Finite Group Databasebeta

← C22×C32×C4×C5×C43 #72207697

Subgroups — C22×C32×C4×C5×C43 #72207697

Order 30960.

648 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×C5×C43C211yesmaximal, characteristic
2C2×C32×C4×C5×C43C216yesmaximal, direct product factor
3C22×C3×C4×C5×C43C314yesmaximal, direct product factor
4C22×C32×C4×C43C511yesmaximal, characteristic, direct product factor, Hall
5C23×C3×C5×C43C2×C314yes—
6C2×C3×C4×C5×C43C2×C3124yesdirect product factor
7C22×C4×C5×C43C3211yescharacteristic, direct product factor, Hall
8C23×C32×C43C2×C511yescharacteristic
9C2×C32×C4×C43C2×C516yesdirect product factor
10C22×C3×C4×C43C3×C514yesdirect product factor
11C22×C32×C5×C43C414yesdirect product factor
12C22×C32×C5×C43C2213yes—
13C32×C4×C5×C43C2214yesdirect product factor
14C2×C32×C5×C43C2×C416yesdirect product factor
15C2×C32×C5×C43C2311yescharacteristic
16C22×C3×C5×C43C3×C4116yesdirect product factor
17C22×C3×C5×C43C22×C3112yes—
18C3×C4×C5×C43C22×C3116yesdirect product factor
19C32×C5×C43C22×C411yescharacteristic, direct product factor, Hall
20C23×C5×C43C2×C3211yescharacteristic
21C2×C4×C5×C43C2×C3216yesdirect product factor
22C22×C32×C43C4×C514yesdirect product factor
23C22×C32×C43C22×C513yes—
24C32×C4×C43C22×C514yesdirect product factor
25C2×C3×C5×C43C2×C3×C4124yesdirect product factor
26C2×C3×C5×C43C23×C314yes—
27C23×C3×C43C2×C3×C514yes—
28C2×C3×C4×C43C2×C3×C5124yesdirect product factor
29C22×C5×C43C32×C414yesdirect product factor
30C22×C5×C43C22×C3213yes—
31C4×C5×C43C22×C3214yesdirect product factor
32C2×C32×C43C2×C4×C516yesdirect product factor
33C2×C32×C43C23×C511yescharacteristic
34C22×C32×C4×C5C4311yesmaximal, characteristic, direct product factor, Hall
35C22×C4×C43C32×C511yescharacteristic, direct product factor, Hall
36C3×C5×C43C22×C3×C414yesdirect product factor
37C22×C3×C43C3×C4×C5116yesdirect product factor
38C22×C3×C43C22×C3×C5112yes—
39C3×C4×C43C22×C3×C5116yesdirect product factor
40C2×C5×C43C2×C32×C416yesdirect product factor
41C2×C5×C43C23×C3211yescharacteristic
42C32×C43C22×C4×C511yescharacteristic, direct product factor, Hall
43C23×C32×C5C2×C4311yescharacteristic
44C2×C32×C4×C5C2×C4316yesdirect product factor
45C23×C43C2×C32×C511yescharacteristic
46C2×C4×C43C2×C32×C516yesdirect product factor
47C2×C3×C43C2×C3×C4×C5124yesdirect product factor
48C2×C3×C43C23×C3×C514yes—
49C22×C3×C4×C5C3×C4314yesdirect product factor
50C5×C43C22×C32×C411yescharacteristic, direct product factor, Hall
51C22×C32×C5C4×C4314yesdirect product factor
52C22×C32×C5C22×C4313yes—
53C32×C4×C5C22×C4314yesdirect product factor
