Finite Group Databasebeta

← C7×D15×D65 #41032011

Subgroups — C7×D15×D65 #41032011

Order 27300.

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×C7×D65C211yesmaximal, characteristic, complemented
2C5×C7×C13×D15C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D65)C211yesmaximal, characteristic, complemented
4C7×D5×D65—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6D3×C7×D65—51nomaximal
7C7×D13×D15—51nomaximal
8C7×C5⋊D65—31no—
9C5×C7×D65D311yescharacteristic, complemented
10C5×C7×D5×C13—31no—
11D15×D65C711yesmaximal, characteristic, direct product factor, Hall
12C7×D195—51no—
13C7×D195—51no—
14C7×D195—102no—
15C7×C13×D15D511yescharacteristic, complemented
16C5×D3×C7×C13—51no—
17C3×C7×D65D511yescharacteristic, complemented
18C3×C5×C7×D13—51no—
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20C7×D5×D15—131nomaximal, Hall
21C3⋊(C5⋊D65)C2×C711yescharacteristic, complemented
22C5×C13×D15C2×C711yescharacteristic, complemented
23C3×C5×D65C2×C711yescharacteristic, complemented
24C2×C7×D65—151no—
25C7×D5×D13—151no—
26C3×C5×C7×C13—22no—
27C3×C5×C7×C13C2×D511yescharacteristic, complemented
28C3×C5×C7×C13C2×D511yescharacteristic, complemented
29D5×D65—31noHall
30D3×C7×D13—251noHall
31C7×C3⋊(C5⋊D5)—131no—
32C5×C7×D15D1311yescharacteristic, complemented
33C3×C5×C7×D5—131no—
34C3×C52×C13C22×C711yescharacteristic, complemented, Hall
35C2×C5×C7×C13—151no—
36C7×D65—151no—
37C7×D65—151no—
38C7×D65—302no—
39C7×D65D1511yescharacteristic, direct product factor
40C7×D5×C13—31no—
41C5×C7×D13—51no—
42D3×D65—51no—
43D13×D15—51no—
44C7×D52—391noHall
45C5⋊D65—31no—
46C5×D65D3×C711yescharacteristic, complemented
47C5×D5×C13—31no—
48C7×D39—251no—
49D3×C7×C13—51no—
50C3×C7×D13—51no—
51C3×C52×C7C2×D1311yescharacteristic, complemented, Hall
52C5×C7×C13—22no—
53C5×C7×C13D3×D511yescharacteristic, complemented
54C5×C7×C13C2×D1511yescharacteristic, complemented
55C2×C7×D15—651no—
56D3×C7×D5—651no—
57D195—51no—
58D195—51no—
59D195—102no—
60C13×D15C7×D511yescharacteristic, complemented
61C5×D3×C13—51no—
62C3×D65C7×D511yescharacteristic, complemented
63C3×C5×D13—51no—
64C2×C7×D13—751noHall
65C7×C5⋊D5—391no—
66C5×C7×D5—31no—
67C5×C7×D5—131no—
68C52×C13C2×D3×C711yescharacteristic, complemented, Hall
69D5×D15—131noHall
70C3×C7×C13D5211yescharacteristic, complemented, Hall
71C2×D65—151no—
72D5×D13—151no—
73C2×C3×C5×C7—651no—
74C7×D15—651no—
75C7×D15—651no—
76C7×D15—1302no—
77C7×D15D6511yescharacteristic, direct product factor
78C5×D3×C7—51no—
79C3×C7×D5—131no—
80C3×C5×C13—22no—
81C3×C5×C13C2×C7×D511yescharacteristic, complemented
82C3×C5×C13C2×C7×D511yescharacteristic, complemented
83C2×C7×C13—151no—
84C7×D13—51no—
85C7×D13—751no—
86C52×C7D3×D1311yescharacteristic, complemented, Hall
87D3×D13—251noHall
88C3⋊(C5⋊D5)—131no—
89C5×D15C7×D1311yescharacteristic, complemented
90C3×C5×D5—131no—
91C2×C7×D5—1951no—
92C2×C7×D5—1951no—
93C2×C5×C13—151no—
94D65—151no—
95D65—151no—
96D65—302no—
97D65C7×D1511yescharacteristic, direct product factor
98C5×D13—51no—
99D5×C13—31no—
100C3×C5×C7—22no—
101C3×C5×C7D5×D1311yescharacteristic, complemented
102C3×C5×C7C2×D6511yescharacteristic, complemented
103D52—391noHall
104C7×C13D5×D1511yescharacteristic, complemented, Hall
105C2×D3×C7—3251noHall
106D39—251no—
107C3×D13—51no—
108D3×C13—51no—
109C3×C52C2×C7×D1311yescharacteristic, complemented, Hall
