Finite Group Databasebeta

← C7×D5×(C13⋊C3)⋊D7 #50304085

Subgroups — C7×D5×(C13⋊C3)⋊D7 #50304085

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
1C7×C5⋊((C13⋊C3)⋊D7)C211yesmaximal, characteristic, complemented
2C72×D5×C13⋊C3C211yesmaximal, characteristic, complemented
3C5×C7×(C13⋊C3)⋊D7C211yesmaximal, characteristic, complemented
4C7×D5×D91C311yesmaximal, characteristic, complemented, Hall
5C5×C72×C13⋊C3C2211yescharacteristic, complemented, Hall
6C2×C7×(C13⋊C3)⋊D7—51nomaximal, Hall
7C7×D455C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C7×D91C2×C311yescharacteristic, complemented
10D5×(C13⋊C3)⋊D7C711yesmaximal, characteristic, direct product factor
11C7×D5×D13⋊C3—71nomaximal
12C2×C72×C13⋊C3—51no—
13C7×(C13⋊C3)⋊D7—51no—
14C7×(C13⋊C3)⋊D7D511yescharacteristic, direct product factor
15C5×C72×C13C22×C311yescharacteristic, complemented, Hall
16C3×C7×D5×D7—131nomaximal, Hall
17C5⋊((C13⋊C3)⋊D7)C2×C711yescharacteristic, complemented
18C7×C5⋊(D13⋊C3)—71no—
19C7×D5×C13⋊C3—23no—
20C7×D5×C13⋊C3D711yescharacteristic, complemented
21C7×D5×C13⋊C3C2×C711yescharacteristic, complemented
22C5×(C13⋊C3)⋊D7C2×C711yescharacteristic, complemented
23C5×C7×D13⋊C3—71no—
24C2×C7×D91—51noHall
25C72×C13⋊C3C2×D511yescharacteristic, complemented, Hall
26D5×D91C3×C711yescharacteristic, complemented
27C7×D5×D13—71no—
28C3×C7×D35—131no—
29C3×C72×D5—131no—
30C3×C5×C7×D7—131no—
31C5×C7×C13⋊C3—23no—
32C5×C7×C13⋊C3C2×D711yescharacteristic, complemented
33C5×C7×C13⋊C3C22×C711yescharacteristic, complemented
34C2×C72×C13—51no—
35C7×D91—51no—
36C7×D91C3×D511yescharacteristic, complemented
37C2×(C13⋊C3)⋊D7—51no—
38C2×C7×D13⋊C3—351no—
39C7×D5×D7—131noHall
40D455C2×C3×C711yescharacteristic, complemented
41C7×D65—71no—
42C7×D5×C13—23no—
43C7×D5×C13C3×D711yescharacteristic, complemented
44C7×D5×C13C2×C3×C711yescharacteristic, complemented
45C5×D91C2×C3×C711yescharacteristic, complemented
46C5×C7×D13—71no—
47D5×D13⋊C3—71noHall
48C3×C5×C72—131noHall
49C72×C13C2×C3×D511yescharacteristic, complemented, Hall
50C2×C3×C7×D7—651noHall
51C2×C7×C13⋊C3—51no—
52C2×C7×C13⋊C3—51no—
53C2×C7×C13⋊C3—103no—
54(C13⋊C3)⋊D7—51no—
55(C13⋊C3)⋊D7C7×D511yescharacteristic, direct product factor
56C7×D13⋊C3—71no—
57C7×D13⋊C3—351no—
58C7×D35—131no—
59C72×D5D13⋊C311yescharacteristic, complemented
60C5×C7×D7—131no—
61C5×C7×C13—23no—
62C5×C7×C13C2×C3×D711yescharacteristic, complemented
63C5×C7×C13C22×C3×C711yescharacteristic, complemented
64C2×C3×C7×D5—911no—
65C3×D5×D7—131no—
66C5⋊(D13⋊C3)—71no—
67D5×C13⋊C3C7×D711yescharacteristic, complemented
68C5×D13⋊C3—71no—
69C2×D91—51no—
70C2×C7×D13—351no—
71C2×C3×C72—651no—
72C3×C7×D7—131no—
73C3×C7×D7—651no—
74C7×C13⋊C3—23no—
75C7×C13⋊C3D5×D711yescharacteristic, complemented
76C7×C13⋊C3C2×C7×D511yescharacteristic, complemented
77D5×D13—71noHall
78C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
79C2×C3×C5×C7—911no—
80C3×D35—131no—
81C3×C7×D5—131no—
82C3×C7×D5—131no—
83C3×C7×D5—263no—
84C3×C7×D5—911no—
85C3×C5×D7—131no—
86C2×C7×D7—651noHall
87C5×C13⋊C3C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—51no—
89C2×C7×C13—51no—
90C2×C7×C13—103no—
91D91—51no—
92D91C3×C7×D511yescharacteristic, complemented
93C7×D13—71no—
94C7×D13—351no—
95C2×D13⋊C3—351noHall
96C3×C72—131noHall
97C2×C7×D5—911no—
98D5×D7—131no—
99D65—71no—
100C5×D13—71no—
101D5×C13C3×C7×D711yescharacteristic, complemented
102C3×C5×C7—131no—
103C3×C5×C7—131no—
104C3×C5×C7—263no—
105C2×C72—51no—
106C7×D7—131no—
107C7×D7—651no—
108C7×C13—23no—
109C7×C13C3×D5×D711yescharacteristic, complemented
