Finite Group Databasebeta

← C5×D3×C7×D5×C17 #49087937

Subgroups — C5×D3×C7×D5×C17 #49087937

Order 35700.

192 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 80 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×C17C211yesmaximal, characteristic, complemented
2C52×D3×C7×C17C211yesmaximal, characteristic, complemented
3C5×C7×C17×D15C211yesmaximal, characteristic, complemented
4C2×C5×C7×D5×C17—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6C2×C5×D3×C7×C17—51nomaximal
7D3×C7×D5×C17C511yesmaximal, characteristic, direct product factor
8C5×C7×D5×C17—31no—
9C5×C7×D5×C17D311yescharacteristic, direct product factor
10C2×C52×C7×C17—31no—
11C5×D3×D5×C17C711yesmaximal, characteristic, direct product factor, Hall
12C7×C17×D15C2×C511yescharacteristic, complemented
13C5×D3×C7×C17—22no—
14C5×D3×C7×C17—51no—
15C5×D3×C7×C17D511yescharacteristic, direct product factor
16C5×D3×C7×C17C2×C511yescharacteristic, complemented
17C3×C7×D5×C17C2×C511yescharacteristic, complemented
18C2×C3×C5×C7×C17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C5×C17×D15C2×C711yescharacteristic, complemented
21C52×D3×C17C2×C711yescharacteristic, complemented
22C3×C5×D5×C17C2×C711yescharacteristic, complemented
23C2×C7×D5×C17—31no—
24C22×C5×C7×C17—151no—
25C5×D3×C7×D5C1711yesmaximal, characteristic, direct product factor, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C22×C511yescharacteristic, complemented
29C2×C5×D5×C17—31noHall
30C2×D3×C7×C17—51noHall
31C3×C52×C17C22×C711yescharacteristic, complemented, Hall
32C2×C5×C7×C17—31no—
33C2×C5×C7×C17—31no—
34C2×C5×C7×C17—51no—
35C2×C5×C7×C17—62no—
36C2×C5×C7×C17—151no—
37C7×D5×C17—31no—
38C7×D5×C17C5×D311yescharacteristic, direct product factor
39C5×C7×D15C2×C1711yescharacteristic, complemented
40C52×D3×C7C2×C1711yescharacteristic, complemented
41C3×C5×C7×D5C2×C1711yescharacteristic, complemented
42C2×C5×D3×C17—51no—
43D3×D5×C17C5×C711yescharacteristic, direct product factor
44C2×C52×C17—31no—
45C5×D5×C17—31no—
46C5×D5×C17D3×C711yescharacteristic, direct product factor
47C2×C3×C7×C17—51no—
48D3×C7×C17—51no—
49D3×C7×C17C5×D511yescharacteristic, direct product factor
50C2×C5×C7×D5—31noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, direct product factor
53C5×C7×C17C2×C5×D311yescharacteristic, complemented
54C3×C52×C7C22×C1711yescharacteristic, complemented, Hall
55C2×C3×C5×C17—51no—
56C17×D15C2×C5×C711yescharacteristic, complemented
57C5×D3×C17—22no—
58C5×D3×C17—51no—
59C5×D3×C17C7×D511yescharacteristic, direct product factor
60C5×D3×C17C2×C5×C711yescharacteristic, complemented
61C3×D5×C17C2×C5×C711yescharacteristic, complemented
62C22×C7×C17—151noHall
63C52×C17C2×D3×C711yescharacteristic, complemented, Hall
64C2×C5×D3×C7—51no—
65D3×C7×D5C5×C1711yescharacteristic, direct product factor
66C3×C7×C17C2×C5×D511yescharacteristic, complemented, Hall
67C2×C52×C7—31no—
68C5×C7×D5—31no—
69C5×C7×D5D3×C1711yescharacteristic, direct product factor
70C22×C5×C17—151no—
71C2×D5×C17—31no—
72C5×D3×D5C7×C1711yescharacteristic, direct product factor, Hall
73C3×C5×C17—22no—
74C3×C5×C17C2×C7×D511yescharacteristic, complemented
75C3×C5×C17C22×C5×C711yescharacteristic, complemented
76C2×C7×C17—31no—
77C2×C7×C17—51no—
78C2×C7×C17—151no—
79C2×C3×C5×C7—51no—
80C7×D15C2×C5×C1711yescharacteristic, complemented
