Finite Group Databasebeta

← C3×C7×D13×D35 #50304369

Subgroups — C3×C7×D13×D35 #50304369

Order 38220.

208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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×C72×D13C211yesmaximal, characteristic, complemented
2C3×C7×C13×D35C211yesmaximal, characteristic, complemented
3C3×C7×D455C211yesmaximal, characteristic, complemented
4C7×D13×D35C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C3×C7×D7×D13—51nomaximal, Hall
7C7×D455C2×C311yescharacteristic, complemented
8C7×C13×D35C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10C3×D13×D35C711yesmaximal, characteristic, direct product factor
11C3×C7×D5×D13—71nomaximal
12C3×C7×D91—51no—
13C3×C7×C13×D7—51no—
14C3×C72×D13D511yescharacteristic, complemented
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16C2×C3×C7×D35—131nomaximal, Hall
17C3×D455C2×C711yescharacteristic, complemented
18C3×C13×D35C2×C711yescharacteristic, complemented
19C3×C7×D65—71no—
20C3×C7×D5×C13—71no—
21C3×C5×C7×D13—23no—
22C3×C5×C7×D13D711yescharacteristic, complemented
23C3×C5×C7×D13C2×C711yescharacteristic, complemented
24C7×D7×D13—51noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26D13×D35C3×C711yescharacteristic, direct product factor
27C7×D5×D13—71no—
28C2×C3×C5×C72—131no—
29C3×C7×D35—131no—
30C3×C7×D35D1311yescharacteristic, direct product factor
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C22×C711yescharacteristic, complemented
34C7×D91—51no—
35C7×C13×D7—51no—
36C72×D13C3×D511yescharacteristic, complemented
37C2×C3×C7×D13—351no—
38C3×D7×D13—51no—
39C2×C7×D35—131noHall
40D455C2×C3×C711yescharacteristic, complemented
41C13×D35C2×C3×C711yescharacteristic, complemented
42C7×D65—71no—
43C7×D5×C13—71no—
44C5×C7×D13—23no—
45C5×C7×D13C3×D711yescharacteristic, complemented
46C5×C7×D13C2×C3×C711yescharacteristic, complemented
47C3×D5×D13—71noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13C2×C3×D511yescharacteristic, complemented, Hall
50C2×C3×C7×D7—651noHall
51C2×C3×C7×C13—351no—
52C3×D91—51no—
53C3×C13×D7—51no—
54C3×C7×D13—23no—
55C3×C7×D13—351no—
56C3×C7×D13C7×D511yescharacteristic, complemented
57C3×C7×D13D3511yescharacteristic, direct product factor
58C2×C5×C72—131no—
59C7×D35—131no—
60C7×D35C3×D1311yescharacteristic, direct product factor
61C5×C7×C13—23no—
62C5×C7×C13C2×C3×D711yescharacteristic, complemented
63C5×C7×C13C22×C3×C711yescharacteristic, complemented
64C2×C3×D35—131no—
65C2×C3×C7×D5—911no—
66C3×D65—71no—
67C3×D5×C13—71no—
68C3×C5×D13C7×D711yescharacteristic, complemented
69C2×C7×D13—351no—
70D7×D13—51no—
71C2×C3×C72—131no—
72C3×C7×D7—51no—
73C3×C7×D7—651no—
74C3×C7×C13—23no—
75C3×C7×C13C2×C7×D511yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77D5×D13—71noHall
78C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
79C2×C3×C5×C7—131no—
80C2×C3×C5×C7—131no—
81C2×C3×C5×C7—263no—
82C3×D35—131no—
83C3×D35C7×D1311yescharacteristic, direct product factor
84C3×C7×D5—71no—
85C3×C7×D5—911no—
86C2×C7×D7—651noHall
87C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—351no—
89D91—51no—
90C7×D13—23no—
91C7×D13—351no—
92C7×D13C3×C7×D511yescharacteristic, complemented
93C7×D13C3×D3511yescharacteristic, direct product factor
94C13×D7—51no—
95C2×C3×D13—351noHall
96C3×C72D5×D1311yescharacteristic, complemented, Hall
97C2×D35—131no—
98C2×C7×D5—911no—
99D65—71no—
100C5×D13C3×C7×D711yescharacteristic, complemented
101D5×C13—71no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, complemented
104C3×C5×C7C2×C7×D1311yescharacteristic, complemented
105C2×C72—131no—
106C7×D7—51no—
107C7×D7—651no—
108C7×C13—23no—
109C7×C13C2×C3×C7×D511yescharacteristic, complemented
110C7×C13C2×C3×D3511yescharacteristic, complemented
111C22×C3×C7—4551no—
112C2×C3×D7—651no—
113C2×C3×C13—351no—
114C3×D13—351no—
