Finite Group Databasebeta

← C2×C32×C4×C52×C17 #72207367

Subgroups — C2×C32×C4×C52×C17 #72207367

Order 30600.

768 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×C3×C4×C52×C17C314yesmaximal, direct product factor
2C2×C32×C4×C5×C17C516yesmaximal, direct product factor
3C2×C4×C52×C17C3211yescharacteristic, direct product factor, Hall
4C2×C3×C4×C5×C17C3×C5124yesdirect product factor
5C22×C32×C52×C17C211yesmaximal, characteristic
6C32×C4×C52×C17C212yesmaximal, direct product factor
7C2×C32×C52×C17C412yesdirect product factor
8C2×C32×C52×C17C2211yescharacteristic
9C22×C3×C52×C17C2×C314yes—
10C3×C4×C52×C17C2×C318yesdirect product factor
11C32×C52×C17C2×C411yescharacteristic, direct product factor, Hall
12C22×C32×C5×C17C2×C516yes—
13C32×C4×C5×C17C2×C5112yesdirect product factor
14C2×C3×C52×C17C3×C418yesdirect product factor
15C2×C3×C52×C17C22×C314yes—
16C2×C32×C4×C52C1711yesmaximal, characteristic, direct product factor, Hall
17C22×C52×C17C2×C3211yescharacteristic
18C4×C52×C17C2×C3212yesdirect product factor
19C2×C32×C5×C17C4×C5112yesdirect product factor
20C2×C32×C5×C17C22×C516yes—
21C3×C52×C17C2×C3×C414yesdirect product factor
22C2×C32×C4×C17C5211yescharacteristic, direct product factor, Hall
23C22×C3×C5×C17C2×C3×C5124yes—
24C3×C4×C5×C17C2×C3×C5148yesdirect product factor
25C22×C32×C52C2×C1711yescharacteristic
26C32×C4×C52C2×C1712yesdirect product factor
27C2×C52×C17C32×C412yesdirect product factor
28C2×C52×C17C22×C3211yescharacteristic
29C32×C5×C17C2×C4×C516yesdirect product factor
30C2×C4×C5×C17C32×C516yesdirect product factor
31C22×C32×C17C2×C5211yescharacteristic
32C32×C4×C17C2×C5212yesdirect product factor
33C2×C3×C4×C52C3×C1714yesdirect product factor
34C2×C3×C5×C17C3×C4×C5148yesdirect product factor
35C2×C3×C5×C17C22×C3×C5124yes—
36C2×C32×C52C4×C1712yesdirect product factor
37C2×C32×C52C22×C1711yescharacteristic
38C52×C17C2×C32×C411yescharacteristic, direct product factor, Hall
39C2×C3×C4×C17C3×C5214yesdirect product factor
40C2×C32×C4×C5C5×C1716yesdirect product factor
41C22×C5×C17C2×C32×C516yes—
42C4×C5×C17C2×C32×C5112yesdirect product factor
43C2×C32×C17C4×C5212yesdirect product factor
44C2×C32×C17C22×C5211yescharacteristic
45C22×C3×C52C2×C3×C1714yes—
46C3×C4×C52C2×C3×C1718yesdirect product factor
47C3×C5×C17C2×C3×C4×C5124yesdirect product factor
48C32×C52C2×C4×C1711yescharacteristic, direct product factor, Hall
49C22×C3×C17C2×C3×C5214yes—
50C3×C4×C17C2×C3×C5218yesdirect product factor
51C2×C4×C52C32×C1711yescharacteristic, direct product factor, Hall
52C22×C32×C5C2×C5×C1716yes—
53C32×C4×C5C2×C5×C17112yesdirect product factor