81C5×D3×C7—22no—
82C5×D3×C7—51no—
83C5×D3×C7D5×C1711yescharacteristic, direct product factor
84C5×D3×C7C2×C5×C1711yescharacteristic, complemented
85C3×C7×D5C2×C5×C1711yescharacteristic, complemented
86C2×D3×C17—51noHall
87C52×C7C2×D3×C1711yescharacteristic, complemented, Hall
88C2×C5×C17—31no—
89C2×C5×C17—31no—
90C2×C5×C17—51no—
91C2×C5×C17—62no—
92C2×C5×C17—151no—
93D5×C17—31no—
94D5×C17C5×D3×C711yescharacteristic, direct product factor
95C5×D15C2×C7×C1711yescharacteristic, complemented
96C52×D3C2×C7×C1711yescharacteristic, complemented
97C3×C5×D5C2×C7×C1711yescharacteristic, complemented
98C22×C5×C7—151no—
99C2×C7×D5—31no—
100C7×C17C5×D3×D511yescharacteristic, direct product factor, Hall
101C3×C5×C7—22no—
102C3×C5×C7C2×D5×C1711yescharacteristic, complemented
103C3×C5×C7C22×C5×C1711yescharacteristic, complemented
104C2×C3×C17—51no—
105D3×C17—51no—
106D3×C17C5×C7×D511yescharacteristic, direct product factor
107C2×C5×D5—31noHall
108C5×C17—22no—
109C5×C17D3×C7×D511yescharacteristic, direct product factor
110C5×C17C2×C5×D3×C711yescharacteristic, complemented
111C2×D3×C7—51noHall
112C3×C52C22×C7×C1711yescharacteristic, complemented, Hall
113C2×C5×C7—31no—
114C2×C5×C7—31no—
115C2×C5×C7—51no—
116C2×C5×C7—62no—
117C2×C5×C7—151no—
118C7×D5—31no—
119C7×D5C5×D3×C1711yescharacteristic, direct product factor
120C22×C17—151noHall
121C2×C5×D3—51no—
122D3×D5C5×C7×C1711yescharacteristic, direct product factor
123C3×C17C2×C5×C7×D511yescharacteristic, complemented, Hall
124C2×C52—31no—
125C5×D5—31no—
126C5×D5D3×C7×C1711yescharacteristic, direct product factor
127C2×C3×C7—51no—
128D3×C7—51no—
129D3×C7C5×D5×C1711yescharacteristic, direct product factor
130C5×C7—22no—
131C5×C7D3×D5×C1711yescharacteristic, direct product factor
132C5×C7C2×C5×D3×C1711yescharacteristic, complemented
133C2×C17—31no—
134C2×C17—51no—
135C2×C17—151no—
136C2×C3×C5—51no—
137D15C2×C5×C7×C1711yescharacteristic, complemented
138C3×D5C2×C5×C7×C1711yescharacteristic, complemented
139C5×D3—22no—
140C5×D3—51no—
141C5×D3C7×D5×C1711yescharacteristic, direct product factor
142C5×D3C2×C5×C7×C1711yescharacteristic, complemented
143C22×C7—151noHall
144C52C2×D3×C7×C1711yescharacteristic, complemented, Sylow
145C3×C7C2×C5×D5×C1711yescharacteristic, complemented, Hall
146C22×C5—151no—
147C2×D5—31no—
148C17C5×D3×C7×D511yescharacteristic, direct product factor, Sylow
149C3×C5—22no—
150C3×C5C22×C5×C7×C1711yescharacteristic, complemented
151C3×C5C2×C7×D5×C1711yescharacteristic, complemented
152C2×C7—31no—
153C2×C7—51no—
154C2×C7—151no—
155C2×D3—51noHall
156C2×C5—31no—
157C2×C5—31no—
158C2×C5—51no—
159C2×C5—62no—
160C2×C5—151no—
161D5—31no—
162D5C5×D3×C7×C1711yescharacteristic, direct product factor
163C7C5×D3×D5×C1711yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—51no—
166D3C5×C7×D5×C1711yescharacteristic, direct product factor
167C5—22no—
168C5D3×C7×D5×C1711yescharacteristic, direct product factor
169C5C2×C5×D3×C7×C1711yescharacteristic, complemented
170C22—151noSylow
171C3C2×C5×C7×D5×C1711yescharacteristic, complemented, Sylow
172C2—31no—
173C2—51no—
174C2—151no—
subgroupG/H
center, hypercenterC5×C7×C17D3×D5
commutator, cosocle, hypocenterC3×C5C22×C5×C7×C17
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C5
UCSC1 ◁ C5×C7×C17

