Finite Group Databasebeta

← C7×D5×D195 #41032010

Subgroups — C7×D5×D195 #41032010

Order 27300.

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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×D5×C13C211yesmaximal, characteristic, complemented
2C5×C7×D195C211yesmaximal, characteristic, complemented
3C7×C3⋊(C5⋊D65)C211yesmaximal, characteristic, complemented
4C7×D5×D65—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C2×C7×D195—51nomaximal
7C7×D5×D39—51nomaximal
8C7×C5⋊D65—31no—
9C5×C7×D65—31no—
10C5×C7×D5×C13D311yescharacteristic, complemented
11D5×D195C711yesmaximal, characteristic, direct product factor, Hall
12C7×D195—51no—
13C7×D195—51no—
14C7×D195—102no—
15C7×D195D511yescharacteristic, direct product factor
16C5×C7×D39—51no—
17C3×C7×D5×C13D511yescharacteristic, complemented
18C2×C3×C5×C7×C13—51no—
19C52×C7×C13C2×D311yescharacteristic, complemented, Hall
20C7×D5×D15—131nomaximal, Hall
21C3⋊(C5⋊D65)C2×C711yescharacteristic, complemented
22C5×D195C2×C711yescharacteristic, complemented
23C3×C5×D5×C13C2×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
30C2×C7×D39—251noHall
31C7×C3⋊(C5⋊D5)—131no—
32C5×C7×D15—131no—
33C3×C5×C7×D5D1311yescharacteristic, complemented
34C3×C52×C13C22×C711yescharacteristic, complemented, Hall
35C2×C5×C7×C13—51no—
36C7×D65—31no—
37C7×D65—151no—
38C7×D65—151no—
39C7×D65—302no—
40C7×D5×C13D1511yescharacteristic, complemented
41C5×C7×D13—151no—
42C2×D195—51no—
43D5×D39—51no—
44C7×D52—391noHall
45C5⋊D65—31no—
46C5×D65—31no—
47C5×D5×C13D3×C711yescharacteristic, complemented
48C2×C3×C7×C13—51no—
49C7×D39—51no—
50C7×D39—251no—
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—
57C2×C3×C5×C13—51no—
58D195—51no—
59D195—51no—
60D195—102no—
61D195C7×D511yescharacteristic, direct product factor
62C5×D39—51no—
63C3×D5×C13C7×D511yescharacteristic, complemented
64C2×C7×D13—751noHall
65C7×C5⋊D5—391no—
66C5×C7×D5—391no—
67C5×C7×D5D3911yescharacteristic, complemented
68C52×C13C2×D3×C711yescharacteristic, complemented, Hall
69D5×D15—131noHall
70C3×C7×C13D5211yescharacteristic, complemented, Hall
71C2×D65—151no—
72D5×D13—151no—
73C2×C3×C5×C7—51no—
74C7×D15—131no—
75C7×D15—651no—
76C7×D15—651no—
77C7×D15—1302no—
78C5×D3×C7—651no—
79C3×C7×D5D6511yescharacteristic, complemented
80C3×C5×C13—22no—
81C3×C5×C13C2×C7×D511yescharacteristic, complemented
82C3×C5×C13C2×C7×D511yescharacteristic, complemented
83C2×C7×C13—51no—
84C7×D13—151no—
85C7×D13—751no—
86C52×C7C2×D3911yescharacteristic, complemented, Hall
87C2×D39—251noHall
88C3⋊(C5⋊D5)—131no—
89C5×D15—131no—
90C3×C5×D5C7×D1311yescharacteristic, complemented
91C2×C7×D5—1951no—
92C2×C7×D5—1951no—
93C2×C5×C13—51no—
94D65—31no—
95D65—151no—
96D65—151no—
97D65—302no—
98C5×D13—151no—
99D5×C13C7×D1511yescharacteristic, complemented
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
106C2×C3×C13—51no—
107D39—51no—
108D39—251no—
109C3×C52C2×C7×D1311yescharacteristic, complemented, Hall
110C2×C5×C7—51no—
111C2×C5×C7—1951no—
112C7×D5—391no—
113C7×D5—3902no—
114C7×D5—1951no—
115C7×D5—1951no—