110C2×C5×C7—151no—
111C2×C5×C7—651no—
112C7×D5—31no—
113C7×D5—131no—
114C7×D5—3902no—
115C7×D5—1951no—
116C7×D5—1951no—
117C5×C13—22no—
118C5×C13D3×C7×D511yescharacteristic, complemented
119C5×C13C2×C7×D1511yescharacteristic, complemented
120C2×D15—651no—
121D3×D5—651no—
122C2×D13—751noHall
123C5⋊D5—391no—
124C5×D5—31no—
125C5×D5—131no—
126C2×C3×C7—651no—
127D3×C7—51no—
128D3×C7—3251no—
129C3×C13C7×D5211yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7D13×D1511yescharacteristic, complemented
132C5×C7D3×D6511yescharacteristic, complemented
133C2×C3×C5—651no—
134D15—651no—
135D15—651no—
136D15—1302no—
137D15C7×D6511yescharacteristic, direct product factor
138C3×D5—131no—
139C5×D3—51no—
140C22×C7—9751noHall
141C2×C13—151no—
142D13—51no—
143D13—751no—
144C52D3×C7×D1311yescharacteristic, complemented, Sylow
145C3×C7D5×D6511yescharacteristic, complemented, Hall
146C2×D5—1951no—
147C2×D5—1951no—
148C3×C5—22no—
149C3×C5C7×D5×D1311yescharacteristic, complemented
150C3×C5C2×C7×D6511yescharacteristic, complemented
151C2×C7—151no—
152C2×C7—651no—
153C2×C7—9751no—
154C13C7×D5×D1511yescharacteristic, complemented, Sylow
155C2×D3—3251noHall
156C2×C5—151no—
157C2×C5—651no—
158D5—31no—
159D5—131no—
160D5—3902no—
161D5—1951no—
162D5—1951no—
163C7D15×D6511yescharacteristic, direct product factor, Sylow
164C2×C3—651no—
165D3—51no—
166D3—3251no—
167C5—22no—
168C5C7×D13×D1511yescharacteristic, complemented
169C5D3×C7×D6511yescharacteristic, complemented
170C22—9751noSylow
171C3C7×D5×D6511yescharacteristic, complemented, Sylow
172C2—151no—
173C2—651no—
174C2—9751no—
subgroupG/H
center, hypercenterC7D15×D65
commutator, cosocle, hypocenterC3×C52×C13C22×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C52×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D65C2semidirect
2. C5×C7×C13×D15C2semidirect
3. C7×C3⋊(C5⋊D65)C2semidirect
5. C3×C52×C7×C13C22semidirect
9. C5×C7×D65D3semidirect
11. D15×D65C7direct (N × H)
15. C7×C13×D15D5semidirect
17. C3×C7×D65D5semidirect
19. C52×C7×C13C2×D3semidirect
21. C3⋊(C5⋊D65)C2×C7semidirect
22. C5×C13×D15C2×C7semidirect
23. C3×C5×D65C2×C7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C2×D5semidirect
32. C5×C7×D15D13semidirect
34. C3×C52×C13C22×C7semidirect
39. C7×D65D15direct (N × H)
46. C5×D65D3×C7semidirect
51. C3×C52×C7C2×D13semidirect
53. C5×C7×C13D3×D5semidirect
54. C5×C7×C13C2×D15semidirect
60. C13×D15C7×D5semidirect
62. C3×D65C7×D5semidirect
68. C52×C13C2×D3×C7semidirect
70. C3×C7×C13D52semidirect
77. C7×D15D65direct (N × H)
81. C3×C5×C13C2×C7×D5semidirect
82. C3×C5×C13C2×C7×D5semidirect
86. C52×C7D3×D13semidirect
89. C5×D15C7×D13semidirect
97. D65C7×D15direct (N × H)
101. C3×C5×C7D5×D13semidirect
102. C3×C5×C7C2×D65semidirect
104. C7×C13D5×D15semidirect
109. C3×C52C2×C7×D13semidirect
118. C5×C13D3×C7×D5semidirect
119. C5×C13C2×C7×D15semidirect
129. C3×C13C7×D52semidirect
131. C5×C7D13×D15semidirect
132. C5×C7D3×D65semidirect
137. D15C7×D65direct (N × H)
144. C52D3×C7×D13semidirect
145. C3×C7D5×D65semidirect
149. C3×C5C7×D5×D13semidirect
150. C3×C5C2×C7×D65semidirect
154. C13C7×D5×D15semidirect
163. C7D15×D65direct (N × H)
168. C5C7×D13×D15semidirect
169. C5D3×C7×D65semidirect
171. C3C7×D5×D65semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D652
C5×C7×C13×D152
C7×C3⋊(C5⋊D65)2
C7×D5×D653
D3×C7×D655
C7×D13×D155
D15×D657
C7×D5×D1513