Finite Group Databasebeta

← C3×C5×D11×D35 #37528601

Subgroups — C3×C5×D11×D35 #37528601

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×C52×C7×D11C211yesmaximal, characteristic, complemented
2C3×C5×C11×D35C211yesmaximal, characteristic, complemented
3C3×C5×D385C211yesmaximal, characteristic, complemented
4C5×D11×D35C311yesmaximal, characteristic, direct product factor, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6C3×D11×D35C511yesmaximal, characteristic, direct product factor
7C3×C5×D7×D11—51nomaximal
8C5×D385C2×C311yescharacteristic, complemented
9C5×C11×D35C2×C311yescharacteristic, complemented
10C52×C7×D11C2×C311yescharacteristic, complemented
11C3×C5×D5×D11—71nomaximal, Hall
12C3×D385C2×C511yescharacteristic, complemented
13C3×C11×D35C2×C511yescharacteristic, complemented
14C3×C5×D77—51no—
15C3×C5×C11×D7—51no—
16C3×C5×C7×D11—22no—
17C3×C5×C7×D11D511yescharacteristic, complemented
18C3×C5×C7×D11C2×C511yescharacteristic, complemented
19C2×C3×C5×D35—111nomaximal, Hall
20C52×C7×C11C22×C311yescharacteristic, complemented, Hall
21C3×C5×D55—71no—
22C3×C5×D5×C11—71no—
23C3×C52×D11D711yescharacteristic, complemented
24D11×D35C3×C511yescharacteristic, direct product factor
25C5×D7×D11—51no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C22×C511yescharacteristic, complemented
29C5×D5×D11—71noHall
30C2×C3×C52×C7—111no—
31C3×C5×D35—111no—
32C3×C5×D35D1111yescharacteristic, direct product factor
33C3×D7×D11—51noHall
34C3×C52×C11C2×D711yescharacteristic, complemented, Hall
35D385C2×C3×C511yescharacteristic, complemented
36C11×D35C2×C3×C511yescharacteristic, complemented
37C5×D77—51no—
38C5×C11×D7—51no—
39C5×C7×D11—22no—
40C5×C7×D11C3×D511yescharacteristic, complemented
41C5×C7×D11C2×C3×C511yescharacteristic, complemented
42C2×C5×D35—111noHall
43C2×C3×C5×D11—351no—
44C3×D5×D11—71no—
45C5×D55—71no—
46C5×D5×C11—71no—
47C52×D11C3×D711yescharacteristic, complemented
48C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
49C3×D77—51no—
50C3×C11×D7—51no—
51C3×C7×D11C5×D511yescharacteristic, complemented
52C2×C3×D35—111no—
53C2×C3×C5×D7—551no—
54C5×C7×C11—22no—
55C5×C7×C11C2×C3×D511yescharacteristic, complemented
56C5×C7×C11C22×C3×C511yescharacteristic, complemented
57C2×C52×C7—111no—
58C5×D35—111no—
59C5×D35C3×D1111yescharacteristic, direct product factor
60C2×C3×C5×C11—351no—
61C3×D55—71no—
62C3×D5×C11—71no—
63C3×C5×D11—22no—
64C3×C5×D11—351no—
65C3×C5×D11C5×D711yescharacteristic, complemented
66C3×C5×D11D3511yescharacteristic, direct product factor
67D7×D11—51noHall
68C2×C3×C5×D5—771noHall
69C52×C11C2×C3×D711yescharacteristic, complemented, Hall
70C3×C7×C11C2×C5×D511yescharacteristic, complemented, Hall
71C2×C5×D11—351no—
72D5×D11—71no—
73C2×C3×C5×C7—111no—
74C2×C3×C5×C7—111no—
75C2×C3×C5×C7—222no—
76C3×D35—111no—
77C3×D35C5×D1111yescharacteristic, direct product factor
78C3×C5×D7—51no—
79C3×C5×D7—551no—
80C52×C7C2×C3×D1111yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11C2×C5×D711yescharacteristic, complemented
83C3×C5×C11C2×D3511yescharacteristic, complemented
84D77—51no—
85C7×D11C3×C5×D511yescharacteristic, complemented
86C11×D7—51no—
87C2×C3×C52—111no—
88C3×C5×D5—71no—
89C3×C5×D5—771no—
90C2×D35—111no—
91C2×C5×D7—551no—
92C2×C3×D11—351noHall
93C2×C5×C11—351no—
94D55—71no—
95C5×D11—22no—
96C5×D11—351no—
97C5×D11C3×C5×D711yescharacteristic, complemented
98C5×D11C3×D3511yescharacteristic, direct product factor
99D5×C11—71no—
100C3×C5×C7—22no—
101C3×C5×C7D5×D1111yescharacteristic, complemented
102C3×C5×C7C2×C5×D1111yescharacteristic, complemented
103C2×C5×D5—771noHall
104C2×C3×D7—551noHall
105C7×C11C2×C3×C5×D511yescharacteristic, complemented, Hall
106C3×C52D7×D1111yescharacteristic, complemented, Hall
107C2×C5×C7—111no—
108C2×C5×C7—111no—
109C2×C5×C7—222no—
110D35—111no—
111D35C3×C5×D1111yescharacteristic, direct product factor
112C5×D7—51no—
