Finite Group Databasebeta

← C32×C4×C5×C7×C25 #72208262

Subgroups — C32×C4×C5×C7×C25 #72208262

Order 31500.

504 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
1C2×C32×C5×C7×C25C211yesmaximal, characteristic
2C3×C4×C5×C7×C25C314yesmaximal, direct product factor
3C32×C5×C7×C25C411yescharacteristic, direct product factor, Hall
4C2×C3×C5×C7×C25C2×C314yes—
5C32×C4×C5×C25C711yesmaximal, characteristic, direct product factor, Hall
6C4×C5×C7×C25C3211yescharacteristic, direct product factor, Hall
7C3×C5×C7×C25C3×C414yesdirect product factor
8C2×C32×C5×C25C2×C711yescharacteristic
9C32×C4×C52×C7C511yesmaximal, characteristic
10C32×C4×C7×C25C515yesmaximal, direct product factor
11C2×C32×C52×C7C2×C511yescharacteristic
12C2×C32×C7×C25C2×C515yes—
13C3×C4×C52×C7C3×C514yes—
14C3×C4×C7×C25C3×C5120yesdirect product factor
15C2×C5×C7×C25C2×C3211yescharacteristic
16C32×C52×C7C4×C511yescharacteristic
17C32×C7×C25C4×C515yesdirect product factor
18C3×C4×C5×C25C3×C714yesdirect product factor
19C32×C4×C5×C7C2515yesdirect product factor
20C32×C4×C5×C7C5211yescharacteristic
21C32×C5×C25C4×C711yescharacteristic, direct product factor, Hall
22C2×C3×C52×C7C2×C3×C514yes—
23C2×C3×C7×C25C2×C3×C5120yes—
24C32×C4×C52C5×C711yescharacteristic
25C32×C4×C25C5×C715yesdirect product factor
26C5×C7×C25C32×C411yescharacteristic, direct product factor, Hall
27C2×C3×C5×C25C2×C3×C714yes—
28C4×C52×C7C32×C511yescharacteristic
29C4×C7×C25C32×C515yesdirect product factor
30C2×C32×C5×C7C2×C2515yes—
31C2×C32×C5×C7C2×C5211yescharacteristic
32C3×C52×C7C3×C4×C514yes—
33C3×C7×C25C3×C4×C5120yesdirect product factor
34C4×C5×C25C32×C711yescharacteristic, direct product factor, Hall
35C2×C32×C52C2×C5×C711yescharacteristic
36C2×C32×C25C2×C5×C715yes—
37C3×C4×C5×C7C3×C25120yesdirect product factor
38C3×C4×C5×C7C3×C5214yes—
39C3×C5×C25C3×C4×C714yesdirect product factor
40C2×C52×C7C2×C32×C511yescharacteristic
41C2×C7×C25C2×C32×C515yes—
42C32×C5×C7C4×C2515yesdirect product factor
43C32×C5×C7C4×C5211yescharacteristic
44C3×C4×C52C3×C5×C714yes—
45C3×C4×C25C3×C5×C7120yesdirect product factor
46C32×C4×C7C5×C2511yescharacteristic, direct product factor, Hall
47C2×C5×C25C2×C32×C711yescharacteristic
48C32×C52C4×C5×C711yescharacteristic
49C32×C25C4×C5×C715yesdirect product factor
50C2×C3×C5×C7C2×C3×C25120yes—
51C2×C3×C5×C7C2×C3×C5214yes—
52C32×C4×C5C7×C2515yesdirect product factor
53C32×C4×C5C52×C711yescharacteristic
54C52×C7C32×C4×C511yescharacteristic
55C7×C25C32×C4×C515yesdirect product factor
56C2×C3×C52C2×C3×C5×C714yes—
57C2×C3×C25C2×C3×C5×C7120yes—
58C4×C5×C7C32×C2515yesdirect product factor
59C4×C5×C7C32×C5211yescharacteristic
60C2×C32×C7C2×C5×C2511yescharacteristic
61C5×C25C32×C4×C711yescharacteristic, direct product factor, Sylow
62C3×C5×C7C3×C4×C25120yesdirect product factor
63C3×C5×C7C3×C4×C5214yes—
64C4×C52C32×C5×C711yescharacteristic
65C4×C25C32×C5×C715yesdirect product factor
66C2×C32×C5C2×C7×C2515yes—
67C2×C32×C5C2×C52×C711yescharacteristic
68C3×C4×C7C3×C5×C2514yesdirect product factor
69C3×C52C3×C4×C5×C714yes—
70C3×C25C3×C4×C5×C7120yesdirect product factor
71C2×C5×C7C2×C32×C2515yes—
72C2×C5×C7C2×C32×C5211yescharacteristic
73C32×C7C4×C5×C2511yescharacteristic, direct product factor, Hall
