Finite Group Databasebeta

← C2×C32×C42×C5×C17 #72201751

Subgroups — C2×C32×C42×C5×C17 #72201751

Order 24480.

1296 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×C5×C17C213yesmaximal
2C32×C42×C5×C17C214yesmaximal, direct product factor
3C2×C3×C42×C5×C17C314yesmaximal, direct product factor
4C23×C32×C5×C17C2211yescharacteristic
5C2×C32×C4×C5×C17C4112yesdirect product factor
6C2×C32×C4×C5×C17C2216yes—
7C2×C32×C42×C17C511yesmaximal, characteristic, direct product factor, Hall
8C22×C3×C4×C5×C17C2×C3112yes—
9C3×C42×C5×C17C2×C3116yesdirect product factor
10C2×C42×C5×C17C3211yescharacteristic, direct product factor, Hall
11C22×C32×C4×C17C2×C513yes—
12C32×C42×C17C2×C514yesdirect product factor
13C23×C3×C5×C17C22×C314yes—
14C2×C3×C4×C5×C17C3×C4148yesdirect product factor
15C2×C3×C4×C5×C17C22×C3124yes—
16C22×C32×C5×C17C2×C416yes—
17C22×C32×C5×C17C2311yescharacteristic
18C32×C4×C5×C17C2×C4112yesdirect product factor
19C2×C3×C42×C17C3×C514yesdirect product factor
20C2×C32×C5×C17C4214yesdirect product factor
21C2×C32×C5×C17C22×C413yes—
22C2×C32×C42×C5C1711yesmaximal, characteristic, direct product factor, Hall
23C22×C4×C5×C17C2×C3213yes—
24C42×C5×C17C2×C3214yesdirect product factor
25C23×C32×C17C22×C511yescharacteristic
26C2×C32×C4×C17C4×C5112yesdirect product factor
27C2×C32×C4×C17C22×C516yes—
28C22×C3×C5×C17C2×C3×C4124yes—
29C22×C3×C5×C17C23×C314yes—
30C3×C4×C5×C17C2×C3×C4148yesdirect product factor
31C22×C3×C4×C17C2×C3×C5112yes—
32C3×C42×C17C2×C3×C5116yesdirect product factor
33C32×C5×C17C2×C4211yescharacteristic, direct product factor, Hall
34C22×C32×C4×C5C2×C1713yes—
35C32×C42×C5C2×C1714yesdirect product factor
36C23×C5×C17C22×C3211yescharacteristic
37C2×C4×C5×C17C32×C4112yesdirect product factor
38C2×C4×C5×C17C22×C3216yes—
39C22×C32×C17C2×C4×C516yes—
40C22×C32×C17C23×C511yescharacteristic
41C32×C4×C17C2×C4×C5112yesdirect product factor
42C2×C42×C17C32×C511yescharacteristic, direct product factor, Hall
43C2×C3×C5×C17C3×C42116yesdirect product factor
44C2×C3×C5×C17C22×C3×C4112yes—
45C2×C3×C42×C5C3×C1714yesdirect product factor
46C23×C3×C17C22×C3×C514yes—
47C2×C3×C4×C17C3×C4×C5148yesdirect product factor
48C2×C3×C4×C17C22×C3×C5124yes—
49C23×C32×C5C22×C1711yescharacteristic
50C2×C32×C4×C5C4×C17112yesdirect product factor
51C2×C32×C4×C5C22×C1716yes—
52C22×C5×C17C2×C32×C416yes—
53C22×C5×C17C23×C3211yescharacteristic
54C4×C5×C17C2×C32×C4112yesdirect product factor
55C2×C32×C17C42×C514yesdirect product factor
56C2×C32×C17C22×C4×C513yes—
57C2×C32×C42C5×C1711yescharacteristic, direct product factor, Hall
58C22×C4×C17C2×C32×C513yes—
59C42×C17C2×C32×C514yesdirect product factor
60C3×C5×C17C2×C3×C4214yesdirect product factor
61C22×C3×C4×C5C2×C3×C17112yes—
62C3×C42×C5C2×C3×C17116yesdirect product factor
63C22×C3×C17C2×C3×C4×C5124yes—
64C22×C3×C17C23×C3×C514yes—
65C3×C4×C17C2×C3×C4×C5148yesdirect product factor
66C22×C32×C5C2×C4×C1716yes—
67C22×C32×C5C23×C1711yescharacteristic
68C32×C4×C5C2×C4×C17112yesdirect product factor
