Finite Group Databasebeta

← C2×C3×C5×C7×D5×C17 #49088043

Subgroups — C2×C3×C5×C7×D5×C17 #49088043

Order 35700.

192 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×C7×D5×C17C212yesmaximal, direct product factor
2C2×C3×C52×C7×C17C211yesmaximal, characteristic, complemented
3C2×C5×C7×D5×C17C311yesmaximal, characteristic, direct product factor, Hall
4C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
5C2×C3×C7×D5×C17C511yesmaximal, characteristic, direct product factor
6C22×C3×C5×C7×C17—51nomaximal
7C5×C7×D5×C17C2×C312yesdirect product factor
8C2×C52×C7×C17C2×C311yescharacteristic, complemented
9C2×C3×C5×D5×C17C711yesmaximal, characteristic, direct product factor, Hall
10C3×C7×D5×C17C2×C512yesdirect product factor
11C2×C3×C5×C7×C17—22no—
12C2×C3×C5×C7×C17—52no—
13C2×C3×C5×C7×C17D511yescharacteristic, direct product factor
14C2×C3×C5×C7×C17C2×C511yescharacteristic, complemented
15C52×C7×C17C22×C311yescharacteristic, complemented, Hall
16C3×C5×D5×C17C2×C712yesdirect product factor
17C2×C3×C52×C17C2×C711yescharacteristic, complemented
18C2×C7×D5×C17C3×C511yescharacteristic, direct product factor
19C22×C5×C7×C17—51no—
20C2×C3×C5×C7×D5C1711yesmaximal, characteristic, direct product factor, Hall
21C3×C5×C7×C17—22no—
22C3×C5×C7×C17C2×D511yescharacteristic, direct product factor
23C3×C5×C7×C17C22×C511yescharacteristic, complemented
24C2×C5×D5×C17C3×C711yescharacteristic, direct product factor, Hall
25C22×C3×C7×C17—51noHall
26C3×C52×C17C22×C711yescharacteristic, complemented, Hall
27C2×C5×C7×C17—22no—
28C2×C5×C7×C17—52no—
29C2×C5×C7×C17C3×D511yescharacteristic, direct product factor
30C2×C5×C7×C17C2×C3×C511yescharacteristic, complemented
31C7×D5×C17C2×C3×C512yesdirect product factor
32C2×C3×C52×C7C2×C1711yescharacteristic, complemented
33C3×C5×C7×D5C2×C1712yesdirect product factor
34C22×C3×C5×C17—51no—
35C2×C3×D5×C17C5×C711yescharacteristic, direct product factor
36C2×C52×C17C2×C3×C711yescharacteristic, complemented
37C5×D5×C17C2×C3×C712yesdirect product factor
38C2×C3×C7×C17—52no—
39C2×C3×C7×C17C5×D511yescharacteristic, direct product factor
40C2×C5×C7×D5C3×C1711yescharacteristic, direct product factor, Hall
41C5×C7×C17—22no—
42C5×C7×C17C2×C3×D511yescharacteristic, direct product factor
43C5×C7×C17C22×C3×C511yescharacteristic, complemented
44C3×C52×C7C22×C1711yescharacteristic, complemented, Hall
45C2×C3×C5×C17—22no—
46C2×C3×C5×C17—52no—
47C2×C3×C5×C17C7×D511yescharacteristic, direct product factor
48C2×C3×C5×C17C2×C5×C711yescharacteristic, complemented
49C3×D5×C17C2×C5×C712yesdirect product factor
50C22×C7×C17—51noHall
51C52×C17C22×C3×C711yescharacteristic, complemented, Hall
52C22×C3×C5×C7—51no—
53C2×C3×C7×D5C5×C1711yescharacteristic, direct product factor
54C3×C7×C17C2×C5×D511yescharacteristic, direct product factor, Hall
55C2×C52×C7C2×C3×C1711yescharacteristic, complemented
56C5×C7×D5C2×C3×C1712yesdirect product factor
57C22×C5×C17—51no—
58C2×D5×C17C3×C5×C711yescharacteristic, direct product factor
59C2×C3×C5×D5C7×C1711yescharacteristic, direct product factor, Hall
60C3×C5×C17—22no—
61C3×C5×C17C2×C7×D511yescharacteristic, direct product factor
62C3×C5×C17C22×C5×C711yescharacteristic, complemented
63C2×C7×C17—52no—
64C2×C7×C17C3×C5×D511yescharacteristic, direct product factor
65C2×C3×C5×C7—22no—
66C2×C3×C5×C7—52no—
67C2×C3×C5×C7D5×C1711yescharacteristic, direct product factor
68C2×C3×C5×C7C2×C5×C1711yescharacteristic, complemented
