Finite Group Databasebeta

← C11×D15×D35 #37528682

Subgroups — C11×D15×D35 #37528682

Order 23100.

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×C11×D35C211yesmaximal, characteristic, complemented
2C5×C7×C11×D15C211yesmaximal, characteristic, complemented
3C11×C3⋊(C5⋊D35)C211yesmaximal, characteristic, complemented
4D5×C11×D35—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D3×C11×D35—51nomaximal
7C11×D7×D15—51nomaximal
8C11×C5⋊D35—31no—
9C5×C11×D35D311yescharacteristic, complemented
10C5×C7×D5×C11—31no—
11D5×C11×D15—71nomaximal, Hall
12C11×D105—51no—
13C11×D105—51no—
14C11×D105—102no—
15C7×C11×D15D511yescharacteristic, complemented
16C5×D3×C7×C11—51no—
17C3×C11×D35D511yescharacteristic, complemented
18C3×C5×C11×D7—51no—
19D15×D35C1111yesmaximal, characteristic, direct product factor, Hall
20C52×C7×C11C2×D311yescharacteristic, complemented, Hall
21C11×C3⋊(C5⋊D5)—71no—
22C5×C11×D15D711yescharacteristic, complemented
23C3×C5×D5×C11—71no—
24C2×C11×D35—151no—
25D5×C11×D7—151no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C2×D511yescharacteristic, complemented
29D52×C11—211noHall
30C3⋊(C5⋊D35)C2×C1111yescharacteristic, complemented
31C5×C7×D15C2×C1111yescharacteristic, complemented
32C3×C5×D35C2×C1111yescharacteristic, complemented
33D3×C11×D7—251noHall
34C3×C52×C11C2×D711yescharacteristic, complemented, Hall
35C2×C5×C7×C11—151no—
36C11×D35—151no—
37C11×D35—151no—
38C11×D35—302no—
39C11×D35D1511yescharacteristic, direct product factor
40C7×D5×C11—31no—
41C5×C11×D7—51no—
42D5×D35—31noHall
43C2×C11×D15—351no—
44D3×D5×C11—351no—
45C11×C5⋊D5—211no—
46C5×D5×C11—31no—
47C5×D5×C11—71no—
48C3×C52×C7C22×C1111yescharacteristic, complemented, Hall
49C11×D21—251no—
50D3×C7×C11—51no—
51C3×C11×D7—51no—
52D3×D35—51no—
53D7×D15—51no—
54C5×C7×C11—22no—
55C5×C7×C11D3×D511yescharacteristic, complemented
56C5×C7×C11C2×D1511yescharacteristic, complemented
57C5⋊D35—31no—
58C5×D35D3×C1111yescharacteristic, complemented
59C5×C7×D5—31no—
60C2×C3×C5×C11—351no—
61C11×D15—351no—
62C11×D15—351no—
63C11×D15—702no—
64C11×D15D3511yescharacteristic, direct product factor
65C5×D3×C11—51no—
66C3×D5×C11—71no—
67C2×C11×D7—751noHall
68D5×D15—71noHall
69C52×C11D3×D711yescharacteristic, complemented, Hall
70C3×C7×C11D5211yescharacteristic, complemented, Hall
71C2×D5×C11—1051no—
72C2×D5×C11—1051no—
73D105—51no—
74D105—51no—
75D105—102no—
76C7×D15D5×C1111yescharacteristic, complemented
77C5×D3×C7—51no—
78C3×D35D5×C1111yescharacteristic, complemented
79C3×C5×D7—51no—
80C52×C7C2×D3×C1111yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11D5×D711yescharacteristic, complemented
83C3×C5×C11C2×D3511yescharacteristic, complemented
84C2×C7×C11—151no—
85C11×D7—51no—
86C11×D7—751no—
87C3⋊(C5⋊D5)—71no—
88C5×D15C11×D711yescharacteristic, complemented
89C3×C5×D5—71no—
90C2×D35—151no—
91D5×D7—151no—
92C2×D3×C11—1751noHall
93C2×C5×C11—151no—
94C2×C5×C11—351no—
95D5×C11—31no—
96D5×C11—71no—
97D5×C11—1051no—
98D5×C11—1051no—
99D5×C11—2102no—
100C3×C5×C7—22no—
101C3×C5×C7C2×D5×C1111yescharacteristic, complemented
102C3×C5×C7C2×D5×C1111yescharacteristic, complemented
103D52—211noHall
104D3×D7—251noHall
105C7×C11D5×D1511yescharacteristic, complemented, Hall
106C3×C52C2×C11×D711yescharacteristic, complemented, Hall
107C2×C5×C7—151no—
108D35—151no—
109D35—151no—
110D35—302no—
