Finite Group Databasebeta

← D3×#10597126 #72231370

Subgroups — D3×#10597126 #72231370

Order 3600.

602 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C2×C3×D3×C5⋊D5C211yesmaximal, characteristic
2#14268306C212yesmaximal, complemented
3C5×D3×Dic15C212yesmaximal, complemented
4#14268268C211yesmaximal, characteristic, complemented
5C3×#10597126C211yesmaximal, characteristic, complemented
6C2×#10597126—31nomaximal
7D3×#6036—31nomaximal
8C2×C3×C3⋊(C5⋊D5)C2211yescharacteristic
9C2×C3×C52×D3C2211yescharacteristic
10C2×C32×C5⋊D5C2211yescharacteristic
11C3×D3×C5⋊D5C414yescomplemented
12C5×C3⋊Dic15C2212yescomplemented
13C3×C5×Dic15C2212yescomplemented
14D3×D5×Dic3—52nomaximal
15C22×C3×C5⋊D5—31no—
16C2×D3×C5⋊D5D311yescharacteristic
17C2×C5×Dic15—32no—
18#10597126—31no—
19#10597126—31no—
20#10597126—32no—
21#10597126—61no—
22#10597126D311yescharacteristic, direct product factor
23#10597120—32no—
24C5×D3×Dic5—32no—
25C3×#6036—31no—
26C2×C32×C52C2311yescharacteristic
27C3×C3⋊(C5⋊D5)C2×C412yescomplemented
28C3×C52×D3C2×C412yescomplemented
29C32×C5⋊D5C2×C412yescomplemented
30C2×#6036—91noHall
31C2×C3×D3×D5—52no—
32C2×C3×D3×D5—102no—
33#67154—52no—
34D3×Dic15D512yescomplemented
35Dic3×D15—52no—
36C5×D3×Dic3—52no—
37D5×C3⋊Dic3—52no—
38C3×D5×Dic3—52no—
39C22×C3×C52—31no—
40C2×C3⋊(C5⋊D5)C2×D311yescharacteristic
41C2×C52×D3C2×D311yescharacteristic
42C2×C3×C5⋊D5—21no—
43C2×C3×C5⋊D5—31no—
44C2×C3×C5⋊D5—34no—
45C2×C3×C5⋊D5C2×D311yescharacteristic
46C2×C3×C5⋊D5C2×D311yescharacteristic
47D3×C5⋊D5Dic314yescomplemented
48C5×Dic15—32no—
49C5×Dic15—32no—
50C5×Dic15—62no—
51C5×Dic15C2×D312yescomplemented
52C3×C5×Dic5—32no—
53C2×D5×Dic3—152no—
54C4×D3×D5—152no—
55C32×C52C22×C411yescharacteristic, complemented, Hall
56C22×C5⋊D5—31no—
57C2×C5×Dic5—92no—
58#6036—31no—
59#6036—92no—
60#6036—91no—
61C2×C3×D15—52no—
62C2×C3×D15—102no—
63C2×C3×C5×D3—22no—
64C2×C3×C5×D3C2×D512yes—
65C2×C32×D5—52no—
66C2×C32×D5—102no—
67C3×D3×D5—58no—
68C3×D3×D5—108no—
69C3⋊Dic15C2×D512yescomplemented
70C5×C3⋊Dic3—52no—
71C3×Dic15C2×D512yescomplemented
72C3×C5×Dic3—52no—
73C2×C3×C52—21no—
74C2×C3×C52—32no—
75C2×C3×C52C22×D311yescharacteristic
76C2×C3×C52C22×D311yescharacteristic
77C3⋊(C5⋊D5)C2×Dic312yescomplemented
78C52×D3C2×Dic312yescomplemented
79C3×C5⋊D5—22no—
80C3×C5⋊D5—32no—
81C3×C5⋊D5C4×D312yescomplemented
82C3×C5⋊D5C2×Dic312yescomplemented
83C2×D3×Dic3—251noHall
84C22×C3×D5—152no—
85C22×C3×D5—302no—
86C2×D3×D5—52no—
87C2×D3×D5—102no—
88C2×Dic15—32no—
89C4×D15—152no—
90C2×C5×Dic3—152no—
91C4×C5×D3—152no—
92C3×C4×D5—152no—
93#1200—152no—