54C22×C43C32×C4×C514yesdirect product factor
55C22×C43C22×C32×C513yes—
56C4×C43C22×C32×C514yesdirect product factor
57C22×C32×C4C5×C4311yescharacteristic, direct product factor, Hall
58C3×C43C22×C3×C4×C514yesdirect product factor
59C23×C3×C5C2×C3×C4314yes—
60C2×C3×C4×C5C2×C3×C43124yesdirect product factor
61C2×C32×C5C2×C4×C4316yesdirect product factor
62C2×C32×C5C23×C4311yescharacteristic
63C2×C43C2×C32×C4×C516yesdirect product factor
64C2×C43C23×C32×C511yescharacteristic
65C22×C4×C5C32×C4311yescharacteristic, direct product factor, Hall
66C23×C32C2×C5×C4311yescharacteristic
67C2×C32×C4C2×C5×C4316yesdirect product factor
68C22×C3×C5C3×C4×C43116yesdirect product factor
69C22×C3×C5C22×C3×C43112yes—
70C3×C4×C5C22×C3×C43116yesdirect product factor
71C22×C3×C4C3×C5×C4314yesdirect product factor
72C32×C5C22×C4×C4311yescharacteristic, direct product factor, Hall
73C43C22×C32×C4×C511yescharacteristic, direct product factor, Sylow
74C23×C5C2×C32×C4311yescharacteristic
75C2×C4×C5C2×C32×C4316yesdirect product factor
76C22×C32C4×C5×C4314yesdirect product factor
77C22×C32C22×C5×C4313yes—
78C32×C4C22×C5×C4314yesdirect product factor
79C2×C3×C5C2×C3×C4×C43124yesdirect product factor
80C2×C3×C5C23×C3×C4314yes—
81C23×C3C2×C3×C5×C4314yes—
82C2×C3×C4C2×C3×C5×C43124yesdirect product factor
83C22×C5C32×C4×C4314yesdirect product factor
84C22×C5C22×C32×C4313yes—
85C4×C5C22×C32×C4314yesdirect product factor
86C2×C32C2×C4×C5×C4316yesdirect product factor
87C2×C32C23×C5×C4311yescharacteristic
88C22×C4C32×C5×C4311yescharacteristic, direct product factor, Sylow
89C3×C5C22×C3×C4×C4314yesdirect product factor
90C22×C3C3×C4×C5×C43116yesdirect product factor
91C22×C3C22×C3×C5×C43112yes—
92C3×C4C22×C3×C5×C43116yesdirect product factor
93C2×C5C2×C32×C4×C4316yesdirect product factor
94C2×C5C23×C32×C4311yescharacteristic
95C32C22×C4×C5×C4311yescharacteristic, direct product factor, Sylow
96C23C2×C32×C5×C4311yescharacteristic
97C2×C4C2×C32×C5×C4316yesdirect product factor
98C2×C3C2×C3×C4×C5×C43124yesdirect product factor
99C2×C3C23×C3×C5×C4314yes—
100C5C22×C32×C4×C4311yescharacteristic, direct product factor, Sylow
101C22C32×C4×C5×C4314yesdirect product factor
102C22C22×C32×C5×C4313yes—
103C4C22×C32×C5×C4314yesdirect product factor
104C3C22×C3×C4×C5×C4314yesdirect product factor
105C2C2×C32×C4×C5×C4316yesdirect product factor
106C2C23×C32×C5×C4311yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C32×C5×C43
socle, prime radicalC23×C32×C5×C43C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4×C5×C43C2direct (N × H)
3. C22×C3×C4×C5×C43C3direct (N × H)
4. C22×C32×C4×C43C5direct (N × H)