69C3×C7×D5C2×C5×C1712yesdirect product factor
70C22×C3×C17—51noHall
71C52×C7C22×C3×C1711yescharacteristic, complemented, Hall
72C2×C5×C17—22no—
73C2×C5×C17—52no—
74C2×C5×C17C3×C7×D511yescharacteristic, direct product factor
75C2×C5×C17C2×C3×C5×C711yescharacteristic, complemented
76D5×C17C2×C3×C5×C712yesdirect product factor
77C2×C3×C52C2×C7×C1711yescharacteristic, complemented
78C3×C5×D5C2×C7×C1712yesdirect product factor
79C22×C5×C7—51no—
80C2×C7×D5C3×C5×C1711yescharacteristic, direct product factor
81C7×C17C2×C3×C5×D511yescharacteristic, direct product factor, Hall
82C3×C5×C7—22no—
83C3×C5×C7C2×D5×C1711yescharacteristic, direct product factor
84C3×C5×C7C22×C5×C1711yescharacteristic, complemented
85C2×C3×C17—52no—
86C2×C3×C17C5×C7×D511yescharacteristic, direct product factor
87C2×C5×D5C3×C7×C1711yescharacteristic, direct product factor, Hall
88C5×C17—22no—
89C5×C17C2×C3×C7×D511yescharacteristic, direct product factor
90C5×C17C22×C3×C5×C711yescharacteristic, complemented
91C22×C3×C7—51noHall
92C3×C52C22×C7×C1711yescharacteristic, complemented, Hall
93C2×C5×C7—22no—
94C2×C5×C7—52no—
95C2×C5×C7C3×D5×C1711yescharacteristic, direct product factor
96C2×C5×C7C2×C3×C5×C1711yescharacteristic, complemented
97C7×D5C2×C3×C5×C1712yesdirect product factor
98C22×C17—51noHall
99C22×C3×C5—51no—
100C2×C3×D5C5×C7×C1711yescharacteristic, direct product factor
101C3×C17C2×C5×C7×D511yescharacteristic, direct product factor, Hall
102C2×C52C2×C3×C7×C1711yescharacteristic, complemented
103C5×D5C2×C3×C7×C1712yesdirect product factor
104C2×C3×C7—52no—
105C2×C3×C7C5×D5×C1711yescharacteristic, direct product factor
106C5×C7—22no—
107C5×C7C2×C3×D5×C1711yescharacteristic, direct product factor
108C5×C7C22×C3×C5×C1711yescharacteristic, complemented
109C2×C17—52no—
110C2×C17C3×C5×C7×D511yescharacteristic, direct product factor
111C2×C3×C5—22no—
112C2×C3×C5—52no—
113C2×C3×C5C7×D5×C1711yescharacteristic, direct product factor
114C2×C3×C5C2×C5×C7×C1711yescharacteristic, complemented
115C3×D5C2×C5×C7×C1712yesdirect product factor
116C22×C7—51noHall
117C52C22×C3×C7×C1711yescharacteristic, complemented, Sylow
118C3×C7C2×C5×D5×C1711yescharacteristic, direct product factor, Hall
119C22×C5—51no—
120C2×D5C3×C5×C7×C1711yescharacteristic, direct product factor
121C17C2×C3×C5×C7×D511yescharacteristic, direct product factor, Sylow
122C3×C5—22no—
123C3×C5C22×C5×C7×C1711yescharacteristic, complemented
124C3×C5C2×C7×D5×C1711yescharacteristic, direct product factor
125C2×C7—52no—
126C2×C7C3×C5×D5×C1711yescharacteristic, direct product factor
127C22×C3—51noHall
128C2×C5—22no—
129C2×C5—52no—
130C2×C5C2×C3×C5×C7×C1711yescharacteristic, complemented
131C2×C5C3×C7×D5×C1711yescharacteristic, direct product factor
132D5C2×C3×C5×C7×C1712yesdirect product factor
133C7C2×C3×C5×D5×C1711yescharacteristic, direct product factor, Sylow
134C2×C3—52no—
135C2×C3C5×C7×D5×C1711yescharacteristic, direct product factor
136C5—22no—
137C5C22×C3×C5×C7×C1711yescharacteristic, complemented
138C5C2×C3×C7×D5×C1711yescharacteristic, direct product factor
139C22—51noSylow
140C3C2×C5×C7×D5×C1711yescharacteristic, direct product factor, Sylow
141C2—52no—
142C2C3×C5×C7×D5×C1711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C5×C7×C17D5
commutator, cosocle, hypocenterC5C22×C3×C5×C7×C17
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C17C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C5×C7×C17