116C7×D5D19511yescharacteristic, direct product factor
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—391no—
125C5×D5C7×D3911yescharacteristic, complemented
126C2×C3×C7—51no—
127D3×C7—651no—
128D3×C7—3251no—
129C3×C13C7×D5211yescharacteristic, complemented, Hall
130C5×C7—22no—
131C5×C7D5×D3911yescharacteristic, complemented
132C5×C7C2×D19511yescharacteristic, complemented
133C2×C3×C5—51no—
134D15—131no—
135D15—651no—
136D15—651no—
137D15—1302no—
138C3×D5C7×D6511yescharacteristic, complemented
139C5×D3—651no—
140C22×C7—9751noHall
141C2×C13—51no—
142D13—151no—
143D13—751no—
144C52C2×C7×D3911yescharacteristic, 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—51no—
152C2×C7—1951no—
153C2×C7—9751no—
154C13C7×D5×D1511yescharacteristic, complemented, Sylow
155C2×D3—3251noHall
156C2×C5—51no—
157C2×C5—1951no—
158D5—391no—
159D5—3902no—
160D5—1951no—
161D5—1951no—
162D5C7×D19511yescharacteristic, direct product factor
163C7D5×D19511yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—651no—
166D3—3251no—
167C5—22no—
168C5C7×D5×D3911yescharacteristic, complemented
169C5C2×C7×D19511yescharacteristic, complemented
170C22—9751noSylow
171C3C7×D5×D6511yescharacteristic, complemented, Sylow
172C2—51no—
173C2—1951no—
174C2—9751no—
subgroupG/H
center, hypercenterC7D5×D195
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×D5×C13C2semidirect
2. C5×C7×D195C2semidirect
3. C7×C3⋊(C5⋊D65)C2semidirect
5. C3×C52×C7×C13C22semidirect
10. C5×C7×D5×C13D3semidirect
11. D5×D195C7direct (N × H)
15. C7×D195D5direct (N × H)
17. C3×C7×D5×C13D5semidirect
19. C52×C7×C13C2×D3semidirect
21. C3⋊(C5⋊D65)C2×C7semidirect
22. C5×D195C2×C7semidirect
23. C3×C5×D5×C13C2×C7semidirect
27. C3×C5×C7×C13C2×D5semidirect
28. C3×C5×C7×C13C2×D5semidirect
33. C3×C5×C7×D5D13semidirect
34. C3×C52×C13C22×C7semidirect
40. C7×D5×C13D15semidirect
47. C5×D5×C13D3×C7semidirect
51. C3×C52×C7C2×D13semidirect
53. C5×C7×C13D3×D5semidirect
54. C5×C7×C13C2×D15semidirect
61. D195C7×D5direct (N × H)
63. C3×D5×C13C7×D5semidirect
67. C5×C7×D5D39semidirect
68. C52×C13C2×D3×C7semidirect
70. C3×C7×C13D52semidirect
79. C3×C7×D5D65semidirect
81. C3×C5×C13C2×C7×D5semidirect
82. C3×C5×C13C2×C7×D5semidirect
86. C52×C7C2×D39semidirect
90. C3×C5×D5C7×D13semidirect
99. D5×C13C7×D15semidirect
101. C3×C5×C7D5×D13semidirect
102. C3×C5×C7C2×D65semidirect
104. C7×C13D5×D15semidirect
109. C3×C52C2×C7×D13semidirect
116. C7×D5D195direct (N × H)
118. C5×C13D3×C7×D5semidirect
119. C5×C13C2×C7×D15semidirect
125. C5×D5C7×D39semidirect
129. C3×C13C7×D52semidirect
131. C5×C7D5×D39semidirect
132. C5×C7C2×D195semidirect
138. C3×D5C7×D65semidirect
144. C52C2×C7×D39semidirect
145. C3×C7D5×D65semidirect
149. C3×C5C7×D5×D13semidirect
150. C3×C5C2×C7×D65semidirect
154. C13C7×D5×D15semidirect
162. D5C7×D195direct (N × H)
163. C7D5×D195direct (N × H)
168. C5C7×D5×D39semidirect
169. C5C2×C7×D195semidirect
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×D5×C132
C5×C7×D1952
C7×C3⋊(C5⋊D65)2
C7×D5×D653
C2×C7×D1955
C7×D5×D395
D5×D1957
C7×D5×D1513