54C2×C5×C17C32×C4×C5112yesdirect product factor
55C2×C5×C17C22×C32×C516yes—
56C32×C17C2×C4×C5211yescharacteristic, direct product factor, Hall
57C2×C3×C52C3×C4×C1718yesdirect product factor
58C2×C3×C52C22×C3×C1714yes—
59C2×C4×C17C32×C5211yescharacteristic, direct product factor, Hall
60C2×C3×C4×C5C3×C5×C17124yesdirect product factor
61C2×C3×C17C3×C4×C5218yesdirect product factor
62C2×C3×C17C22×C3×C5214yes—
63C22×C52C2×C32×C1711yescharacteristic
64C4×C52C2×C32×C1712yesdirect product factor
65C2×C32×C5C4×C5×C17112yesdirect product factor
66C2×C32×C5C22×C5×C1716yes—
67C5×C17C2×C32×C4×C516yesdirect product factor
68C3×C52C2×C3×C4×C1714yesdirect product factor
69C2×C32×C4C52×C1711yescharacteristic, direct product factor, Hall
70C22×C17C2×C32×C5211yescharacteristic
71C4×C17C2×C32×C5212yesdirect product factor
72C22×C3×C5C2×C3×C5×C17124yes—
73C3×C4×C5C2×C3×C5×C17148yesdirect product factor
74C3×C17C2×C3×C4×C5214yesdirect product factor
75C2×C52C32×C4×C1712yesdirect product factor
76C2×C52C22×C32×C1711yescharacteristic
77C32×C5C2×C4×C5×C1716yesdirect product factor
78C2×C4×C5C32×C5×C1716yesdirect product factor
79C22×C32C2×C52×C1711yescharacteristic
80C32×C4C2×C52×C1712yesdirect product factor
81C2×C17C32×C4×C5212yesdirect product factor
82C2×C17C22×C32×C5211yescharacteristic
83C2×C3×C5C3×C4×C5×C17148yesdirect product factor
84C2×C3×C5C22×C3×C5×C17124yes—
85C52C2×C32×C4×C1711yescharacteristic, direct product factor, Sylow
86C2×C3×C4C3×C52×C1714yesdirect product factor
87C22×C5C2×C32×C5×C1716yes—
88C4×C5C2×C32×C5×C17112yesdirect product factor
89C2×C32C4×C52×C1712yesdirect product factor
90C2×C32C22×C52×C1711yescharacteristic
91C17C2×C32×C4×C5211yescharacteristic, direct product factor, Sylow
92C3×C5C2×C3×C4×C5×C17124yesdirect product factor
93C22×C3C2×C3×C52×C1714yes—
94C3×C4C2×C3×C52×C1718yesdirect product factor
95C2×C5C32×C4×C5×C17112yesdirect product factor
96C2×C5C22×C32×C5×C1716yes—
97C32C2×C4×C52×C1711yescharacteristic, direct product factor, Sylow
98C2×C4C32×C52×C1711yescharacteristic, direct product factor, Sylow
99C2×C3C3×C4×C52×C1718yesdirect product factor
100C2×C3C22×C3×C52×C1714yes—
101C5C2×C32×C4×C5×C1716yesdirect product factor
102C22C2×C32×C52×C1711yescharacteristic
103C4C2×C32×C52×C1712yesdirect product factor
104C3C2×C3×C4×C52×C1714yesdirect product factor
105C2C32×C4×C52×C1712yesdirect product factor
106C2C22×C32×C52×C1711yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C32×C52×C17
socle, prime radicalC22×C32×C52×C17C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C52×C17C3direct (N × H)
2. C2×C32×C4×C5×C17C5direct (N × H)
