Finite Group Databasebeta

← C5×D3×C11×D35 #37528658

Subgroups — C5×D3×C11×D35 #37528658

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×C11×D35C211yesmaximal, characteristic, complemented
2C52×D3×C7×C11C211yesmaximal, characteristic, complemented
3C5×C11×D105C211yesmaximal, characteristic, complemented
4C2×C5×C11×D35—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D3×C11×D35C511yesmaximal, characteristic, direct product factor
7C5×D3×C11×D7—51nomaximal
8C5×C11×D35—31no—
9C5×C11×D35D311yescharacteristic, direct product factor
10C2×C52×C7×C11—31no—
11C5×D3×D5×C11—71nomaximal, Hall
12C11×D105C2×C511yescharacteristic, complemented
13C5×C11×D21—51no—
14C5×D3×C7×C11—22no—
15C5×D3×C7×C11D511yescharacteristic, complemented
16C5×D3×C7×C11C2×C511yescharacteristic, complemented
17C3×C11×D35C2×C511yescharacteristic, complemented
18C3×C5×C11×D7—51no—
19C5×D3×D35C1111yesmaximal, characteristic, direct product factor, Hall
20C52×C7×C11C2×D311yescharacteristic, complemented, Hall
21C5×C11×D15—71no—
22C52×D3×C11D711yescharacteristic, complemented
23C3×C5×D5×C11—71no—
24C2×C11×D35—31no—
25C2×C5×C11×D7—151no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C22×C511yescharacteristic, complemented
29C2×C5×D5×C11—211noHall
30C5×D105C2×C1111yescharacteristic, complemented
31C52×D3×C7C2×C1111yescharacteristic, complemented
32C3×C5×D35C2×C1111yescharacteristic, complemented
33D3×C11×D7—51noHall
34C3×C52×C11C2×D711yescharacteristic, complemented, Hall
35C2×C5×C7×C11—31no—
36C2×C5×C7×C11—31no—
37C2×C5×C7×C11—62no—
38C11×D35—31no—
39C11×D35C5×D311yescharacteristic, direct product factor
40C5×C11×D7—51no—
41C5×C11×D7—151no—
42C2×C5×D35—31noHall
43C2×C5×D3×C11—351no—
44D3×D5×C11—71no—
45C2×C52×C11—31no—
46C5×D5×C11—71no—
47C5×D5×C11—211no—
48C3×C52×C7C22×C1111yescharacteristic, complemented, Hall
49C11×D21—51no—
50D3×C7×C11C5×D511yescharacteristic, complemented
51C3×C11×D7—51no—
52D3×D35C5×C1111yescharacteristic, direct product factor
53C5×D3×D7—51no—
54C5×C7×C11—22no—
55C5×C7×C11D3×D511yescharacteristic, complemented
56C5×C7×C11C2×C5×D311yescharacteristic, complemented
57C2×C52×C7—31no—
58C5×D35—31no—
59C5×D35D3×C1111yescharacteristic, direct product factor
60C2×C3×C5×C11—351no—
61C11×D15—71no—
62C5×D3×C11—22no—
63C5×D3×C11—351no—
64C5×D3×C11C5×D711yescharacteristic, complemented
65C5×D3×C11D3511yescharacteristic, direct product factor
66C3×D5×C11—71no—
67C2×C11×D7—151noHall
68C5×D3×D5—71noHall
69C52×C11D3×D711yescharacteristic, complemented, Hall
70C3×C7×C11C2×C5×D511yescharacteristic, complemented, Hall
71C22×C5×C11—1051no—
72C2×D5×C11—211no—
73D105C2×C5×C1111yescharacteristic, complemented
74C5×D21—51no—
75C5×D3×C7—22no—
76C5×D3×C7D5×C1111yescharacteristic, complemented
77C5×D3×C7C2×C5×C1111yescharacteristic, complemented
78C3×D35C2×C5×C1111yescharacteristic, complemented
79C3×C5×D7—51no—
80C52×C7C2×D3×C1111yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11C2×C5×D711yescharacteristic, complemented
83C3×C5×C11C2×D3511yescharacteristic, complemented
84C2×C7×C11—31no—
85C11×D7—51no—
86C11×D7—151no—
87C5×D15—71no—
88C52×D3C11×D711yescharacteristic, complemented
89C3×C5×D5—71no—
90C2×D35—31no—
91C2×C5×D7—151no—
92C2×D3×C11—351noHall
93C2×C5×C11—31no—
94C2×C5×C11—31no—
95C2×C5×C11—62no—
96C2×C5×C11—351no—
97C2×C5×C11—1051no—
98D5×C11—71no—
99D5×C11—211no—
100C3×C5×C7—22no—
101C3×C5×C7C2×D5×C1111yescharacteristic, complemented
102C3×C5×C7C22×C5×C1111yescharacteristic, complemented
103C2×C5×D5—211noHall
104D3×D7—51noHall
105C7×C11C5×D3×D511yescharacteristic, complemented, Hall
106C3×C52C2×C11×D711yescharacteristic, complemented, Hall
107C2×C5×C7—31no—
108C2×C5×C7—31no—
109C2×C5×C7—62no—
110D35—31no—
111D35C5×D3×C1111yescharacteristic, direct product factor
112C5×D7—51no—
113C5×D7—151no—
114C2×C3×C11—351no—
115D3×C11—351no—
116D3×C11C5×D3511yescharacteristic, direct product factor
