Finite Group Databasebeta

← C7×D5×C11×D15 #37528674

Subgroups — C7×D5×C11×D15 #37528674

Order 23100.

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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×C11C211yesmaximal, characteristic, complemented
2C5×C7×C11×D15C211yesmaximal, characteristic, complemented
3C7×C11×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4C7×D52×C11—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6C2×C7×C11×D15—51nomaximal
7D3×C7×D5×C11—51nomaximal
8C7×C11×C5⋊D5—31no—
9C5×C7×D5×C11—31no—
10C5×C7×D5×C11D311yescharacteristic, complemented
11D5×C11×D15C711yesmaximal, characteristic, direct product factor, Hall
12C7×C11×D15—51no—
13C7×C11×D15—51no—
14C7×C11×D15—102no—
15C7×C11×D15D511yescharacteristic, direct product factor
16C5×D3×C7×C11—51no—
17C3×C7×D5×C11D511yescharacteristic, complemented
18C2×C3×C5×C7×C11—51no—
19C7×D5×D15C1111yesmaximal, characteristic, direct product factor, Hall
20C52×C7×C11C2×D311yescharacteristic, complemented, Hall
21C11×C3⋊(C5⋊D5)C2×C711yescharacteristic, complemented
22C5×C11×D15C2×C711yescharacteristic, complemented
23C3×C5×D5×C11C2×C711yescharacteristic, complemented
24C2×C7×D5×C11—151no—
25C2×C7×D5×C11—151no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C2×D511yescharacteristic, complemented
29D52×C11—31noHall
30C7×C3⋊(C5⋊D5)C2×C1111yescharacteristic, complemented
31C5×C7×D15C2×C1111yescharacteristic, complemented
32C3×C5×C7×D5C2×C1111yescharacteristic, complemented
33C2×D3×C7×C11—251noHall
34C3×C52×C11C22×C711yescharacteristic, complemented, Hall
35C2×C5×C7×C11—51no—
36C2×C5×C7×C11—151no—
37C7×D5×C11—31no—
38C7×D5×C11—151no—
39C7×D5×C11—151no—
40C7×D5×C11—302no—
41C7×D5×C11D1511yescharacteristic, direct product factor
42C7×D52—31noHall
43C2×C11×D15—51no—
44D3×D5×C11—51no—
45C11×C5⋊D5—31no—
46C5×D5×C11—31no—
47C5×D5×C11D3×C711yescharacteristic, complemented
48C3×C52×C7C22×C1111yescharacteristic, complemented, Hall
49C2×C3×C7×C11—51no—
50D3×C7×C11—51no—
51D3×C7×C11—251no—
52C2×C7×D15—51no—
53D3×C7×D5—51no—
54C5×C7×C11—22no—
55C5×C7×C11D3×D511yescharacteristic, complemented
56C5×C7×C11C2×D1511yescharacteristic, complemented
57C7×C5⋊D5—31no—
58C5×C7×D5—31no—
59C5×C7×D5D3×C1111yescharacteristic, complemented
60C2×C3×C5×C11—51no—
61C11×D15—51no—
62C11×D15—51no—
63C11×D15—102no—
64C11×D15C7×D511yescharacteristic, direct product factor
65C5×D3×C11—51no—
66C3×D5×C11C7×D511yescharacteristic, complemented
67C22×C7×C11—751noHall
68D5×D15C7×C1111yescharacteristic, direct product factor, Hall
69C52×C11C2×D3×C711yescharacteristic, complemented, Hall
70C3×C7×C11D5211yescharacteristic, complemented, Hall
71C2×D5×C11—151no—
72C2×D5×C11—151no—
73C2×C3×C5×C7—51no—
74C7×D15—51no—
75C7×D15—51no—
76C7×D15—102no—
77C7×D15D5×C1111yescharacteristic, direct product factor
78C5×D3×C7—51no—
79C3×C7×D5D5×C1111yescharacteristic, complemented
80C52×C7C2×D3×C1111yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11C2×C7×D511yescharacteristic, complemented
83C3×C5×C11C2×C7×D511yescharacteristic, complemented
84C2×C7×C11—51no—
85C2×C7×C11—151no—
86C2×C7×C11—751no—
87C3⋊(C5⋊D5)C2×C7×C1111yescharacteristic, complemented
88C5×D15C2×C7×C1111yescharacteristic, complemented
89C3×C5×D5C2×C7×C1111yescharacteristic, complemented
90C2×C7×D5—151no—
91C2×C7×D5—151no—
92C2×D3×C11—251noHall
93C2×C5×C11—51no—
94C2×C5×C11—151no—
95D5×C11—31no—
96D5×C11—151no—
97D5×C11—151no—
98D5×C11—302no—
99D5×C11C7×D1511yescharacteristic, direct product factor
100C3×C5×C7—22no—
101C3×C5×C7C2×D5×C1111yescharacteristic, complemented
102C3×C5×C7C2×D5×C1111yescharacteristic, complemented
103D52—31noHall
104C2×D3×C7—251noHall
105C7×C11D5×D1511yescharacteristic, direct product factor, Hall
106C3×C52C22×C7×C1111yescharacteristic, complemented, Hall
107C2×C5×C7—51no—
108C2×C5×C7—151no—
109C7×D5—31no—
110C7×D5—151no—
111C7×D5—151no—
112C7×D5—302no—
113C7×D5C11×D1511yescharacteristic, direct product factor
114C2×C3×C11—51no—