3. C2×C4×C52×C17C32direct (N × H)
4. C2×C3×C4×C5×C17C3×C5direct (N × H)
6. C32×C4×C52×C17C2direct (N × H)
7. C2×C32×C52×C17C4direct (N × H)
10. C3×C4×C52×C17C2×C3direct (N × H)
11. C32×C52×C17C2×C4direct (N × H)
13. C32×C4×C5×C17C2×C5direct (N × H)
14. C2×C3×C52×C17C3×C4direct (N × H)
16. C2×C32×C4×C52C17direct (N × H)
18. C4×C52×C17C2×C32direct (N × H)
19. C2×C32×C5×C17C4×C5direct (N × H)
21. C3×C52×C17C2×C3×C4direct (N × H)
22. C2×C32×C4×C17C52direct (N × H)
24. C3×C4×C5×C17C2×C3×C5direct (N × H)
26. C32×C4×C52C2×C17direct (N × H)
27. C2×C52×C17C32×C4direct (N × H)
29. C32×C5×C17C2×C4×C5direct (N × H)
30. C2×C4×C5×C17C32×C5direct (N × H)
32. C32×C4×C17C2×C52direct (N × H)
33. C2×C3×C4×C52C3×C17direct (N × H)
34. C2×C3×C5×C17C3×C4×C5direct (N × H)
36. C2×C32×C52C4×C17direct (N × H)
38. C52×C17C2×C32×C4direct (N × H)
39. C2×C3×C4×C17C3×C52direct (N × H)
40. C2×C32×C4×C5C5×C17direct (N × H)
42. C4×C5×C17C2×C32×C5direct (N × H)
43. C2×C32×C17C4×C52direct (N × H)
46. C3×C4×C52C2×C3×C17direct (N × H)
47. C3×C5×C17C2×C3×C4×C5direct (N × H)
48. C32×C52C2×C4×C17direct (N × H)
50. C3×C4×C17C2×C3×C52direct (N × H)
51. C2×C4×C52C32×C17direct (N × H)
53. C32×C4×C5C2×C5×C17direct (N × H)
54. C2×C5×C17C32×C4×C5direct (N × H)
56. C32×C17C2×C4×C52direct (N × H)
57. C2×C3×C52C3×C4×C17direct (N × H)
59. C2×C4×C17C32×C52direct (N × H)
60. C2×C3×C4×C5C3×C5×C17direct (N × H)
61. C2×C3×C17C3×C4×C52direct (N × H)
64. C4×C52C2×C32×C17direct (N × H)
65. C2×C32×C5C4×C5×C17direct (N × H)
67. C5×C17C2×C32×C4×C5direct (N × H)
68. C3×C52C2×C3×C4×C17direct (N × H)
69. C2×C32×C4C52×C17direct (N × H)
71. C4×C17C2×C32×C52direct (N × H)
73. C3×C4×C5C2×C3×C5×C17direct (N × H)
74. C3×C17C2×C3×C4×C52direct (N × H)
75. C2×C52C32×C4×C17direct (N × H)
77. C32×C5C2×C4×C5×C17direct (N × H)
78. C2×C4×C5C32×C5×C17direct (N × H)
80. C32×C4C2×C52×C17direct (N × H)
81. C2×C17C32×C4×C52direct (N × H)
83. C2×C3×C5C3×C4×C5×C17direct (N × H)
85. C52C2×C32×C4×C17direct (N × H)
86. C2×C3×C4C3×C52×C17direct (N × H)
88. C4×C5C2×C32×C5×C17direct (N × H)
89. C2×C32C4×C52×C17direct (N × H)
91. C17C2×C32×C4×C52direct (N × H)
92. C3×C5C2×C3×C4×C5×C17direct (N × H)
94. C3×C4C2×C3×C52×C17direct (N × H)
95. C2×C5C32×C4×C5×C17direct (N × H)
97. C32C2×C4×C52×C17direct (N × H)
98. C2×C4C32×C52×C17direct (N × H)
99. C2×C3C3×C4×C52×C17direct (N × H)
101. C5C2×C32×C4×C5×C17direct (N × H)
103. C4C2×C32×C52×C17direct (N × H)
104. C3C2×C3×C4×C52×C17direct (N × H)
105. C2C32×C4×C52×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C52×C173
C2×C32×C4×C5×C175
C22×C32×C52×C172
C32×C4×C52×C172
C2×C32×C4×C5217