117C2×C5×D3—351no—
118D3×D5—71no—
119C5×C11—22no—
120C5×C11C5×D3×D711yescharacteristic, complemented
121C5×C11D3×D3511yescharacteristic, direct product factor
122C2×C52—31no—
123C5×D5—71no—
124C5×D5—211no—
125C22×C11—1051noHall
126D21—51no—
127C3×D7—51no—
128D3×C7C5×D5×C1111yescharacteristic, complemented
129C5×C7—22no—
130C5×C7D3×D5×C1111yescharacteristic, complemented
131C5×C7C2×C5×D3×C1111yescharacteristic, complemented
132C3×C11C2×C5×D3511yescharacteristic, complemented, Hall
133C2×C3×C5—351no—
134D15—71no—
135C3×D5—71no—
136C5×D3—22no—
137C5×D3—351no—
138C5×D3C5×C11×D711yescharacteristic, complemented
139C5×D3C11×D3511yescharacteristic, direct product factor
140C2×D7—151noHall
141C52D3×C11×D711yescharacteristic, complemented, Sylow
142C2×C11—31no—
143C2×C11—351no—
144C2×C11—1051no—
145C3×C7C2×C5×D5×C1111yescharacteristic, complemented, Hall
146C22×C5—1051no—
147C2×D5—211no—
148C3×C5—22no—
149C3×C5C2×C5×C11×D711yescharacteristic, complemented
150C3×C5C2×C11×D3511yescharacteristic, complemented
151C2×C7—31no—
152D7—51no—
153D7—151no—
154C2×D3—351noHall
155C11C5×D3×D3511yescharacteristic, direct product factor, Sylow
156C2×C5—31no—
157C2×C5—31no—
158C2×C5—62no—
159C2×C5—351no—
160C2×C5—1051no—
161D5—71no—
162D5—211no—
163C7C5×D3×D5×C1111yescharacteristic, complemented, Sylow
164C2×C3—351no—
165D3—351no—
166D3C5×C11×D3511yescharacteristic, direct product factor
167C5—22no—
168C5C5×D3×C11×D711yescharacteristic, complemented
169C5D3×C11×D3511yescharacteristic, direct product factor
170C22—1051noSylow
171C3C2×C5×C11×D3511yescharacteristic, complemented, Sylow
172C2—31no—
173C2—351no—
174C2—1051no—
subgroupG/H
center, hypercenterC5×C11D3×D35
commutator, cosocle, hypocenterC3×C5×C7C22×C5×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C3×C5×C11×D35C2semidirect
2. C52×D3×C7×C11C2semidirect
3. C5×C11×D105C2semidirect
5. C3×C52×C7×C11C22semidirect
6. D3×C11×D35C5direct (N × H)
9. C5×C11×D35D3direct (N × H)
12. C11×D105C2×C5semidirect
15. C5×D3×C7×C11D5semidirect
16. C5×D3×C7×C11C2×C5semidirect
17. C3×C11×D35C2×C5semidirect
19. C5×D3×D35C11direct (N × H)
20. C52×C7×C11C2×D3semidirect
22. C52×D3×C11D7semidirect
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C22×C5semidirect
30. C5×D105C2×C11semidirect
31. C52×D3×C7C2×C11semidirect
32. C3×C5×D35C2×C11semidirect
34. C3×C52×C11C2×D7semidirect
39. C11×D35C5×D3direct (N × H)
48. C3×C52×C7C22×C11semidirect
50. D3×C7×C11C5×D5semidirect
52. D3×D35C5×C11direct (N × H)
55. C5×C7×C11D3×D5semidirect
56. C5×C7×C11C2×C5×D3semidirect
59. C5×D35D3×C11direct (N × H)
64. C5×D3×C11C5×D7semidirect
65. C5×D3×C11D35direct (N × H)
69. C52×C11D3×D7semidirect
70. C3×C7×C11C2×C5×D5semidirect
73. D105C2×C5×C11semidirect
76. C5×D3×C7D5×C11semidirect
77. C5×D3×C7C2×C5×C11semidirect
78. C3×D35C2×C5×C11semidirect
80. C52×C7C2×D3×C11semidirect
82. C3×C5×C11C2×C5×D7semidirect
83. C3×C5×C11C2×D35semidirect
88. C52×D3C11×D7semidirect
101. C3×C5×C7C2×D5×C11semidirect
102. C3×C5×C7C22×C5×C11semidirect
105. C7×C11C5×D3×D5semidirect
106. C3×C52C2×C11×D7semidirect
111. D35C5×D3×C11direct (N × H)
116. D3×C11C5×D35direct (N × H)
120. C5×C11C5×D3×D7semidirect
121. C5×C11D3×D35direct (N × H)
128. D3×C7C5×D5×C11semidirect
130. C5×C7D3×D5×C11semidirect
131. C5×C7C2×C5×D3×C11semidirect
132. C3×C11C2×C5×D35semidirect
138. C5×D3C5×C11×D7semidirect
139. C5×D3C11×D35direct (N × H)
141. C52D3×C11×D7semidirect
145. C3×C7C2×C5×D5×C11semidirect
149. C3×C5C2×C5×C11×D7semidirect
150. C3×C5C2×C11×D35semidirect
155. C11C5×D3×D35direct (N × H)
163. C7C5×D3×D5×C11semidirect
166. D3C5×C11×D35direct (N × H)
168. C5C5×D3×C11×D7semidirect
169. C5D3×C11×D35direct (N × H)
171. C3C2×C5×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
C52×D3×C7×C112
C5×C11×D1052
C2×C5×C11×D353
D3×C11×D355
C5×D3×C11×D75
C5×D3×D5×C117
C5×D3×D3511