Finite Group Databasebeta

← C3×D35×D55 #37528619

Subgroups — C3×D35×D55 #37528619

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×C7×D55C211yesmaximal, characteristic, complemented
2C3×C5×C11×D35C211yesmaximal, characteristic, complemented
3C3×C5⋊D385C211yesmaximal, characteristic, complemented
4D35×D55C311yesmaximal, characteristic, direct product factor, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6C3×D7×D55—51nomaximal
7C3×D11×D35—51nomaximal
8C5⋊D385C2×C311yescharacteristic, complemented
9C5×C11×D35C2×C311yescharacteristic, complemented
10C5×C7×D55C2×C311yescharacteristic, complemented
11C3×D5×D55—71nomaximal, Hall
12C3×D385—51no—
13C3×D385—51no—
14C3×D385—102no—
15C3×C11×D35D511yescharacteristic, complemented
16C3×C7×D55D511yescharacteristic, complemented
17C3×C5×C11×D7—51no—
18C3×C5×C7×D11—51no—
19C3×D5×D35—111nomaximal, Hall
20C52×C7×C11C22×C311yescharacteristic, complemented, Hall
21C3×C5⋊D55—71no—
22C3×C5×D55D711yescharacteristic, complemented
23C3×C5×D5×C11—71no—
24D7×D55—51no—
25D11×D35—51no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C2×D511yescharacteristic, complemented
29D5×D55—71noHall
30C3×C5⋊D35—111no—
31C3×C5×D35D1111yescharacteristic, complemented
32C3×C5×C7×D5—111no—
33C3×D7×D11—251noHall
34C3×C52×C11C2×D711yescharacteristic, complemented, Hall
35D385—51no—
36D385—51no—
37D385—102no—
38C11×D35C3×D511yescharacteristic, complemented
39C7×D55C3×D511yescharacteristic, complemented
40C5×C11×D7—51no—
41C5×C7×D11—51no—
42D5×D35—111noHall
43C2×C3×D55—351no—
44C3×D5×D11—351no—
45C5⋊D55—71no—
46C5×D55C3×D711yescharacteristic, complemented
47C5×D5×C11—71no—
48C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
49C3×D77—251no—
50C3×C11×D7—51no—
51C3×C7×D11—51no—
52C2×C3×D35—551no—
53C3×D5×D7—551no—
54C5×C7×C11—22no—
55C5×C7×C11C2×C3×D511yescharacteristic, complemented
56C5×C7×C11C2×C3×D511yescharacteristic, complemented
57C5⋊D35—111no—
58C5×D35C3×D1111yescharacteristic, complemented
59C5×C7×D5—111no—
60C2×C3×C5×C11—351no—
61C3×D55—351no—
62C3×D55—351no—
63C3×D55—702no—
64C3×D55D3511yescharacteristic, direct product factor
65C3×D5×C11—71no—
66C3×C5×D11—51no—
67D7×D11—251noHall
68C3×D52—771noHall
69C52×C11C2×C3×D711yescharacteristic, complemented, Hall
70C3×C7×C11D5211yescharacteristic, complemented, Hall
71C2×D55—351no—
72D5×D11—351no—
73C2×C3×C5×C7—551no—
74C3×D35—551no—
75C3×D35—551no—
76C3×D35—1102no—
77C3×D35D5511yescharacteristic, direct product factor
78C3×C7×D5—111no—
79C3×C5×D7—51no—
80C52×C7C2×C3×D1111yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11D5×D711yescharacteristic, complemented
83C3×C5×C11C2×D3511yescharacteristic, complemented
84D77—251no—
85C7×D11—51no—
86C11×D7—51no—
87C3×C5⋊D5—771no—
88C3×C5×D5—71no—
89C3×C5×D5—111no—
90C2×D35—551no—
91D5×D7—551no—
92C2×C3×D11—1751noHall
93C2×C5×C11—351no—
94D55—351no—
95D55—351no—
96D55—702no—
97D55C3×D3511yescharacteristic, direct product factor
98C5×D11—51no—
99D5×C11—71no—
100C3×C5×C7—22no—
101C3×C5×C7D5×D1111yescharacteristic, complemented
102C3×C5×C7C2×D5511yescharacteristic, complemented
103D52—771noHall
104C2×C3×D7—2751noHall
105C7×C11C3×D5211yescharacteristic, complemented, Hall
106C3×C52D7×D1111yescharacteristic, complemented, Hall
107C2×C5×C7—551no—
108D35—551no—
109D35—551no—
110D35—1102no—