94D3×Dic5—32no—
95D5×Dic3—52no—
96D5×Dic3—152no—
97D5×Dic3—152no—
98D5×Dic3—152no—
99D5×Dic3—152no—
100D5×Dic3—302no—
101C22×C52—31no—
102C2×C5⋊D5—31no—
103C2×C5⋊D5—34no—
104C2×C5⋊D5D3211yescharacteristic
105C5×Dic5—32no—
106C5×Dic5—92no—
107C2×C32×C5—22no—
108C2×C32×C5C22×D512yes—
109C3×D15—54no—
110C3×D15—104no—
111C3×C5×D3—24no—
112C3×C5×D3C4×D514yescomplemented
113C32×D5—54no—
114C32×D5—104no—
115C2×C4×D5—452no—
116C3×C52—21no—
117C3×C52C2×C4×D311yescharacteristic, complemented
118C3×C52C22×Dic311yescharacteristic, complemented
119C22×C3×D3—251no—
120C2×C3⋊Dic3—251no—
121C2×C3×Dic3—251no—
122D3×Dic3—52no—
123D3×Dic3—252no—
124C22×C3×C5—32no—
125C22×C3×C5—62no—
126C2×D15—52no—
127C2×D15—102no—
128C2×C5×D3—22no—
129C2×C5×D3D3×D512yes—
130C2×C3×D5—52no—
131C2×C3×D5—52no—
132C2×C3×D5—102no—
133C2×C3×D5—102no—
134C2×C3×D5—102no—
135C2×C3×D5—158no—
136C2×C3×D5—152no—
137C2×C3×D5—202no—
138C2×C3×D5—308no—
139C2×C3×D5—302no—
140D3×D5—58no—
141D3×D5—108no—
142C3×C4×C5—152no—
143Dic15—32no—
144Dic15—32no—
145Dic15—62no—
146Dic15D3×D512yescomplemented
147C3×Dic5—32no—
148C5×Dic3—52no—
149C5×Dic3—152no—
150C5×Dic3—152no—
151C5×Dic3—302no—
152C2×C52—32no—
153C2×C52C2×D3211yescharacteristic
154C5⋊D5—32no—
155C5⋊D5D3×Dic312yescomplemented
156C22×Dic3—751no—
157C2×C4×D3—751no—
158C32×C5—22no—
159C32×C5C2×C4×D512yescomplemented
160C22×D5—152no—
161C22×D5—302no—
162C2×C4×C5—452no—
163C2×Dic5—92no—
164C4×D5—152no—
165C4×D5—452no—
166C4×D5—452no—
167C4×D5—452no—
168C22×C32—251no—
169C2×C3×D3—251no—
170C2×C3×D3—254no—
171C2×C3×D3D5211yescharacteristic
172C3⋊Dic3—52no—
173C3×Dic3—52no—
174C2×C3×C5—22no—
175C2×C3×C5—22no—
176C2×C3×C5—22no—
177C2×C3×C5—34no—
178C2×C3×C5—42no—
179C2×C3×C5—64no—
180C2×C3×C5C2×D3×D512yes—
181C2×C3×C5C2×D3×D512yes—
182D15—54no—
183D15—104no—
184C3×D5—54no—
185C3×D5—54no—
186C3×D5—104no—
187C3×D5—104no—
188C3×D5—104no—
189C3×D5—154no—
190C3×D5—204no—
191C3×D5—304no—
192C5×D3—24no—
193C5×D3D5×Dic314yescomplemented
194C52C2×D3×Dic311yescharacteristic, complemented, Sylow
195C23×C3—751no—
196C22×D3—251no—
197C2×C3×C4—751no—
198C2×Dic3—152no—
199C2×Dic3—251no—
200C2×Dic3—752no—
201C2×Dic3—751no—
202C2×Dic3—751no—
203C2×Dic3—1501no—
204C4×D3—152no—
205C4×D3—752no—
206C22×C5—32no—
207C22×C5—62no—
208C2×D5—52no—
209C2×D5—102no—
210C2×D5—158no—
211C2×D5—152no—
212C2×D5—308no—
213C2×D5—302no—
214C4×C5—152no—
215C4×C5—452no—
216Dic5—32no—
217Dic5—92no—
218C2×C32—252no—
219C2×C32C2×D5211yescharacteristic
220C3×D3—252no—
221C3×D3#603612yescomplemented
222C22×C4—2251noSylow
223C3×C5—22no—