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C17C2direct (N × H)
2. C2×C3×C52×C7×C17C2semidirect
3. C2×C5×C7×D5×C17C3direct (N × H)
4. C3×C52×C7×C17C22semidirect
5. C2×C3×C7×D5×C17C5direct (N × H)
7. C5×C7×D5×C17C2×C3direct (N × H)
8. C2×C52×C7×C17C2×C3semidirect
9. C2×C3×C5×D5×C17C7direct (N × H)
10. C3×C7×D5×C17C2×C5direct (N × H)
13. C2×C3×C5×C7×C17D5direct (N × H)
14. C2×C3×C5×C7×C17C2×C5semidirect
15. C52×C7×C17C22×C3semidirect
16. C3×C5×D5×C17C2×C7direct (N × H)
17. C2×C3×C52×C17C2×C7semidirect
18. C2×C7×D5×C17C3×C5direct (N × H)
20. C2×C3×C5×C7×D5C17direct (N × H)
22. C3×C5×C7×C17C2×D5direct (N × H)
23. C3×C5×C7×C17C22×C5semidirect
24. C2×C5×D5×C17C3×C7direct (N × H)
26. C3×C52×C17C22×C7semidirect
29. C2×C5×C7×C17C3×D5direct (N × H)
30. C2×C5×C7×C17C2×C3×C5semidirect
31. C7×D5×C17C2×C3×C5direct (N × H)
32. C2×C3×C52×C7C2×C17semidirect
33. C3×C5×C7×D5C2×C17direct (N × H)
35. C2×C3×D5×C17C5×C7direct (N × H)
36. C2×C52×C17C2×C3×C7semidirect
37. C5×D5×C17C2×C3×C7direct (N × H)
39. C2×C3×C7×C17C5×D5direct (N × H)
40. C2×C5×C7×D5C3×C17direct (N × H)
42. C5×C7×C17C2×C3×D5direct (N × H)
43. C5×C7×C17C22×C3×C5semidirect
44. C3×C52×C7C22×C17semidirect
47. C2×C3×C5×C17C7×D5direct (N × H)
48. C2×C3×C5×C17C2×C5×C7semidirect
49. C3×D5×C17C2×C5×C7direct (N × H)
51. C52×C17C22×C3×C7semidirect
53. C2×C3×C7×D5C5×C17direct (N × H)
54. C3×C7×C17C2×C5×D5direct (N × H)
55. C2×C52×C7C2×C3×C17semidirect
56. C5×C7×D5C2×C3×C17direct (N × H)
58. C2×D5×C17C3×C5×C7direct (N × H)
59. C2×C3×C5×D5C7×C17direct (N × H)
61. C3×C5×C17C2×C7×D5direct (N × H)
62. C3×C5×C17C22×C5×C7semidirect
64. C2×C7×C17C3×C5×D5direct (N × H)
67. C2×C3×C5×C7D5×C17direct (N × H)
68. C2×C3×C5×C7C2×C5×C17semidirect
69. C3×C7×D5C2×C5×C17direct (N × H)
71. C52×C7C22×C3×C17semidirect
74. C2×C5×C17C3×C7×D5direct (N × H)
75. C2×C5×C17C2×C3×C5×C7semidirect
76. D5×C17C2×C3×C5×C7direct (N × H)
77. C2×C3×C52C2×C7×C17semidirect
78. C3×C5×D5C2×C7×C17direct (N × H)
80. C2×C7×D5C3×C5×C17direct (N × H)
81. C7×C17C2×C3×C5×D5direct (N × H)
83. C3×C5×C7C2×D5×C17direct (N × H)
84. C3×C5×C7C22×C5×C17semidirect
86. C2×C3×C17C5×C7×D5direct (N × H)
87. C2×C5×D5C3×C7×C17direct (N × H)
89. C5×C17C2×C3×C7×D5direct (N × H)
90. C5×C17C22×C3×C5×C7semidirect
92. C3×C52C22×C7×C17semidirect
95. C2×C5×C7C3×D5×C17direct (N × H)
96. C2×C5×C7C2×C3×C5×C17semidirect
97. C7×D5C2×C3×C5×C17direct (N × H)
100. C2×C3×D5C5×C7×C17direct (N × H)
101. C3×C17C2×C5×C7×D5direct (N × H)
102. C2×C52C2×C3×C7×C17semidirect
103. C5×D5C2×C3×C7×C17direct (N × H)
105. C2×C3×C7C5×D5×C17direct (N × H)
107. C5×C7C2×C3×D5×C17direct (N × H)
108. C5×C7C22×C3×C5×C17semidirect
110. C2×C17C3×C5×C7×D5direct (N × H)
113. C2×C3×C5C7×D5×C17direct (N × H)
114. C2×C3×C5C2×C5×C7×C17semidirect
115. C3×D5C2×C5×C7×C17direct (N × H)
117. C52C22×C3×C7×C17semidirect
118. C3×C7C2×C5×D5×C17direct (N × H)
120. C2×D5C3×C5×C7×C17direct (N × H)
121. C17C2×C3×C5×C7×D5direct (N × H)
123. C3×C5C22×C5×C7×C17semidirect
124. C3×C5C2×C7×D5×C17direct (N × H)
126. C2×C7C3×C5×D5×C17direct (N × H)
130. C2×C5C2×C3×C5×C7×C17semidirect
131. C2×C5C3×C7×D5×C17direct (N × H)
132. D5C2×C3×C5×C7×C17direct (N × H)
133. C7C2×C3×C5×D5×C17direct (N × H)
135. C2×C3C5×C7×D5×C17direct (N × H)
137. C5C22×C3×C5×C7×C17semidirect
138. C5C2×C3×C7×D5×C17direct (N × H)
140. C3C2×C5×C7×D5×C17direct (N × H)
142. C2C3×C5×C7×D5×C17direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C172
C2×C3×C52×C7×C172
C2×C5×C7×D5×C173
C2×C3×C7×D5×C175
C22×C3×C5×C7×C175
C2×C3×C5×D5×C177
C2×C3×C5×C7×D517