111D35C3×D5511yescharacteristic, direct product factor
112C5×D7—51no—
113C7×D5—111no—
114C2×C3×C11—351no—
115C3×D11—51no—
116C3×D11—1751no—
117C2×C3×D5—3851no—
118C2×C3×D5—3851no—
119C5×C11—22no—
120C5×C11C3×D5×D711yescharacteristic, complemented
121C5×C11C2×C3×D3511yescharacteristic, complemented
122C5⋊D5—771no—
123C5×D5—71no—
124C5×D5—111no—
125C2×D11—1751noHall
126C2×C3×C7—551no—
127C3×D7—51no—
128C3×D7—2751no—
129C5×C7—22no—
130C5×C7C3×D5×D1111yescharacteristic, complemented
131C5×C7C2×C3×D5511yescharacteristic, complemented
132C3×C11D5×D3511yescharacteristic, complemented, Hall
133C2×C3×C5—351no—
134C2×C3×C5—551no—
135C3×D5—7702no—
136C3×D5—71no—
137C3×D5—111no—
138C3×D5—3851no—
139C3×D5—3851no—
140C2×D7—2751noHall
141C52C3×D7×D1111yescharacteristic, complemented, Sylow
142C2×C11—351no—
143D11—51no—
144D11—1751no—
145C3×C7D5×D5511yescharacteristic, complemented, Hall
146C2×D5—3851no—
147C2×D5—3851no—
148C3×C5—22no—
149C3×C5D11×D3511yescharacteristic, complemented
150C3×C5D7×D5511yescharacteristic, complemented
151C2×C7—551no—
152D7—51no—
153D7—2751no—
154C22×C3—19251noHall
155C11C3×D5×D3511yescharacteristic, complemented, Sylow
156C2×C5—351no—
157C2×C5—551no—
158D5—7702no—
159D5—71no—
160D5—111no—
161D5—3851no—
162D5—3851no—
163C7C3×D5×D5511yescharacteristic, complemented, Sylow
164C2×C3—351no—
165C2×C3—551no—
166C2×C3—19251no—
167C5—22no—
168C5C3×D11×D3511yescharacteristic, complemented
169C5C3×D7×D5511yescharacteristic, complemented
170C22—19251noSylow
171C3D35×D5511yescharacteristic, direct product factor, Sylow
172C2—351no—
173C2—551no—
174C2—19251no—
subgroupG/H
center, hypercenterC3D35×D55
commutator, cosocle, hypocenterC52×C7×C11C22×C3
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D55C2semidirect
2. C3×C5×C11×D35C2semidirect
3. C3×C5⋊D385C2semidirect
4. D35×D55C3direct (N × H)
5. C3×C52×C7×C11C22semidirect
8. C5⋊D385C2×C3semidirect
9. C5×C11×D35C2×C3semidirect
10. C5×C7×D55C2×C3semidirect
15. C3×C11×D35D5semidirect
16. C3×C7×D55D5semidirect
20. C52×C7×C11C22×C3semidirect
22. C3×C5×D55D7semidirect
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C2×D5semidirect
31. C3×C5×D35D11semidirect
34. C3×C52×C11C2×D7semidirect
38. C11×D35C3×D5semidirect
39. C7×D55C3×D5semidirect
46. C5×D55C3×D7semidirect
48. C3×C52×C7C2×D11semidirect
55. C5×C7×C11C2×C3×D5semidirect
56. C5×C7×C11C2×C3×D5semidirect
58. C5×D35C3×D11semidirect
64. C3×D55D35direct (N × H)
69. C52×C11C2×C3×D7semidirect
70. C3×C7×C11D52semidirect
77. C3×D35D55direct (N × H)
80. C52×C7C2×C3×D11semidirect
82. C3×C5×C11D5×D7semidirect
83. C3×C5×C11C2×D35semidirect
97. D55C3×D35direct (N × H)
101. C3×C5×C7D5×D11semidirect
102. C3×C5×C7C2×D55semidirect
105. C7×C11C3×D52semidirect
106. C3×C52D7×D11semidirect
111. D35C3×D55direct (N × H)
120. C5×C11C3×D5×D7semidirect
121. C5×C11C2×C3×D35semidirect
130. C5×C7C3×D5×D11semidirect
131. C5×C7C2×C3×D55semidirect
132. C3×C11D5×D35semidirect
141. C52C3×D7×D11semidirect
145. C3×C7D5×D55semidirect
149. C3×C5D11×D35semidirect
150. C3×C5D7×D55semidirect
155. C11C3×D5×D35semidirect
163. C7C3×D5×D55semidirect
168. C5C3×D11×D35semidirect
169. C5C3×D7×D55semidirect
171. C3D35×D55direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D552
C3×C5×C11×D352
C3×C5⋊D3852
D35×D553
C3×D7×D555
C3×D11×D355
C3×D5×D557
C3×D5×D3511