113C5×D7—551no—
114C2×C3×C11—351no—
115C3×D11—351no—
116C3×D11C5×D3511yescharacteristic, direct product factor
117C22×C3×C5—3851no—
118C2×C3×D5—771no—
119C5×C11—22no—
120C5×C11C2×C3×C5×D711yescharacteristic, complemented
121C5×C11C2×C3×D3511yescharacteristic, complemented
122C2×C52—111no—
123C5×D5—71no—
124C5×D5—771no—
125C2×D11—351noHall
126C2×C3×C7—111no—
127C3×D7—51no—
128C3×D7—551no—
129C5×C7—22no—
130C5×C7C3×D5×D1111yescharacteristic, complemented
131C5×C7C2×C3×C5×D1111yescharacteristic, complemented
132C3×C11C2×C5×D3511yescharacteristic, complemented, Hall
133C2×C3×C5—111no—
134C2×C3×C5—111no—
135C2×C3×C5—222no—
136C2×C3×C5—351no—
137C2×C3×C5—3851no—
138C3×D5—71no—
139C3×D5—771no—
140C2×D7—551noHall
141C52C3×D7×D1111yescharacteristic, complemented, Sylow
142C2×C11—351no—
143D11—351no—
144D11C3×C5×D3511yescharacteristic, direct product factor
145C3×C7C5×D5×D1111yescharacteristic, complemented, Hall
146C22×C5—3851no—
147C2×D5—771no—
148C3×C5—22no—
149C3×C5C5×D7×D1111yescharacteristic, complemented
150C3×C5D11×D3511yescharacteristic, direct product factor
151C2×C7—111no—
152D7—51no—
153D7—551no—
154C22×C3—3851noHall
155C11C2×C3×C5×D3511yescharacteristic, complemented, Sylow
156C2×C5—111no—
157C2×C5—111no—
158C2×C5—222no—
159C2×C5—351no—
160C2×C5—3851no—
161D5—71no—
162D5—771no—
163C7C3×C5×D5×D1111yescharacteristic, complemented, Sylow
164C2×C3—111no—
165C2×C3—351no—
166C2×C3—3851no—
167C5—22no—
168C5C3×C5×D7×D1111yescharacteristic, complemented
169C5C3×D11×D3511yescharacteristic, direct product factor
170C22—3851noSylow
171C3C5×D11×D3511yescharacteristic, direct product factor, Sylow
172C2—111no—
173C2—351no—
174C2—3851no—
subgroupG/H
center, hypercenterC3×C5D11×D35
commutator, cosocle, hypocenterC5×C7×C11C22×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C52×C7×D11C2semidirect
2. C3×C5×C11×D35C2semidirect
3. C3×C5×D385C2semidirect
4. C5×D11×D35C3direct (N × H)
5. C3×C52×C7×C11C22semidirect
6. C3×D11×D35C5direct (N × H)
8. C5×D385C2×C3semidirect
9. C5×C11×D35C2×C3semidirect
10. C52×C7×D11C2×C3semidirect
12. C3×D385C2×C5semidirect
13. C3×C11×D35C2×C5semidirect
17. C3×C5×C7×D11D5semidirect
18. C3×C5×C7×D11C2×C5semidirect
20. C52×C7×C11C22×C3semidirect
23. C3×C52×D11D7semidirect
24. D11×D35C3×C5direct (N × H)
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C22×C5semidirect
32. C3×C5×D35D11direct (N × H)
34. C3×C52×C11C2×D7semidirect
35. D385C2×C3×C5semidirect
36. C11×D35C2×C3×C5semidirect
40. C5×C7×D11C3×D5semidirect
41. C5×C7×D11C2×C3×C5semidirect
47. C52×D11C3×D7semidirect
48. C3×C52×C7C2×D11semidirect
51. C3×C7×D11C5×D5semidirect
55. C5×C7×C11C2×C3×D5semidirect
56. C5×C7×C11C22×C3×C5semidirect
59. C5×D35C3×D11direct (N × H)
65. C3×C5×D11C5×D7semidirect
66. C3×C5×D11D35direct (N × H)
69. C52×C11C2×C3×D7semidirect
70. C3×C7×C11C2×C5×D5semidirect
77. C3×D35C5×D11direct (N × H)
80. C52×C7C2×C3×D11semidirect
82. C3×C5×C11C2×C5×D7semidirect
83. C3×C5×C11C2×D35semidirect
85. C7×D11C3×C5×D5semidirect
97. C5×D11C3×C5×D7semidirect
98. C5×D11C3×D35direct (N × H)
101. C3×C5×C7D5×D11semidirect
102. C3×C5×C7C2×C5×D11semidirect
105. C7×C11C2×C3×C5×D5semidirect
106. C3×C52D7×D11semidirect
111. D35C3×C5×D11direct (N × H)
116. C3×D11C5×D35direct (N × H)
120. C5×C11C2×C3×C5×D7semidirect
121. C5×C11C2×C3×D35semidirect
130. C5×C7C3×D5×D11semidirect
131. C5×C7C2×C3×C5×D11semidirect
132. C3×C11C2×C5×D35semidirect
141. C52C3×D7×D11semidirect
144. D11C3×C5×D35direct (N × H)
145. C3×C7C5×D5×D11semidirect
149. C3×C5C5×D7×D11semidirect
150. C3×C5D11×D35direct (N × H)
155. C11C2×C3×C5×D35semidirect
163. C7C3×C5×D5×D11semidirect
168. C5C3×C5×D7×D11semidirect
169. C5C3×D11×D35direct (N × H)
171. C3C5×D11×D35direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C52×C7×D112
C3×C5×C11×D352
C3×C5×D3852
C5×D11×D353
C3×D11×D355
C3×C5×D7×D115
C3×C5×D5×D117
C2×C3×C5×D3511