Finite Group Databasebeta

← C7×D21×D65 #50304457

Subgroups — C7×D21×D65 #50304457

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×C72×D65C211yesmaximal, characteristic, complemented
2C5×C7×C13×D21C211yesmaximal, characteristic, complemented
3C7×D1365C211yesmaximal, characteristic, complemented
4C7×D7×D65—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C7×D13×D21—51nomaximal, Hall
7C7×D455—31no—
8C72×D65D311yescharacteristic, complemented
9C5×C7×C13×D7—31no—
10D21×D65C711yesmaximal, characteristic, direct product factor
11D3×C7×D65—71nomaximal
12C7×D273—51no—
13C7×C13×D21D511yescharacteristic, complemented
14C3×C72×D13—51no—
15C5×C72×C13C2×D311yescharacteristic, complemented, Hall
16C7×D5×D21—131nomaximal, Hall
17D1365C2×C711yescharacteristic, complemented
18C7×D195—71no—
19C5×C13×D21C2×C711yescharacteristic, complemented
20C5×D3×C7×C13—71no—
21C3×C7×D65—23no—
22C3×C7×D65D711yescharacteristic, complemented
23C3×C7×D65C2×C711yescharacteristic, complemented
24C7×D7×D13—151noHall
25C3×C72×C13C2×D511yescharacteristic, complemented, Hall
26C2×C7×D65—211no—
27D7×D65—31no—
28C7×D105—131no—
29C5×C7×D21D1311yescharacteristic, complemented
30C3×C72×D5—131no—
31C3×C5×C7×C13—23no—
32C3×C5×C7×C13C2×D711yescharacteristic, complemented
33C3×C5×C7×C13C22×C711yescharacteristic, complemented
34C7×D91—151no—
35C7×C13×D7—31no—
36C72×D13—51no—
37D13×D21—51no—
38D3×C7×D13—351no—
39C7×D5×D7—391noHall
40C2×C5×C7×C13—211no—
41D455—31no—
42C7×D65—23no—
43C7×D65—211no—
44C7×D65D3×C711yescharacteristic, complemented
45C7×D65D2111yescharacteristic, direct product factor
46C5×C13×D7—31no—
47D3×D65—71noHall
48C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
49C72×C13D3×D511yescharacteristic, complemented, Hall
50C2×C7×D21—651noHall
51D273—51no—
52C13×D21C7×D511yescharacteristic, complemented
53C7×D39—351no—
54D3×C7×C13—71no—
55C3×C7×D13—51no—
56C3×C7×D13—51no—
57C3×C7×D13—103no—
58C7×D35—391no—
59C72×D5—131no—
60C5×C7×D7—31no—
61C5×C7×C13—23no—
62C5×C7×C13C2×D3×C711yescharacteristic, complemented
63C5×C7×C13C2×D2111yescharacteristic, complemented
64D5×D21—131no—
65D3×C7×D5—911no—
66D195—71no—
67C5×D3×C13—71no—
68C3×D65C7×D711yescharacteristic, complemented
69C2×C7×D13—1051no—
70D7×D13—151no—
71C2×C3×C72—651no—
72C7×D21—651no—
73C7×D21D6511yescharacteristic, direct product factor
74C3×C7×C13—23no—
75C3×C7×C13D5×D711yescharacteristic, complemented
76C3×C7×C13C2×C7×D511yescharacteristic, complemented
77C2×D65—211noHall
78C5×C72D3×D1311yescharacteristic, complemented, Hall
79D105—131no—
80C7×D15—911no—
81C5×D21C7×D1311yescharacteristic, complemented
82C5×D3×C7—71no—
83C3×C7×D5—131no—
84C3×C7×D5—131no—
85C3×C7×D5—263no—
86C2×C7×D7—1951noHall
87C3×C5×C13C2×C7×D711yescharacteristic, complemented, Hall
88C2×C7×C13—211no—
89D91—151no—
90C7×D13—51no—
91C7×D13—51no—
92C7×D13—103no—
93C7×D13—1051no—
94C13×D7—31no—
95D3×D13—351noHall
96C3×C72C2×D6511yescharacteristic, complemented, Hall
97C2×C7×D5—2731no—
98D5×D7—391no—
99C2×C5×C13—211no—
100D65—211no—
101D65C7×D2111yescharacteristic, direct product factor
102C3×C5×C7—23no—
103C3×C5×C7D7×D1311yescharacteristic, complemented
104C3×C5×C7C2×C7×D1311yescharacteristic, complemented
105C2×C72—651no—
106C7×D7—31no—
107C7×D7—1951no—
108C7×C13—23no—
109C7×C13D3×C7×D511yescharacteristic, complemented
