Finite Group Databasebeta

← C17×D15×D35 #49087977

Subgroups — C17×D15×D35 #49087977

Order 35700.

192 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 52 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×C17×D35C211yesmaximal, characteristic, complemented
2C5×C7×C17×D15C211yesmaximal, characteristic, complemented
3C17×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4D5×C17×D35—31nomaximal, Hall
5C3×C52×C7×C17C2211yescharacteristic, complemented, Hall
6D3×C17×D35—51nomaximal
7D7×C17×D15—51nomaximal
8C17×C5⋊D35—31no—
9C5×C17×D35D311yescharacteristic, complemented
10C5×C7×D5×C17—31no—
11D5×C17×D15—71nomaximal, Hall
12C17×D105—51no—
13C17×D105—51no—
14C17×D105—102no—
15C7×C17×D15D511yescharacteristic, complemented
16C5×D3×C7×C17—51no—
17C3×C17×D35D511yescharacteristic, complemented
18C3×C5×D7×C17—51no—
19C52×C7×C17C2×D311yescharacteristic, complemented, Hall
20C17×C3⋊(C5⋊D5)—71no—
21C5×C17×D15D711yescharacteristic, complemented
22C3×C5×D5×C17—71no—
23C2×C17×D35—151no—
24D5×D7×C17—151no—
25D15×D35C1711yesmaximal, characteristic, direct product factor, Hall
26C3×C5×C7×C17—22no—
27C3×C5×C7×C17C2×D511yescharacteristic, complemented
28C3×C5×C7×C17C2×D511yescharacteristic, complemented
29D52×C17—211noHall
30D3×D7×C17—251noHall
31C3×C52×C17C2×D711yescharacteristic, complemented, Hall
32C2×C5×C7×C17—151no—
33C17×D35—151no—
34C17×D35—151no—
35C17×D35—302no—
36C17×D35D1511yescharacteristic, direct product factor
37C7×D5×C17—31no—
38C5×D7×C17—51no—
39C3⋊(C5⋊D35)C2×C1711yescharacteristic, complemented
40C5×C7×D15C2×C1711yescharacteristic, complemented
41C3×C5×D35C2×C1711yescharacteristic, complemented
42C2×C17×D15—351no—
43D3×D5×C17—351no—
44C17×C5⋊D5—211no—
45C5×D5×C17—31no—
46C5×D5×C17—71no—
47C17×D21—251no—
48D3×C7×C17—51no—
49C3×D7×C17—51no—
50D5×D35—31noHall
51C5×C7×C17—22no—
52C5×C7×C17D3×D511yescharacteristic, complemented
53C5×C7×C17C2×D1511yescharacteristic, complemented
54C3×C52×C7C22×C1711yescharacteristic, complemented, Hall
55C2×C3×C5×C17—351no—
56C17×D15—351no—
57C17×D15—351no—
58C17×D15—702no—
59C17×D15D3511yescharacteristic, direct product factor
60C5×D3×C17—51no—
61C3×D5×C17—71no—
62C2×D7×C17—751noHall
63C52×C17D3×D711yescharacteristic, complemented, Hall
64D3×D35—51no—
65D7×D15—51no—
66C3×C7×C17D5211yescharacteristic, complemented, Hall
67C5⋊D35—31no—
68C5×D35D3×C1711yescharacteristic, complemented
69C5×C7×D5—31no—
70C2×D5×C17—1051no—
71C2×D5×C17—1051no—
72D5×D15—71noHall
73C3×C5×C17—22no—
74C3×C5×C17D5×D711yescharacteristic, complemented
75C3×C5×C17C2×D3511yescharacteristic, complemented
76C2×C7×C17—151no—
77D7×C17—51no—
78D7×C17—751no—
79D105—51no—
80D105—51no—
81D105—102no—
82C7×D15D5×C1711yescharacteristic, complemented
83C5×D3×C7—51no—
84C3×D35D5×C1711yescharacteristic, complemented
85C3×C5×D7—51no—
86C2×D3×C17—1751noHall
87C52×C7C2×D3×C1711yescharacteristic, complemented, Hall
88C2×C5×C17—151no—
89C2×C5×C17—351no—
90D5×C17—31no—
91D5×C17—71no—
92D5×C17—1051no—
93D5×C17—1051no—
94D5×C17—2102no—
95C3⋊(C5⋊D5)—71no—
96C5×D15D7×C1711yescharacteristic, complemented
97C3×C5×D5—71no—
98C2×D35—151no—
99D5×D7—151no—
100C7×C17D5×D1511yescharacteristic, complemented, Hall
101C3×C5×C7—22no—
102C3×C5×C7C2×D5×C1711yescharacteristic, complemented
103C3×C5×C7C2×D5×C1711yescharacteristic, complemented
104C2×C3×C17—351no—
105D3×C17—51no—
106D3×C17—1751no—
107D52—211noHall
108C5×C17—22no—
109C5×C17D7×D1511yescharacteristic, complemented