6. C2×C3×C4×C5×C43C2×C3direct (N × H)
7. C22×C4×C5×C43C32direct (N × H)
9. C2×C32×C4×C43C2×C5direct (N × H)
10. C22×C3×C4×C43C3×C5direct (N × H)
11. C22×C32×C5×C43C4direct (N × H)
13. C32×C4×C5×C43C22direct (N × H)
14. C2×C32×C5×C43C2×C4direct (N × H)
16. C22×C3×C5×C43C3×C4direct (N × H)
18. C3×C4×C5×C43C22×C3direct (N × H)
19. C32×C5×C43C22×C4direct (N × H)
21. C2×C4×C5×C43C2×C32direct (N × H)
22. C22×C32×C43C4×C5direct (N × H)
24. C32×C4×C43C22×C5direct (N × H)
25. C2×C3×C5×C43C2×C3×C4direct (N × H)
28. C2×C3×C4×C43C2×C3×C5direct (N × H)
29. C22×C5×C43C32×C4direct (N × H)
31. C4×C5×C43C22×C32direct (N × H)
32. C2×C32×C43C2×C4×C5direct (N × H)
34. C22×C32×C4×C5C43direct (N × H)
35. C22×C4×C43C32×C5direct (N × H)
36. C3×C5×C43C22×C3×C4direct (N × H)
37. C22×C3×C43C3×C4×C5direct (N × H)
39. C3×C4×C43C22×C3×C5direct (N × H)
40. C2×C5×C43C2×C32×C4direct (N × H)
42. C32×C43C22×C4×C5direct (N × H)
44. C2×C32×C4×C5C2×C43direct (N × H)
46. C2×C4×C43C2×C32×C5direct (N × H)
47. C2×C3×C43C2×C3×C4×C5direct (N × H)
49. C22×C3×C4×C5C3×C43direct (N × H)
50. C5×C43C22×C32×C4direct (N × H)
51. C22×C32×C5C4×C43direct (N × H)
53. C32×C4×C5C22×C43direct (N × H)
54. C22×C43C32×C4×C5direct (N × H)
56. C4×C43C22×C32×C5direct (N × H)
57. C22×C32×C4C5×C43direct (N × H)
58. C3×C43C22×C3×C4×C5direct (N × H)
60. C2×C3×C4×C5C2×C3×C43direct (N × H)
61. C2×C32×C5C2×C4×C43direct (N × H)
63. C2×C43C2×C32×C4×C5direct (N × H)
65. C22×C4×C5C32×C43direct (N × H)
67. C2×C32×C4C2×C5×C43direct (N × H)
68. C22×C3×C5C3×C4×C43direct (N × H)
70. C3×C4×C5C22×C3×C43direct (N × H)
71. C22×C3×C4C3×C5×C43direct (N × H)
72. C32×C5C22×C4×C43direct (N × H)
73. C43C22×C32×C4×C5direct (N × H)
75. C2×C4×C5C2×C32×C43direct (N × H)
76. C22×C32C4×C5×C43direct (N × H)
78. C32×C4C22×C5×C43direct (N × H)
79. C2×C3×C5C2×C3×C4×C43direct (N × H)
82. C2×C3×C4C2×C3×C5×C43direct (N × H)
83. C22×C5C32×C4×C43direct (N × H)
85. C4×C5C22×C32×C43direct (N × H)
86. C2×C32C2×C4×C5×C43direct (N × H)
88. C22×C4C32×C5×C43direct (N × H)
89. C3×C5C22×C3×C4×C43direct (N × H)
90. C22×C3C3×C4×C5×C43direct (N × H)
92. C3×C4C22×C3×C5×C43direct (N × H)
93. C2×C5C2×C32×C4×C43direct (N × H)
95. C32C22×C4×C5×C43direct (N × H)
97. C2×C4C2×C32×C5×C43direct (N × H)
98. C2×C3C2×C3×C4×C5×C43direct (N × H)
100. C5C22×C32×C4×C43direct (N × H)
101. C22C32×C4×C5×C43direct (N × H)
103. C4C22×C32×C5×C43direct (N × H)
104. C3C22×C3×C4×C5×C43direct (N × H)
105. C2C2×C32×C4×C5×C43direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C32×C5×C432
C2×C32×C4×C5×C432
C22×C3×C4×C5×C433
C22×C32×C4×C435
C22×C32×C4×C543