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C17C2semidirect
2. C52×D3×C7×C17C2semidirect
3. C5×C7×C17×D15C2semidirect
5. C3×C52×C7×C17C22semidirect
7. D3×C7×D5×C17C5direct (N × H)
9. C5×C7×D5×C17D3direct (N × H)
11. C5×D3×D5×C17C7direct (N × H)
12. C7×C17×D15C2×C5semidirect
15. C5×D3×C7×C17D5direct (N × H)
16. C5×D3×C7×C17C2×C5semidirect
17. C3×C7×D5×C17C2×C5semidirect
19. C52×C7×C17C2×D3semidirect
20. C5×C17×D15C2×C7semidirect
21. C52×D3×C17C2×C7semidirect
22. C3×C5×D5×C17C2×C7semidirect
25. C5×D3×C7×D5C17direct (N × H)
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C22×C5semidirect
31. C3×C52×C17C22×C7semidirect
38. C7×D5×C17C5×D3direct (N × H)
39. C5×C7×D15C2×C17semidirect
40. C52×D3×C7C2×C17semidirect
41. C3×C5×C7×D5C2×C17semidirect
43. D3×D5×C17C5×C7direct (N × H)
46. C5×D5×C17D3×C7direct (N × H)
49. D3×C7×C17C5×D5direct (N × H)
52. C5×C7×C17D3×D5direct (N × H)
53. C5×C7×C17C2×C5×D3semidirect
54. C3×C52×C7C22×C17semidirect
56. C17×D15C2×C5×C7semidirect
59. C5×D3×C17C7×D5direct (N × H)
60. C5×D3×C17C2×C5×C7semidirect
61. C3×D5×C17C2×C5×C7semidirect
63. C52×C17C2×D3×C7semidirect
65. D3×C7×D5C5×C17direct (N × H)
66. C3×C7×C17C2×C5×D5semidirect
69. C5×C7×D5D3×C17direct (N × H)
72. C5×D3×D5C7×C17direct (N × H)
74. C3×C5×C17C2×C7×D5semidirect
75. C3×C5×C17C22×C5×C7semidirect
80. C7×D15C2×C5×C17semidirect
83. C5×D3×C7D5×C17direct (N × H)
84. C5×D3×C7C2×C5×C17semidirect
85. C3×C7×D5C2×C5×C17semidirect
87. C52×C7C2×D3×C17semidirect
94. D5×C17C5×D3×C7direct (N × H)
95. C5×D15C2×C7×C17semidirect
96. C52×D3C2×C7×C17semidirect
97. C3×C5×D5C2×C7×C17semidirect
100. C7×C17C5×D3×D5direct (N × H)
102. C3×C5×C7C2×D5×C17semidirect
103. C3×C5×C7C22×C5×C17semidirect
106. D3×C17C5×C7×D5direct (N × H)
109. C5×C17D3×C7×D5direct (N × H)
110. C5×C17C2×C5×D3×C7semidirect
112. C3×C52C22×C7×C17semidirect
119. C7×D5C5×D3×C17direct (N × H)
122. D3×D5C5×C7×C17direct (N × H)
123. C3×C17C2×C5×C7×D5semidirect
126. C5×D5D3×C7×C17direct (N × H)
129. D3×C7C5×D5×C17direct (N × H)
131. C5×C7D3×D5×C17direct (N × H)
132. C5×C7C2×C5×D3×C17semidirect
137. D15C2×C5×C7×C17semidirect
138. C3×D5C2×C5×C7×C17semidirect
141. C5×D3C7×D5×C17direct (N × H)
142. C5×D3C2×C5×C7×C17semidirect
144. C52C2×D3×C7×C17semidirect
145. C3×C7C2×C5×D5×C17semidirect
148. C17C5×D3×C7×D5direct (N × H)
150. C3×C5C22×C5×C7×C17semidirect
151. C3×C5C2×C7×D5×C17semidirect
162. D5C5×D3×C7×C17direct (N × H)
163. C7C5×D3×D5×C17direct (N × H)
166. D3C5×C7×D5×C17direct (N × H)
168. C5D3×C7×D5×C17direct (N × H)
169. C5C2×C5×D3×C7×C17semidirect
171. C3C2×C5×C7×D5×C17semidirect

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
C52×D3×C7×C172
C5×C7×C17×D152
C2×C5×C7×D5×C173
C2×C5×D3×C7×C175
D3×C7×D5×C175
C5×D3×D5×C177
C5×D3×C7×D517