110C7×C13D5×D2111yescharacteristic, complemented
111C2×D21—651no—
112C2×D3×C7—4551no—
113D39—351no—
114C3×D13—51no—
115D3×C13—71no—
116C2×C5×C7—211no—
117D35—391no—
118C5×D7—31no—
119C7×D5—131no—
120C7×D5—131no—
121C7×D5—2731no—
122C7×D5—263no—
123C5×C13C2×C7×D2111yescharacteristic, complemented, Hall
124D3×D5—911noHall
125C2×D13—1051noHall
126C72D3×D6511yescharacteristic, complemented, Sylow
127C2×C3×C7—651no—
128C2×C3×C7—651no—
129C2×C3×C7—1303no—
130D21—651no—
131D21C7×D6511yescharacteristic, direct product factor
132D3×C7—71no—
133D3×C7—4551no—
134C3×C13C7×D5×D711yescharacteristic, complemented, Hall
135C5×C7—23no—
136C5×C7D3×C7×D1311yescharacteristic, complemented
137C5×C7D13×D2111yescharacteristic, complemented
138D15—911no—
139C3×D5—131no—
140C5×D3—71no—
141C22×C7—13651no—
142C2×D7—1951no—
143C2×C13—211no—
144D13—51no—
145D13—1051no—
146C3×C7—23no—
147C3×C7D7×D6511yescharacteristic, complemented
148C3×C7C2×C7×D6511yescharacteristic, complemented
149C2×D5—2731noHall
150C3×C5C7×D7×D1311yescharacteristic, complemented, Hall
151C2×C7—211no—
152C2×C7—651no—
153C2×C7—651no—
154C2×C7—13651no—
155C2×C7—1303no—
156D7—31no—
157D7—1951no—
158C13C7×D5×D2111yescharacteristic, complemented, Sylow
159C2×D3—4551noHall
160C2×C5—211no—
161D5—131no—
162D5—2731no—
163C7—23no—
164C7D3×C7×D6511yescharacteristic, complemented
165C7D21×D6511yescharacteristic, direct product factor
166C2×C3—651no—
167D3—71no—
168D3—4551no—
169C5C7×D13×D2111yescharacteristic, complemented, Sylow
170C22—13651noSylow
171C3C7×D7×D6511yescharacteristic, complemented, Sylow
172C2—211no—
173C2—651no—
174C2—13651no—
subgroupG/H
center, hypercenterC7D21×D65
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×C72×D65C2semidirect
2. C5×C7×C13×D21C2semidirect
3. C7×D1365C2semidirect
5. C3×C5×C72×C13C22semidirect
8. C72×D65D3semidirect
10. D21×D65C7direct (N × H)
13. C7×C13×D21D5semidirect
15. C5×C72×C13C2×D3semidirect
17. D1365C2×C7semidirect
19. C5×C13×D21C2×C7semidirect
22. C3×C7×D65D7semidirect
23. C3×C7×D65C2×C7semidirect
25. C3×C72×C13C2×D5semidirect
29. C5×C7×D21D13semidirect
32. C3×C5×C7×C13C2×D7semidirect
33. C3×C5×C7×C13C22×C7semidirect
44. C7×D65D3×C7semidirect
45. C7×D65D21direct (N × H)
48. C3×C5×C72C2×D13semidirect
49. C72×C13D3×D5semidirect
52. C13×D21C7×D5semidirect
62. C5×C7×C13C2×D3×C7semidirect
63. C5×C7×C13C2×D21semidirect
68. C3×D65C7×D7semidirect
73. C7×D21D65direct (N × H)
75. C3×C7×C13D5×D7semidirect
76. C3×C7×C13C2×C7×D5semidirect
78. C5×C72D3×D13semidirect
81. C5×D21C7×D13semidirect
87. C3×C5×C13C2×C7×D7semidirect
96. C3×C72C2×D65semidirect
101. D65C7×D21direct (N × H)
103. C3×C5×C7D7×D13semidirect
104. C3×C5×C7C2×C7×D13semidirect
109. C7×C13D3×C7×D5semidirect
110. C7×C13D5×D21semidirect
123. C5×C13C2×C7×D21semidirect
126. C72D3×D65semidirect
131. D21C7×D65direct (N × H)
134. C3×C13C7×D5×D7semidirect
136. C5×C7D3×C7×D13semidirect
137. C5×C7D13×D21semidirect
147. C3×C7D7×D65semidirect
148. C3×C7C2×C7×D65semidirect
150. C3×C5C7×D7×D13semidirect
158. C13C7×D5×D21semidirect
164. C7D3×C7×D65semidirect
165. C7D21×D65direct (N × H)
169. C5C7×D13×D21semidirect
171. C3C7×D7×D65semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D652
C5×C7×C13×D212
C7×D13652
C7×D7×D653
C7×D13×D215
D21×D657
D3×C7×D657
C7×D5×D2113