Finite Group Databasebeta

← C7×D35×D39 #50304460

Subgroups — C7×D35×D39 #50304460

Order 38220.

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

normal subgroups only

This group has 208 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×C7×C13×D35C211yesmaximal, characteristic, complemented
2C5×C72×D39C211yesmaximal, characteristic, complemented
3C7×D1365C211yesmaximal, characteristic, complemented
4C7×D13×D35—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C7×D7×D39—51nomaximal, Hall
7C7×D455—31no—
8C7×C13×D35D311yescharacteristic, complemented
9C5×C72×D13—31no—
10D35×D39C711yesmaximal, characteristic, direct product factor
11C7×D5×D39—71nomaximal
12C7×D273—51no—
13C72×D39D511yescharacteristic, complemented
14C3×C7×C13×D7—51no—
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16D3×C7×D35—131nomaximal, Hall
17D1365C2×C711yescharacteristic, complemented
18C7×D195—71no—
19C5×C7×D39—23no—
20C5×C7×D39D711yescharacteristic, complemented
21C5×C7×D39C2×C711yescharacteristic, complemented
22C3×C13×D35C2×C711yescharacteristic, complemented
23C3×C7×D5×C13—71no—
24C7×D7×D13—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26D13×D35—31no—
27C7×D5×D13—211no—
28C7×D105—131no—
29C5×D3×C72—131no—
30C3×C7×D35D1311yescharacteristic, complemented
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C22×C711yescharacteristic, complemented
34C7×D91—151no—
35C7×C13×D7—51no—
36C72×D13—31no—
37C2×C7×D39—351no—
38D7×D39—51no—
39C2×C7×D35—391noHall
40D455—31no—
41C13×D35D3×C711yescharacteristic, complemented
42C7×D65—211no—
43C7×D5×C13—71no—
44C5×C7×D13—31no—
45C5×C7×D13—31no—
46C5×C7×D13—63no—
47D5×D39—71noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13D3×D511yescharacteristic, complemented, Hall
50D3×C7×D7—651noHall
51C2×C3×C7×C13—351no—
52D273—51no—
53C7×D39—23no—
54C7×D39—351no—
55C7×D39C7×D511yescharacteristic, complemented
56C7×D39D3511yescharacteristic, direct product factor
57C3×C13×D7—51no—
58C2×C5×C72—391no—
59C7×D35—391no—
60C7×D35D3911yescharacteristic, direct product factor
61C5×C7×C13—23no—
62C5×C7×C13D3×D711yescharacteristic, complemented
63C5×C7×C13C2×D3×C711yescharacteristic, complemented
64D3×D35—131no—
65D3×C7×D5—911no—
66D195—71no—
67C5×D39C7×D711yescharacteristic, complemented
68C3×D5×C13—71no—
69C2×C7×D13—1051no—
70D7×D13—151no—
71C7×D21—651no—
72D3×C72—131no—
73C3×C7×D7—51no—
74C3×C7×C13—23no—
75C3×C7×C13C2×C7×D511yescharacteristic, complemented
76C3×C7×C13C2×D3511yescharacteristic, complemented
77D5×D13—211noHall
78C5×C72C2×D3911yescharacteristic, complemented, Hall
79D105—131no—
80C7×D15—911no—
81C5×D3×C7—131no—
82C5×D3×C7—131no—
83C5×D3×C7—263no—
84C3×D35C7×D1311yescharacteristic, complemented
85C3×C7×D5—71no—
86C2×C7×D7—1951noHall
87C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—351no—
89D91—151no—
90C7×D13—31no—
91C7×D13—31no—
92C7×D13—63no—
93C7×D13—1051no—
94C13×D7—51no—
95C2×D39—351noHall
96C3×C72D5×D1311yescharacteristic, complemented, Hall
97C2×D35—391no—
98C2×C7×D5—2731no—
99D65—211no—
100C5×D13—31no—
101D5×C13—71no—
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, complemented
104C3×C5×C7C2×C7×D1311yescharacteristic, complemented
105C2×C72—391no—
106C7×D7—51no—
107C7×D7—1951no—
108C7×C13—23no—
109C7×C13D3×C7×D511yescharacteristic, complemented