110C7×C13C2×C3×C7×D511yescharacteristic, complemented
111C22×C3×C7—4551no—
112C2×C3×D7—651no—
113C2×C13⋊C3—51no—
114D13⋊C3—71no—
115D13⋊C3—351no—
116C2×C5×C7—911no—
117D35—131no—
118C5×D7—131no—
119C7×D5—23no—
120C7×D5—911no—
121C7×D5C7×D13⋊C311yescharacteristic, complemented
122C7×D5(C13⋊C3)⋊D711yescharacteristic, direct product factor
123C5×C13C2×C3×C7×D711yescharacteristic, complemented, Hall
124C2×C3×D5—911noHall
125C2×D13—351noHall
126C72D5×D13⋊C311yescharacteristic, complemented, Sylow
127C2×C3×C7—651no—
128C2×C3×C7—651no—
129C2×C3×C7—911no—
130C2×C3×C7—1303no—
131C2×C3×C7—4551no—
132C3×D7—131no—
133C3×D7—651no—
134C13⋊C3C7×D5×D711yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7C2×C7×D13⋊C311yescharacteristic, complemented
137C5×C7C2×(C13⋊C3)⋊D711yescharacteristic, complemented
138C2×C3×C5—911no—
139C3×D5—131no—
140C3×D5—911no—
141C22×C7—4551no—
142C2×D7—651no—
143C2×C13—51no—
144D13—71no—
145D13—351no—
146C3×C7—131no—
147C3×C7—131no—
148C3×C7—263no—
149C2×D5—911noHall
150C3×C5—131noHall
151C2×C7—51no—
152C2×C7—51no—
153C2×C7—103no—
154C2×C7—911no—
155C2×C7—4551no—
156D7—131no—
157D7—651no—
158C13C3×C7×D5×D711yescharacteristic, complemented, Sylow
159C22×C3—4551noHall
160C2×C5—911no—
161D5—911no—
162D5C7×(C13⋊C3)⋊D711yescharacteristic, direct product factor
163C7—23no—
164C7C7×D5×D13⋊C311yescharacteristic, complemented
165C7D5×(C13⋊C3)⋊D711yescharacteristic, direct product factor
166C2×C3—651no—
167C2×C3—911no—
168C2×C3—4551no—
169C5C2×C7×(C13⋊C3)⋊D711yescharacteristic, complemented, Sylow
170C22—4551noSylow
171C3—131noSylow
172C2—51no—
173C2—911no—
174C2—4551no—
subgroupG/H
center, hypercenterC7D5×(C13⋊C3)⋊D7
commutator, cosocle, hypocenterC5×C7×C13C22×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×C5⋊((C13⋊C3)⋊D7)C2semidirect
2. C72×D5×C13⋊C3C2semidirect
3. C5×C7×(C13⋊C3)⋊D7C2semidirect
4. C7×D5×D91C3semidirect
5. C5×C72×C13⋊C3C22semidirect
7. C7×D455C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C7×D91C2×C3semidirect
10. D5×(C13⋊C3)⋊D7C7direct (N × H)
14. C7×(C13⋊C3)⋊D7D5direct (N × H)
15. C5×C72×C13C22×C3semidirect
17. C5⋊((C13⋊C3)⋊D7)C2×C7semidirect
20. C7×D5×C13⋊C3D7semidirect
21. C7×D5×C13⋊C3C2×C7semidirect
22. C5×(C13⋊C3)⋊D7C2×C7semidirect
25. C72×C13⋊C3C2×D5semidirect
26. D5×D91C3×C7semidirect
32. C5×C7×C13⋊C3C2×D7semidirect
33. C5×C7×C13⋊C3C22×C7semidirect
36. C7×D91C3×D5semidirect
40. D455C2×C3×C7semidirect
43. C7×D5×C13C3×D7semidirect
44. C7×D5×C13C2×C3×C7semidirect
45. C5×D91C2×C3×C7semidirect
49. C72×C13C2×C3×D5semidirect
55. (C13⋊C3)⋊D7C7×D5direct (N × H)
59. C72×D5D13⋊C3semidirect
62. C5×C7×C13C2×C3×D7semidirect
63. C5×C7×C13C22×C3×C7semidirect
67. D5×C13⋊C3C7×D7semidirect
75. C7×C13⋊C3D5×D7semidirect
76. C7×C13⋊C3C2×C7×D5semidirect
78. C5×C72C2×D13⋊C3semidirect
87. C5×C13⋊C3C2×C7×D7semidirect
92. D91C3×C7×D5semidirect
101. D5×C13C3×C7×D7semidirect
109. C7×C13C3×D5×D7semidirect
110. C7×C13C2×C3×C7×D5semidirect
121. C7×D5C7×D13⋊C3semidirect
122. C7×D5(C13⋊C3)⋊D7direct (N × H)
123. C5×C13C2×C3×C7×D7semidirect
126. C72D5×D13⋊C3semidirect
134. C13⋊C3C7×D5×D7semidirect
136. C5×C7C2×C7×D13⋊C3semidirect
137. C5×C7C2×(C13⋊C3)⋊D7semidirect
158. C13C3×C7×D5×D7semidirect
162. D5C7×(C13⋊C3)⋊D7direct (N × H)
164. C7C7×D5×D13⋊C3semidirect
165. C7D5×(C13⋊C3)⋊D7direct (N × H)
169. C5C2×C7×(C13⋊C3)⋊D7semidirect

Maximal subgroups

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

subgroupindex
C7×C5⋊((C13⋊C3)⋊D7)2
C72×D5×C13⋊C32
C5×C7×(C13⋊C3)⋊D72
C7×D5×D913
C2×C7×(C13⋊C3)⋊D75
D5×(C13⋊C3)⋊D77
C7×D5×D13⋊C37
C3×C7×D5×D713