Finite Group Databasebeta

← #35208201

Subgroups — #35208201

Order 20700.

212 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 43 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×D345C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D115)C211yesmaximal, characteristic, complemented
3C5×C23×C3⋊D15C211yesmaximal, characteristic, complemented
4D15⋊D115—31nomaximal
5D15×D115—31nomaximal
6C32×C52×C23C2211yescharacteristic, complemented, Hall
7(C3⋊D3)⋊D115—51nomaximal
8D69⋊D15—51nomaximal
9C3⋊(C5⋊D115)D311yescharacteristic, complemented
10C5×D345D311yescharacteristic, complemented
11C5×C23×D15—31no—
12C5×C23×D15—31no—
13C5×C23×D15—61no—
14C3×C5⋊D115—31no—
15C3×C5×D115—31no—
16D5×D115—91noHall
17C23×C3⋊D15D511yescharacteristic, complemented
18C5×C3⋊D3×C23—51no—
19C3×D345—51no—
20C3×D345—51no—
21C3×D345—102no—
22C3×D345D511yescharacteristic, complemented
23C3×C5×D69—51no—
24C3×C52×C23—21no—
25C3×C52×C23C2×D311yescharacteristic, complemented
26C3×C52×C23C2×D311yescharacteristic, complemented
27D15⋊D23—151no—
28D3×D115—151no—
29D3×D115—151no—
30D15×D23—151no—
31C5⋊D115—31no—
32C5×D115—31no—
33C5×D5×C23—91no—
34C32×C5×C23—22no—
35C32×C5×C23C2×D511yescharacteristic, complemented
36C32×C5×C23C2×D511yescharacteristic, complemented
37D15⋊D15—231nomaximal, Hall
38(C3⋊D3)⋊D23—251noHall
39D345—51no—
40D345—51no—
41D345—102no—
42D345D1511yescharacteristic, complemented
43C23×D15—31no—
44C23×D15—31no—
45C23×D15—61no—
46C5×D69—51no—
47C5×D3×C23—151no—
48C5×D3×C23—151no—
49C5×D3×C23—301no—
50C3×D115—31no—
51C3×D115—151no—
52C3×D115—151no—
53C3×D115—302no—
54C3×C5×D23—151no—
55C52×C23D3211yescharacteristic, complemented, Hall
56C2×D115—451no—
57D5×D23—451no—
58C5×C3⋊D15D2311yescharacteristic, complemented
59C3×C3⋊(C5⋊D5)—231no—
60C3×C5×D15—231no—
61C3⋊D3×C23—51no—
62C3×D69—51no—
63C3×D69—251no—
64C3×C5×C23—21no—
65C3×C5×C23—21no—
66C3×C5×C23—22no—
67C3×C5×C23—22no—
68C3×C5×C23—42no—
69C3×C5×C23D3×D511yescharacteristic, complemented
70C3×C5×C23D3×D511yescharacteristic, complemented
71C3×C5×C23D3×D511yescharacteristic, complemented
72C3×C5×C23C2×D1511yescharacteristic, complemented
73D15⋊D5—691no—
74D5×D15—691no—
75D3×D23—751no—
76D3×D23—751no—
77C2×C5×C23—451no—
78D115—31no—
79D115—151no—
80D115—151no—
81D115—302no—
82C5×D23—151no—
83D5×C23—91no—
84C32×C52C2×D2311yescharacteristic, complemented, Hall
85C32×C23D5211yescharacteristic, complemented, Hall
86(C3⋊D3)⋊D5—1151no—
87D3×D15—1151no—
88C3⋊(C5⋊D5)—231no—
89C5×D15—31no—
90C5×D15—31no—
91C5×D15—61no—
92C5×D15—231no—
93C3×C5⋊D5—691no—
94C3×C5×D5—691no—
95D69—51no—
96D69—251no—
97C3×D23—151no—
98C3×D23—751no—
99D3×C23—151no—
100D3×C23—151no—
101D3×C23—301no—
102C5×C23—22no—
103C5×C23D3×D1511yescharacteristic, complemented
104C5×C23(C3⋊D3)⋊D511yescharacteristic, complemented
105D52—2071noHall
106C2×D23—2251noHall
107C3⋊D15D11511yescharacteristic, complemented
108C5×C3⋊D3—51no—
109C3×D15—231no—
110C3×D15—1151no—
111C3×D15—1151no—
112C3×D15—2302no—
113C3×C5×D3—1151no—
114C3×C52—21no—
115C3×C52D3×D2311yescharacteristic, complemented
116C3×C52D3×D2311yescharacteristic, complemented