224C3×C5—22no—
225C3×C5—22no—
226C3×C5—42no—
227C3×C5C4×D3×D512yescomplemented
228C3×C5C2×D5×Dic312yescomplemented
229C22×C3—31no—
230C22×C3—251no—
231C22×C3—251no—
232C22×C3—501no—
233C22×C3—754no—
234C22×C3—751no—
235C2×D3—251no—
236C2×D3—254no—
237C2×D3D15⋊D511yescharacteristic
238C3×C4—152no—
239Dic3—52no—
240Dic3—152no—
241Dic3—152no—
242Dic3—302no—
243C2×C5—22no—
244C2×C5—34no—
245C2×C5—64no—
246C2×C5D32×D512yes—
247D5—54no—
248D5—104no—
249D5—154no—
250D5—304no—
251C32C2×#603611yescharacteristic, complemented, Sylow
252C23—751no—
253C2×C4—452no—
254C2×C4—751no—
255C2×C4—2252no—
256C2×C4—2251no—
257C2×C3—21no—
258C2×C3—32no—
259C2×C3—252no—
260C2×C3—252no—
261C2×C3—502no—
262C2×C3—752no—
263C2×C3D3×D5211yescharacteristic
264C2×C3C2×D15⋊D511yescharacteristic
265D3—252no—
266D3#1059712612yesdirect product factor
267C5—22no—
268C5D3×D5×Dic312yescomplemented
269C22—31no—
270C22—251no—
271C22—754no—
272C22—751no—
273C4—152no—
274C4—452no—
275C3—21no—
276C3D3×#603611yescharacteristic, complemented
277C3C2×#1059712611yescharacteristic, complemented
278C2—32no—
279C2—252no—
280C2—752no—
281C2D3×D15⋊D511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×D15⋊D5
commutator, hypocenterC32×C52C22×C4
Fitting, socle, cosocleC2×C32×C52C23
prime radicalC2×C3×D3×C5⋊D5C2
LCSG ▷ C32×C52
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #14268306C2semidirect
3. C5×D3×Dic15C2semidirect
4. #14268268C2semidirect
5. C3×#10597126C2semidirect
11. C3×D3×C5⋊D5C4semidirect
12. C5×C3⋊Dic15C22semidirect
13. C3×C5×Dic15C22semidirect
22. #10597126D3direct (N × H)
27. C3×C3⋊(C5⋊D5)C2×C4semidirect
28. C3×C52×D3C2×C4semidirect
29. C32×C5⋊D5C2×C4semidirect
34. D3×Dic15D5semidirect
47. D3×C5⋊D5Dic3semidirect
51. C5×Dic15C2×D3semidirect
55. C32×C52C22×C4semidirect
69. C3⋊Dic15C2×D5semidirect
71. C3×Dic15C2×D5semidirect
77. C3⋊(C5⋊D5)C2×Dic3semidirect
78. C52×D3C2×Dic3semidirect
81. C3×C5⋊D5C4×D3semidirect
82. C3×C5⋊D5C2×Dic3semidirect
112. C3×C5×D3C4×D5semidirect
117. C3×C52C2×C4×D3semidirect
118. C3×C52C22×Dic3semidirect
146. Dic15D3×D5semidirect
155. C5⋊D5D3×Dic3semidirect
159. C32×C5C2×C4×D5semidirect
193. C5×D3D5×Dic3semidirect
194. C52C2×D3×Dic3semidirect
221. C3×D3#6036semidirect
227. C3×C5C4×D3×D5semidirect
228. C3×C5C2×D5×Dic3semidirect
251. C32C2×#6036semidirect
266. D3#10597126direct (N × H)
268. C5D3×D5×Dic3semidirect
276. C3D3×#6036semidirect
277. C3C2×#10597126semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C5⋊D52
#142683062
C5×D3×Dic152
#142682682
C3×#105971262
C2×#105971263
D3×#60363
D3×D5×Dic35