74C3×C4×C5C3×C7×C25120yesdirect product factor
75C3×C4×C5C3×C52×C714yes—
76C2×C52C2×C32×C5×C711yescharacteristic
77C2×C25C2×C32×C5×C715yes—
78C32×C5C4×C7×C2515yesdirect product factor
79C32×C5C4×C52×C711yescharacteristic
80C2×C3×C7C2×C3×C5×C2514yes—
81C32×C4C5×C7×C2511yescharacteristic, direct product factor, Hall
82C5×C7C32×C4×C2515yesdirect product factor
83C5×C7C32×C4×C5211yescharacteristic
84C2×C3×C5C2×C3×C7×C25120yes—
85C2×C3×C5C2×C3×C52×C714yes—
86C4×C7C32×C5×C2511yescharacteristic, direct product factor, Hall
87C52C32×C4×C5×C711yescharacteristic
88C25C32×C4×C5×C715yesdirect product factor
89C3×C7C3×C4×C5×C2514yesdirect product factor
90C4×C5C32×C7×C2515yesdirect product factor
91C4×C5C32×C52×C711yescharacteristic
92C2×C32C2×C5×C7×C2511yescharacteristic
93C3×C5C3×C4×C7×C25120yesdirect product factor
94C3×C5C3×C4×C52×C714yes—
95C2×C7C2×C32×C5×C2511yescharacteristic
96C3×C4C3×C5×C7×C2514yesdirect product factor
97C2×C5C2×C32×C7×C2515yes—
98C2×C5C2×C32×C52×C711yescharacteristic
99C32C4×C5×C7×C2511yescharacteristic, direct product factor, Sylow
100C7C32×C4×C5×C2511yescharacteristic, direct product factor, Sylow
101C2×C3C2×C3×C5×C7×C2514yes—
102C5C32×C4×C7×C2515yesdirect product factor
103C5C32×C4×C52×C711yescharacteristic
104C4C32×C5×C7×C2511yescharacteristic, direct product factor, Sylow
105C3C3×C4×C5×C7×C2514yesdirect product factor
106C2C2×C32×C5×C7×C2511yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5C2×C32×C52×C7
socle, prime radicalC2×C32×C52×C7C2×C5
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C7×C25C3direct (N × H)
3. C32×C5×C7×C25C4direct (N × H)
5. C32×C4×C5×C25C7direct (N × H)
6. C4×C5×C7×C25C32direct (N × H)
7. C3×C5×C7×C25C3×C4direct (N × H)
10. C32×C4×C7×C25C5direct (N × H)
14. C3×C4×C7×C25C3×C5direct (N × H)
17. C32×C7×C25C4×C5direct (N × H)
18. C3×C4×C5×C25C3×C7direct (N × H)
19. C32×C4×C5×C7C25direct (N × H)
21. C32×C5×C25C4×C7direct (N × H)
25. C32×C4×C25C5×C7direct (N × H)
26. C5×C7×C25C32×C4direct (N × H)
29. C4×C7×C25C32×C5direct (N × H)
33. C3×C7×C25C3×C4×C5direct (N × H)
34. C4×C5×C25C32×C7direct (N × H)
37. C3×C4×C5×C7C3×C25direct (N × H)
39. C3×C5×C25C3×C4×C7direct (N × H)
42. C32×C5×C7C4×C25direct (N × H)
45. C3×C4×C25C3×C5×C7direct (N × H)
46. C32×C4×C7C5×C25direct (N × H)
49. C32×C25C4×C5×C7direct (N × H)
52. C32×C4×C5C7×C25direct (N × H)
55. C7×C25C32×C4×C5direct (N × H)
58. C4×C5×C7C32×C25direct (N × H)
61. C5×C25C32×C4×C7direct (N × H)
62. C3×C5×C7C3×C4×C25direct (N × H)
65. C4×C25C32×C5×C7direct (N × H)
68. C3×C4×C7C3×C5×C25direct (N × H)
70. C3×C25C3×C4×C5×C7direct (N × H)
73. C32×C7C4×C5×C25direct (N × H)
74. C3×C4×C5C3×C7×C25direct (N × H)
78. C32×C5C4×C7×C25direct (N × H)
81. C32×C4C5×C7×C25direct (N × H)
82. C5×C7C32×C4×C25direct (N × H)
86. C4×C7C32×C5×C25direct (N × H)
88. C25C32×C4×C5×C7direct (N × H)
89. C3×C7C3×C4×C5×C25direct (N × H)
90. C4×C5C32×C7×C25direct (N × H)
93. C3×C5C3×C4×C7×C25direct (N × H)
96. C3×C4C3×C5×C7×C25direct (N × H)
99. C32C4×C5×C7×C25direct (N × H)
100. C7C32×C4×C5×C25direct (N × H)
102. C5C32×C4×C7×C25direct (N × H)
104. C4C32×C5×C7×C25direct (N × H)
105. C3C3×C4×C5×C7×C25direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×C7×C252
C3×C4×C5×C7×C253
C32×C4×C5×C257
C32×C4×C52×C75
C32×C4×C7×C255