117C3×C23—21no—
118C3×C23D5×D1511yescharacteristic, complemented
119C3×C23D15⋊D511yescharacteristic, complemented
120C2×D15—3451no—
121D3×D5—3451no—
122D3×D5—3451no—
123D3×D5—3451no—
124C5⋊D5—691no—
125C5×D5—91no—
126C5×D5—691no—
127C2×C23—451no—
128D23—151no—
129D23—751no—
130C32×C5—22no—
131C32×C5D5×D2311yescharacteristic, complemented
132C32×C5C2×D11511yescharacteristic, complemented
133D32—5751noHall
134C2×C3×C5—3451no—
135D15—31no—
136D15—31no—
137D15—61no—
138D15—231no—
139D15—1151no—
140D15—1151no—
141D15—2302no—
142C3×D5—691no—
143C3×D5—3451no—
144C3×D5—3451no—
145C3×D5—6902no—
146C5×D3—151no—
147C5×D3—151no—
148C5×D3—301no—
149C5×D3—1151no—
150C52(C3⋊D3)⋊D2311yescharacteristic, complemented, Sylow
151C23D15⋊D1511yescharacteristic, complemented, Sylow
152C2×D5—10351no—
153C2×D5—10351no—
154C3⋊D3—51no—
155C3×D3—5751no—
156C3×D3—1151no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D15×D2311yescharacteristic, complemented
163C3×C5D3×D11511yescharacteristic, complemented
164C3×C5D3×D11511yescharacteristic, complemented
165C3×C5D15⋊D2311yescharacteristic, complemented
166C2×D3—17251no—
167C2×D3—17251no—
168C2×C5—451no—
169C2×C5—3451no—
170D5—91no—
171D5—691no—
172D5—3451no—
173D5—3451no—
174D5—6902no—
175C32D5×D11511yescharacteristic, complemented, Sylow
176C2×C3—3451no—
177C2×C3—17251no—
178D3—151no—
179D3—151no—
180D3—301no—
181D3—5751no—
182D3—1151no—
183C5—22no—
184C5D69⋊D1511yescharacteristic, complemented
185C5(C3⋊D3)⋊D11511yescharacteristic, complemented
186C22—51751noSylow
187C3—21no—
188C3D15×D11511yescharacteristic, complemented
189C3D15⋊D11511yescharacteristic, complemented
190C2—451no—
191C2—3451no—
192C2—17251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C23C22
LCSG ▷ C32×C52×C23
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D345C2semidirect
2. C3×C3⋊(C5⋊D115)C2semidirect
3. C5×C23×C3⋊D15C2semidirect
6. C32×C52×C23C22semidirect
9. C3⋊(C5⋊D115)D3semidirect
10. C5×D345D3semidirect
17. C23×C3⋊D15D5semidirect
22. C3×D345D5semidirect
25. C3×C52×C23C2×D3semidirect
26. C3×C52×C23C2×D3semidirect
35. C32×C5×C23C2×D5semidirect
36. C32×C5×C23C2×D5semidirect
42. D345D15semidirect
55. C52×C23D32semidirect
58. C5×C3⋊D15D23semidirect
69. C3×C5×C23D3×D5semidirect
70. C3×C5×C23D3×D5semidirect
71. C3×C5×C23D3×D5semidirect
72. C3×C5×C23C2×D15semidirect
84. C32×C52C2×D23semidirect
85. C32×C23D52semidirect
103. C5×C23D3×D15semidirect
104. C5×C23(C3⋊D3)⋊D5semidirect
107. C3⋊D15D115semidirect
115. C3×C52D3×D23semidirect
116. C3×C52D3×D23semidirect
118. C3×C23D5×D15semidirect
119. C3×C23D15⋊D5semidirect
131. C32×C5D5×D23semidirect
132. C32×C5C2×D115semidirect
150. C52(C3⋊D3)⋊D23semidirect
151. C23D15⋊D15semidirect
162. C3×C5D15×D23semidirect
163. C3×C5D3×D115semidirect
164. C3×C5D3×D115semidirect
165. C3×C5D15⋊D23semidirect
175. C32D5×D115semidirect
184. C5D69⋊D15semidirect
185. C5(C3⋊D3)⋊D115semidirect
188. C3D15×D115semidirect
189. C3D15⋊D115semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3452
C3×C3⋊(C5⋊D115)2
C5×C23×C3⋊D152
D15⋊D1153
D15×D1153
(C3⋊D3)⋊D1155
D69⋊D155
D15⋊D1523