69C2×C5×C17C32×C4214yesdirect product factor
70C2×C5×C17C22×C32×C413yes—
71C2×C42×C5C32×C1711yescharacteristic, direct product factor, Hall
72C32×C17C2×C42×C511yescharacteristic, direct product factor, Hall
73C22×C32×C4C2×C5×C1713yes—
74C32×C42C2×C5×C1714yesdirect product factor
75C23×C17C22×C32×C511yescharacteristic
76C2×C4×C17C32×C4×C5112yesdirect product factor
77C2×C4×C17C22×C32×C516yes—
78C23×C3×C5C22×C3×C1714yes—
79C2×C3×C4×C5C3×C4×C17148yesdirect product factor
80C2×C3×C4×C5C22×C3×C17124yes—
81C2×C3×C17C3×C42×C5116yesdirect product factor
82C2×C3×C17C22×C3×C4×C5112yes—
83C2×C3×C42C3×C5×C1714yesdirect product factor
84C2×C32×C5C42×C1714yesdirect product factor
85C2×C32×C5C22×C4×C1713yes—
86C5×C17C2×C32×C4211yescharacteristic, direct product factor, Hall
87C22×C4×C5C2×C32×C1713yes—
88C42×C5C2×C32×C1714yesdirect product factor
89C23×C32C22×C5×C1711yescharacteristic
90C2×C32×C4C4×C5×C17112yesdirect product factor
91C2×C32×C4C22×C5×C1716yes—
92C22×C17C2×C32×C4×C516yes—
93C22×C17C23×C32×C511yescharacteristic
94C4×C17C2×C32×C4×C5112yesdirect product factor
95C22×C3×C5C2×C3×C4×C17124yes—
96C22×C3×C5C23×C3×C1714yes—
97C3×C4×C5C2×C3×C4×C17148yesdirect product factor
98C3×C17C2×C3×C42×C514yesdirect product factor
99C22×C3×C4C2×C3×C5×C17112yes—
100C3×C42C2×C3×C5×C17116yesdirect product factor
101C32×C5C2×C42×C1711yescharacteristic, direct product factor, Hall
102C23×C5C22×C32×C1711yescharacteristic
103C2×C4×C5C32×C4×C17112yesdirect product factor
104C2×C4×C5C22×C32×C1716yes—
105C22×C32C2×C4×C5×C1716yes—
106C22×C32C23×C5×C1711yescharacteristic
107C32×C4C2×C4×C5×C17112yesdirect product factor
108C2×C17C32×C42×C514yesdirect product factor
109C2×C17C22×C32×C4×C513yes—
110C2×C42C32×C5×C1711yescharacteristic, direct product factor, Sylow
111C2×C3×C5C3×C42×C17116yesdirect product factor
112C2×C3×C5C22×C3×C4×C17112yes—
113C23×C3C22×C3×C5×C1714yes—
114C2×C3×C4C3×C4×C5×C17148yesdirect product factor
115C2×C3×C4C22×C3×C5×C17124yes—
116C22×C5C2×C32×C4×C1716yes—
117C22×C5C23×C32×C1711yescharacteristic
118C4×C5C2×C32×C4×C17112yesdirect product factor
119C2×C32C42×C5×C1714yesdirect product factor
120C2×C32C22×C4×C5×C1713yes—
121C17C2×C32×C42×C511yescharacteristic, direct product factor, Sylow
122C22×C4C2×C32×C5×C1713yes—
123C42C2×C32×C5×C1714yesdirect product factor
124C3×C5C2×C3×C42×C1714yesdirect product factor
125C22×C3C2×C3×C4×C5×C17124yes—
126C22×C3C23×C3×C5×C1714yes—
127C3×C4C2×C3×C4×C5×C17148yesdirect product factor
128C2×C5C32×C42×C1714yesdirect product factor
129C2×C5C22×C32×C4×C1713yes—
130C32C2×C42×C5×C1711yescharacteristic, direct product factor, Sylow
131C23C22×C32×C5×C1711yescharacteristic
132C2×C4C32×C4×C5×C17112yesdirect product factor
133C2×C4C22×C32×C5×C1716yes—
134C2×C3C3×C42×C5×C17116yesdirect product factor
135C2×C3C22×C3×C4×C5×C17112yes—
136C5C2×C32×C42×C1711yescharacteristic, direct product factor, Sylow
137C22C2×C32×C4×C5×C1716yes—
138C22C23×C32×C5×C1711yescharacteristic
139C4C2×C32×C4×C5×C17112yesdirect product factor