110C5×C17D3×D3511yescharacteristic, complemented
111D3×D7—251noHall
112C3×C52C2×D7×C1711yescharacteristic, complemented, Hall
113C2×C5×C7—151no—
114D35—151no—
115D35—151no—
116D35—302no—
117D35C17×D1511yescharacteristic, direct product factor
118C5×D7—51no—
119C7×D5—31no—
120C22×C17—5251noHall
121C2×D15—351no—
122D3×D5—351no—
123C3×C17D5×D3511yescharacteristic, complemented, Hall
124C5⋊D5—211no—
125C5×D5—31no—
126C5×D5—71no—
127D21—251no—
128C3×D7—51no—
129D3×C7—51no—
130C5×C7—22no—
131C5×C7D3×D5×C1711yescharacteristic, complemented
132C5×C7C2×C17×D1511yescharacteristic, complemented
133C2×C17—5251no—
134C2×C17—151no—
135C2×C17—351no—
136C2×C3×C5—351no—
137D15—351no—
138D15—351no—
139D15—702no—
140D15C17×D3511yescharacteristic, direct product factor
141C3×D5—71no—
142C5×D3—51no—
143C2×D7—751noHall
144C52D3×D7×C1711yescharacteristic, complemented, Sylow
145C3×C7D52×C1711yescharacteristic, complemented, Hall
146C2×D5—1051no—
147C2×D5—1051no—
148C17D15×D3511yescharacteristic, direct product factor, Sylow
149C3×C5—22no—
150C3×C5D5×D7×C1711yescharacteristic, complemented
151C3×C5C2×C17×D3511yescharacteristic, complemented
152C2×C7—151no—
153D7—51no—
154D7—751no—
155C2×D3—1751noHall
156C2×C5—151no—
157C2×C5—351no—
158D5—31no—
159D5—71no—
160D5—1051no—
161D5—1051no—
162D5—2102no—
163C7D5×C17×D1511yescharacteristic, complemented, Sylow
164C2×C3—351no—
165D3—51no—
166D3—1751no—
167C5—22no—
168C5D7×C17×D1511yescharacteristic, complemented
169C5D3×C17×D3511yescharacteristic, complemented
170C22—5251noSylow
171C3D5×C17×D3511yescharacteristic, complemented, Sylow
172C2—5251no—
173C2—151no—
174C2—351no—
subgroupG/H
center, hypercenterC17D15×D35
commutator, cosocle, hypocenterC3×C52×C7C22×C17
FrattiniC1G
Fitting, socleC3×C52×C7×C17C22
LCSG ▷ C3×C52×C7
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C3×C5×C17×D35C2semidirect
2. C5×C7×C17×D15C2semidirect
3. C17×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C17C22semidirect
9. C5×C17×D35D3semidirect
15. C7×C17×D15D5semidirect
17. C3×C17×D35D5semidirect
19. C52×C7×C17C2×D3semidirect
21. C5×C17×D15D7semidirect
25. D15×D35C17direct (N × H)
27. C3×C5×C7×C17C2×D5semidirect
28. C3×C5×C7×C17C2×D5semidirect
31. C3×C52×C17C2×D7semidirect
36. C17×D35D15direct (N × H)
39. C3⋊(C5⋊D35)C2×C17semidirect
40. C5×C7×D15C2×C17semidirect
41. C3×C5×D35C2×C17semidirect
52. C5×C7×C17D3×D5semidirect
53. C5×C7×C17C2×D15semidirect
54. C3×C52×C7C22×C17semidirect
59. C17×D15D35direct (N × H)
63. C52×C17D3×D7semidirect
66. C3×C7×C17D52semidirect
68. C5×D35D3×C17semidirect
74. C3×C5×C17D5×D7semidirect
75. C3×C5×C17C2×D35semidirect
82. C7×D15D5×C17semidirect
84. C3×D35D5×C17semidirect
87. C52×C7C2×D3×C17semidirect
96. C5×D15D7×C17semidirect
100. C7×C17D5×D15semidirect
102. C3×C5×C7C2×D5×C17semidirect
103. C3×C5×C7C2×D5×C17semidirect
109. C5×C17D7×D15semidirect
110. C5×C17D3×D35semidirect
112. C3×C52C2×D7×C17semidirect
117. D35C17×D15direct (N × H)
123. C3×C17D5×D35semidirect
131. C5×C7D3×D5×C17semidirect
132. C5×C7C2×C17×D15semidirect
140. D15C17×D35direct (N × H)
144. C52D3×D7×C17semidirect
145. C3×C7D52×C17semidirect
148. C17D15×D35direct (N × H)
150. C3×C5D5×D7×C17semidirect
151. C3×C5C2×C17×D35semidirect
163. C7D5×C17×D15semidirect
168. C5D7×C17×D15semidirect
169. C5D3×C17×D35semidirect
171. C3D5×C17×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C17×D352
C5×C7×C17×D152
C17×C3⋊(C5⋊D35)2
D5×C17×D353
D3×C17×D355
D7×C17×D155
D5×C17×D157
D15×D3517