C3×C5C24×C33×C4direct (N × H)
131. C22×C3C22×C33×C4×C5direct (N × H)
133. C3×C4C24×C33×C5direct (N × H)
134. C2×C5C23×C34×C4direct (N × H)
136. C32C24×C32×C4×C5direct (N × H)
137. C23C2×C34×C4×C5direct (N × H)
139. C2×C4C23×C34×C5direct (N × H)
140. C2×C3C23×C33×C4×C5direct (N × H)
142. C5C24×C34×C4direct (N × H)
143. C22C22×C34×C4×C5direct (N × H)
145. C4C24×C34×C5direct (N × H)
146. C3C24×C33×C4×C5direct (N × H)
147. C2C23×C34×C4×C5direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C34×C52
C23×C34×C4×C52
C24×C33×C4×C53
C24×C34×C45