140C3C2×C3×C42×C5×C1714yesdirect product factor
141C2C32×C42×C5×C1714yesdirect product factor
142C2C22×C32×C4×C5×C1713yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C32×C5×C17
socle, prime radicalC23×C32×C5×C17C22
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C32×C42×C5×C17C2direct (N × H)
3. C2×C3×C42×C5×C17C3direct (N × H)
5. C2×C32×C4×C5×C17C4direct (N × H)
7. C2×C32×C42×C17C5direct (N × H)
9. C3×C42×C5×C17C2×C3direct (N × H)
10. C2×C42×C5×C17C32direct (N × H)
12. C32×C42×C17C2×C5direct (N × H)
14. C2×C3×C4×C5×C17C3×C4direct (N × H)
18. C32×C4×C5×C17C2×C4direct (N × H)
19. C2×C3×C42×C17C3×C5direct (N × H)
20. C2×C32×C5×C17C42direct (N × H)
22. C2×C32×C42×C5C17direct (N × H)
24. C42×C5×C17C2×C32direct (N × H)
26. C2×C32×C4×C17C4×C5direct (N × H)
30. C3×C4×C5×C17C2×C3×C4direct (N × H)
32. C3×C42×C17C2×C3×C5direct (N × H)
33. C32×C5×C17C2×C42direct (N × H)
35. C32×C42×C5C2×C17direct (N × H)
37. C2×C4×C5×C17C32×C4direct (N × H)
41. C32×C4×C17C2×C4×C5direct (N × H)
42. C2×C42×C17C32×C5direct (N × H)
43. C2×C3×C5×C17C3×C42direct (N × H)
45. C2×C3×C42×C5C3×C17direct (N × H)
47. C2×C3×C4×C17C3×C4×C5direct (N × H)
50. C2×C32×C4×C5C4×C17direct (N × H)
54. C4×C5×C17C2×C32×C4direct (N × H)
55. C2×C32×C17C42×C5direct (N × H)
57. C2×C32×C42C5×C17direct (N × H)
59. C42×C17C2×C32×C5direct (N × H)
60. C3×C5×C17C2×C3×C42direct (N × H)
62. C3×C42×C5C2×C3×C17direct (N × H)
65. C3×C4×C17C2×C3×C4×C5direct (N × H)
68. C32×C4×C5C2×C4×C17direct (N × H)
69. C2×C5×C17C32×C42direct (N × H)
71. C2×C42×C5C32×C17direct (N × H)
72. C32×C17C2×C42×C5direct (N × H)
74. C32×C42C2×C5×C17direct (N × H)
76. C2×C4×C17C32×C4×C5direct (N × H)
79. C2×C3×C4×C5C3×C4×C17direct (N × H)
81. C2×C3×C17C3×C42×C5direct (N × H)
83. C2×C3×C42C3×C5×C17direct (N × H)
84. C2×C32×C5C42×C17direct (N × H)
86. C5×C17C2×C32×C42direct (N × H)
88. C42×C5C2×C32×C17direct (N × H)
90. C2×C32×C4C4×C5×C17direct (N × H)
94. C4×C17C2×C32×C4×C5direct (N × H)
97. C3×C4×C5C2×C3×C4×C17direct (N × H)
98. C3×C17C2×C3×C42×C5direct (N × H)
100. C3×C42C2×C3×C5×C17direct (N × H)
101. C32×C5C2×C42×C17direct (N × H)
103. C2×C4×C5C32×C4×C17direct (N × H)
107. C32×C4C2×C4×C5×C17direct (N × H)
108. C2×C17C32×C42×C5direct (N × H)
110. C2×C42C32×C5×C17direct (N × H)
111. C2×C3×C5C3×C42×C17direct (N × H)
114. C2×C3×C4C3×C4×C5×C17direct (N × H)
118. C4×C5C2×C32×C4×C17direct (N × H)
119. C2×C32C42×C5×C17direct (N × H)
121. C17C2×C32×C42×C5direct (N × H)
123. C42C2×C32×C5×C17direct (N × H)
124. C3×C5C2×C3×C42×C17direct (N × H)
127. C3×C4C2×C3×C4×C5×C17direct (N × H)
128. C2×C5C32×C42×C17direct (N × H)
130. C32C2×C42×C5×C17direct (N × H)
132. C2×C4C32×C4×C5×C17direct (N × H)
134. C2×C3C3×C42×C5×C17direct (N × H)
136. C5C2×C32×C42×C17direct (N × H)
139. C4C2×C32×C4×C5×C17direct (N × H)
140. C3C2×C3×C42×C5×C17direct (N × H)
141. C2C32×C42×C5×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4×C5×C172
C32×C42×C5×C172
C2×C3×C42×C5×C173
C2×C32×C42×C175
C2×C32×C42×C517