115C3×D13C7×D3511yescharacteristic, direct product factor
116C2×C5×C7—131no—
117C2×C5×C7—131no—
118C2×C5×C7—263no—
119D35—131no—
120D35C3×C7×D1311yescharacteristic, direct product factor
121C7×D5—71no—
122C7×D5—911no—
123C5×C13C2×C3×C7×D711yescharacteristic, complemented, Hall
124C2×C3×D5—911noHall
125C2×D13—351noHall
126C72C3×D5×D1311yescharacteristic, complemented, Sylow
127C2×C3×C7—131no—
128C2×C3×C7—131no—
129C2×C3×C7—263no—
130C2×C3×C7—351no—
131C2×C3×C7—4551no—
132C3×D7—51no—
133C3×D7—651no—
134C3×C13C2×C7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7C3×D7×D1311yescharacteristic, complemented
137C5×C7C2×C3×C7×D1311yescharacteristic, complemented
138C2×C3×C5—131no—
139C3×D5—71no—
140C3×D5—911no—
141C22×C7—4551no—
142C2×D7—651no—
143C2×C13—351no—
144D13—351no—
145D13C3×C7×D3511yescharacteristic, direct product factor
146C3×C7—23no—
147C3×C7C7×D5×D1311yescharacteristic, complemented
148C3×C7D13×D3511yescharacteristic, direct product factor
149C2×D5—911noHall
150C3×C5C7×D7×D1311yescharacteristic, complemented, Hall
151C2×C7—131no—
152C2×C7—131no—
153C2×C7—263no—
154C2×C7—351no—
155C2×C7—4551no—
156D7—51no—
157D7—651no—
158C13C2×C3×C7×D3511yescharacteristic, complemented, Sylow
159C22×C3—4551noHall
160C2×C5—131no—
161D5—71no—
162D5—911no—
163C7—23no—
164C7C3×C7×D5×D1311yescharacteristic, complemented
165C7C3×D13×D3511yescharacteristic, direct product factor
166C2×C3—131no—
167C2×C3—351no—
168C2×C3—4551no—
169C5C3×C7×D7×D1311yescharacteristic, complemented, Sylow
170C22—4551noSylow
171C3C7×D13×D3511yescharacteristic, direct product factor, Sylow
172C2—131no—
173C2—351no—
174C2—4551no—
subgroupG/H
center, hypercenterC3×C7D13×D35
commutator, cosocle, hypocenterC5×C7×C13C22×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×D13C2semidirect
2. C3×C7×C13×D35C2semidirect
3. C3×C7×D455C2semidirect
4. C7×D13×D35C3direct (N × H)
5. C3×C5×C72×C13C22semidirect
7. C7×D455C2×C3semidirect
8. C7×C13×D35C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
10. C3×D13×D35C7direct (N × H)
14. C3×C72×D13D5semidirect
15. C5×C72×C13C22×C3semidirect
17. C3×D455C2×C7semidirect
18. C3×C13×D35C2×C7semidirect
22. C3×C5×C7×D13D7semidirect
23. C3×C5×C7×D13C2×C7semidirect
25. C3×C72×C13C2×D5semidirect
26. D13×D35C3×C7direct (N × H)
30. C3×C7×D35D13direct (N × H)
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C22×C7semidirect
36. C72×D13C3×D5semidirect
40. D455C2×C3×C7semidirect
41. C13×D35C2×C3×C7semidirect
45. C5×C7×D13C3×D7semidirect
46. C5×C7×D13C2×C3×C7semidirect
48. C3×C5×C72C2×D13semidirect
49. C72×C13C2×C3×D5semidirect
56. C3×C7×D13C7×D5semidirect
57. C3×C7×D13D35direct (N × H)
60. C7×D35C3×D13direct (N × H)
62. C5×C7×C13C2×C3×D7semidirect
63. C5×C7×C13C22×C3×C7semidirect
68. C3×C5×D13C7×D7semidirect
75. C3×C7×C13C2×C7×D5semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72C2×C3×D13semidirect
83. C3×D35C7×D13direct (N × H)
87. C3×C5×C13C2×C7×D7semidirect
92. C7×D13C3×C7×D5semidirect
93. C7×D13C3×D35direct (N × H)
96. C3×C72D5×D13semidirect
100. C5×D13C3×C7×D7semidirect
103. C3×C5×C7D7×D13semidirect
104. C3×C5×C7C2×C7×D13semidirect
109. C7×C13C2×C3×C7×D5semidirect
110. C7×C13C2×C3×D35semidirect
115. C3×D13C7×D35direct (N × H)
120. D35C3×C7×D13direct (N × H)
123. C5×C13C2×C3×C7×D7semidirect
126. C72C3×D5×D13semidirect
134. C3×C13C2×C7×D35semidirect
136. C5×C7C3×D7×D13semidirect
137. C5×C7C2×C3×C7×D13semidirect
145. D13C3×C7×D35direct (N × H)
147. C3×C7C7×D5×D13semidirect
148. C3×C7D13×D35direct (N × H)
150. C3×C5C7×D7×D13semidirect
158. C13C2×C3×C7×D35semidirect
164. C7C3×C7×D5×D13semidirect
165. C7C3×D13×D35direct (N × H)
169. C5C3×C7×D7×D13semidirect
171. C3C7×D13×D35direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C72×D132
C3×C7×C13×D352
C3×C7×D4552
C7×D13×D353
C3×C7×D7×D135
C3×D13×D357
C3×C7×D5×D137
C2×C3×C7×D3513