115D3×C11—51no—
116D3×C11—251no—
117C2×D15—51no—
118D3×D5—51no—
119C5×C11—22no—
120C5×C11D3×C7×D511yescharacteristic, complemented
121C5×C11C2×C7×D1511yescharacteristic, complemented
122C5⋊D5—31no—
123C5×D5—31no—
124C5×D5D3×C7×C1111yescharacteristic, complemented
125C22×C11—751noHall
126C2×C3×C7—51no—
127D3×C7—51no—
128D3×C7—251no—
129C5×C7—22no—
130C5×C7D3×D5×C1111yescharacteristic, complemented
131C5×C7C2×C11×D1511yescharacteristic, complemented
132C3×C11C7×D5211yescharacteristic, complemented, Hall
133C2×C3×C5—51no—
134D15—51no—
135D15—51no—
136D15—102no—
137D15C7×D5×C1111yescharacteristic, direct product factor
138C3×D5C7×D5×C1111yescharacteristic, complemented
139C5×D3—51no—
140C22×C7—751noHall
141C52C2×D3×C7×C1111yescharacteristic, complemented, Sylow
142C2×C11—51no—
143C2×C11—151no—
144C2×C11—751no—
145C3×C7D52×C1111yescharacteristic, complemented, Hall
146C2×D5—151no—
147C2×D5—151no—
148C3×C5—22no—
149C3×C5C2×C7×D5×C1111yescharacteristic, complemented
150C3×C5C2×C7×D5×C1111yescharacteristic, complemented
151C2×C7—51no—
152C2×C7—151no—
153C2×C7—751no—
154C2×D3—251noHall
155C11C7×D5×D1511yescharacteristic, direct product factor, Sylow
156C2×C5—51no—
157C2×C5—151no—
158D5—31no—
159D5—151no—
160D5—151no—
161D5—302no—
162D5C7×C11×D1511yescharacteristic, direct product factor
163C7D5×C11×D1511yescharacteristic, direct product factor, Sylow
164C2×C3—51no—
165D3—51no—
166D3—251no—
167C5—22no—
168C5D3×C7×D5×C1111yescharacteristic, complemented
169C5C2×C7×C11×D1511yescharacteristic, complemented
170C22—751noSylow
171C3C7×D52×C1111yescharacteristic, complemented, Sylow
172C2—51no—
173C2—151no—
174C2—751no—
subgroupG/H
center, hypercenterC7×C11D5×D15
commutator, cosocle, hypocenterC3×C52C22×C7×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52
UCSC1 ◁ C7×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D5×C11C2semidirect
2. C5×C7×C11×D15C2semidirect
3. C7×C11×C3⋊(C5⋊D5)C2semidirect
5. C3×C52×C7×C11C22semidirect
10. C5×C7×D5×C11D3semidirect
11. D5×C11×D15C7direct (N × H)
15. C7×C11×D15D5direct (N × H)
17. C3×C7×D5×C11D5semidirect
19. C7×D5×D15C11direct (N × H)
20. C52×C7×C11C2×D3semidirect
21. C11×C3⋊(C5⋊D5)C2×C7semidirect
22. C5×C11×D15C2×C7semidirect
23. C3×C5×D5×C11C2×C7semidirect
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C2×D5semidirect
30. C7×C3⋊(C5⋊D5)C2×C11semidirect
31. C5×C7×D15C2×C11semidirect
32. C3×C5×C7×D5C2×C11semidirect
34. C3×C52×C11C22×C7semidirect
41. C7×D5×C11D15direct (N × H)
47. C5×D5×C11D3×C7semidirect
48. C3×C52×C7C22×C11semidirect
55. C5×C7×C11D3×D5semidirect
56. C5×C7×C11C2×D15semidirect
59. C5×C7×D5D3×C11semidirect
64. C11×D15C7×D5direct (N × H)
66. C3×D5×C11C7×D5semidirect
68. D5×D15C7×C11direct (N × H)
69. C52×C11C2×D3×C7semidirect
70. C3×C7×C11D52semidirect
77. C7×D15D5×C11direct (N × H)
79. C3×C7×D5D5×C11semidirect
80. C52×C7C2×D3×C11semidirect
82. C3×C5×C11C2×C7×D5semidirect
83. C3×C5×C11C2×C7×D5semidirect
87. C3⋊(C5⋊D5)C2×C7×C11semidirect
88. C5×D15C2×C7×C11semidirect
89. C3×C5×D5C2×C7×C11semidirect
99. D5×C11C7×D15direct (N × H)
101. C3×C5×C7C2×D5×C11semidirect
102. C3×C5×C7C2×D5×C11semidirect
105. C7×C11D5×D15direct (N × H)
106. C3×C52C22×C7×C11semidirect
113. C7×D5C11×D15direct (N × H)
120. C5×C11D3×C7×D5semidirect
121. C5×C11C2×C7×D15semidirect
124. C5×D5D3×C7×C11semidirect
130. C5×C7D3×D5×C11semidirect
131. C5×C7C2×C11×D15semidirect
132. C3×C11C7×D52semidirect
137. D15C7×D5×C11direct (N × H)
138. C3×D5C7×D5×C11semidirect
141. C52C2×D3×C7×C11semidirect
145. C3×C7D52×C11semidirect
149. C3×C5C2×C7×D5×C11semidirect
150. C3×C5C2×C7×D5×C11semidirect
155. C11C7×D5×D15direct (N × H)
162. D5C7×C11×D15direct (N × H)
163. C7D5×C11×D15direct (N × H)
168. C5D3×C7×D5×C11semidirect
169. C5C2×C7×C11×D15semidirect
171. C3C7×D52×C11semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C112
C5×C7×C11×D152
C7×C11×C3⋊(C5⋊D5)2
C7×D52×C113
C2×C7×C11×D155
D3×C7×D5×C115
D5×C11×D157
C7×D5×D1511