111D35C11×D1511yescharacteristic, direct product factor
112C5×D7—51no—
113C7×D5—31no—
114C2×C3×C11—351no—
115D3×C11—51no—
116D3×C11—1751no—
117C2×D15—351no—
118D3×D5—351no—
119C5×C11—22no—
120C5×C11D7×D1511yescharacteristic, complemented
121C5×C11D3×D3511yescharacteristic, complemented
122C5⋊D5—211no—
123C5×D5—31no—
124C5×D5—71no—
125C22×C11—5251noHall
126D21—251no—
127C3×D7—51no—
128D3×C7—51no—
129C5×C7—22no—
130C5×C7D3×D5×C1111yescharacteristic, complemented
131C5×C7C2×C11×D1511yescharacteristic, complemented
132C3×C11D5×D3511yescharacteristic, complemented, Hall
133C2×C3×C5—351no—
134D15—351no—
135D15—351no—
136D15—702no—
137D15C11×D3511yescharacteristic, direct product factor
138C3×D5—71no—
139C5×D3—51no—
140C2×D7—751noHall
141C52D3×C11×D711yescharacteristic, complemented, Sylow
142C2×C11—5251no—
143C2×C11—151no—
144C2×C11—351no—
145C3×C7D52×C1111yescharacteristic, complemented, Hall
146C2×D5—1051no—
147C2×D5—1051no—
148C3×C5—22no—
149C3×C5D5×C11×D711yescharacteristic, complemented
150C3×C5C2×C11×D3511yescharacteristic, complemented
151C2×C7—151no—
152D7—51no—
153D7—751no—
154C2×D3—1751noHall
155C11D15×D3511yescharacteristic, direct product factor, Sylow
156C2×C5—151no—
157C2×C5—351no—
158D5—31no—
159D5—71no—
160D5—1051no—
161D5—1051no—
162D5—2102no—
163C7D5×C11×D1511yescharacteristic, complemented, Sylow
164C2×C3—351no—
165D3—51no—
166D3—1751no—
167C5—22no—
168C5C11×D7×D1511yescharacteristic, complemented
169C5D3×C11×D3511yescharacteristic, complemented
170C22—5251noSylow
171C3D5×C11×D3511yescharacteristic, complemented, Sylow
172C2—5251no—
173C2—151no—
174C2—351no—
subgroupG/H
center, hypercenterC11D15×D35
commutator, cosocle, hypocenterC3×C52×C7C22×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×D35C2semidirect
2. C5×C7×C11×D15C2semidirect
3. C11×C3⋊(C5⋊D35)C2semidirect
5. C3×C52×C7×C11C22semidirect
9. C5×C11×D35D3semidirect
15. C7×C11×D15D5semidirect
17. C3×C11×D35D5semidirect
19. D15×D35C11direct (N × H)
20. C52×C7×C11C2×D3semidirect
22. C5×C11×D15D7semidirect
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C2×D5semidirect
30. C3⋊(C5⋊D35)C2×C11semidirect
31. C5×C7×D15C2×C11semidirect
32. C3×C5×D35C2×C11semidirect
34. C3×C52×C11C2×D7semidirect
39. C11×D35D15direct (N × H)
48. C3×C52×C7C22×C11semidirect
55. C5×C7×C11D3×D5semidirect
56. C5×C7×C11C2×D15semidirect
58. C5×D35D3×C11semidirect
64. C11×D15D35direct (N × H)
69. C52×C11D3×D7semidirect
70. C3×C7×C11D52semidirect
76. C7×D15D5×C11semidirect
78. C3×D35D5×C11semidirect
80. C52×C7C2×D3×C11semidirect
82. C3×C5×C11D5×D7semidirect
83. C3×C5×C11C2×D35semidirect
88. C5×D15C11×D7semidirect
101. C3×C5×C7C2×D5×C11semidirect
102. C3×C5×C7C2×D5×C11semidirect
105. C7×C11D5×D15semidirect
106. C3×C52C2×C11×D7semidirect
111. D35C11×D15direct (N × H)
120. C5×C11D7×D15semidirect
121. C5×C11D3×D35semidirect
130. C5×C7D3×D5×C11semidirect
131. C5×C7C2×C11×D15semidirect
132. C3×C11D5×D35semidirect
137. D15C11×D35direct (N × H)
141. C52D3×C11×D7semidirect
145. C3×C7D52×C11semidirect
149. C3×C5D5×C11×D7semidirect
150. C3×C5C2×C11×D35semidirect
155. C11D15×D35direct (N × H)
163. C7D5×C11×D15semidirect
168. C5C11×D7×D15semidirect
169. C5D3×C11×D35semidirect
171. C3D5×C11×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C11×D352
C5×C7×C11×D152
C11×C3⋊(C5⋊D35)2
D5×C11×D353
D3×C11×D355
C11×D7×D155
D5×C11×D157
D15×D3511