110C7×C13D3×D3511yescharacteristic, complemented
111C2×D3×C7—4551no—
112D3×D7—651no—
113C2×C3×C13—351no—
114D39—351no—
115D39C7×D3511yescharacteristic, direct product factor
116C2×C5×C7—391no—
117C2×C5×C7—391no—
118C2×C5×C7—783no—
119D35—391no—
120D35C7×D3911yescharacteristic, direct product factor
121C7×D5—71no—
122C7×D5—2731no—
123C5×C13D3×C7×D711yescharacteristic, complemented, Hall
124D3×D5—911noHall
125C2×D13—1051noHall
126C72D5×D3911yescharacteristic, complemented, Sylow
127C2×C3×C7—351no—
128D21—651no—
129C3×D7—51no—
130D3×C7—131no—
131D3×C7—131no—
132D3×C7—263no—
133D3×C7—4551no—
134C3×C13C2×C7×D3511yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D7×D3911yescharacteristic, complemented
137C5×C7C2×C7×D3911yescharacteristic, complemented
138D15—911no—
139C3×D5—71no—
140C5×D3—131no—
141C22×C7—13651no—
142C2×D7—1951no—
143C2×C13—351no—
144D13—31no—
145D13—1051no—
146C3×C7—23no—
147C3×C7C7×D5×D1311yescharacteristic, complemented
148C3×C7D13×D3511yescharacteristic, complemented
149C2×D5—2731noHall
150C3×C5C7×D7×D1311yescharacteristic, complemented, Hall
151C2×C7—351no—
152C2×C7—391no—
153C2×C7—391no—
154C2×C7—783no—
155C2×C7—13651no—
156D7—51no—
157D7—1951no—
158C13D3×C7×D3511yescharacteristic, complemented, Sylow
159C2×D3—4551noHall
160C2×C5—391no—
161D5—71no—
162D5—2731no—
163C7—23no—
164C7C7×D5×D3911yescharacteristic, complemented
165C7D35×D3911yescharacteristic, direct product factor
166C2×C3—351no—
167D3—131no—
168D3—4551no—
169C5C7×D7×D3911yescharacteristic, complemented, Sylow
170C22—13651noSylow
171C3C7×D13×D3511yescharacteristic, complemented, Sylow
172C2—351no—
173C2—391no—
174C2—13651no—
subgroupG/H
center, hypercenterC7D35×D39
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C13×D35C2semidirect
2. C5×C72×D39C2semidirect
3. C7×D1365C2semidirect
5. C3×C5×C72×C13C22semidirect
8. C7×C13×D35D3semidirect
10. D35×D39C7direct (N × H)
13. C72×D39D5semidirect
15. C5×C72×C13C2×D3semidirect
17. D1365C2×C7semidirect
20. C5×C7×D39D7semidirect
21. C5×C7×D39C2×C7semidirect
22. C3×C13×D35C2×C7semidirect
25. C3×C72×C13C2×D5semidirect
30. C3×C7×D35D13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C22×C7semidirect
41. C13×D35D3×C7semidirect
48. C3×C5×C72C2×D13semidirect
49. C72×C13D3×D5semidirect
55. C7×D39C7×D5semidirect
56. C7×D39D35direct (N × H)
60. C7×D35D39direct (N × H)
62. C5×C7×C13D3×D7semidirect
63. C5×C7×C13C2×D3×C7semidirect
67. C5×D39C7×D7semidirect
75. C3×C7×C13C2×C7×D5semidirect
76. C3×C7×C13C2×D35semidirect
78. C5×C72C2×D39semidirect
84. C3×D35C7×D13semidirect
87. C3×C5×C13C2×C7×D7semidirect
96. C3×C72D5×D13semidirect
103. C3×C5×C7D7×D13semidirect
104. C3×C5×C7C2×C7×D13semidirect
109. C7×C13D3×C7×D5semidirect
110. C7×C13D3×D35semidirect
115. D39C7×D35direct (N × H)
120. D35C7×D39direct (N × H)
123. C5×C13D3×C7×D7semidirect
126. C72D5×D39semidirect
134. C3×C13C2×C7×D35semidirect
136. C5×C7D7×D39semidirect
137. C5×C7C2×C7×D39semidirect
147. C3×C7C7×D5×D13semidirect
148. C3×C7D13×D35semidirect
150. C3×C5C7×D7×D13semidirect
158. C13D3×C7×D35semidirect
164. C7C7×D5×D39semidirect
165. C7D35×D39direct (N × H)
169. C5C7×D7×D39semidirect
171. C3C7×D13×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C13×D352
C5×C72×D392
C7×D13652
C7×D13×D353
C7×D7×D395
D35×D397
C7×D5×D397
D3×C7×D3513