Finite Group Databasebeta

← #13088918

Subgroups — #13088918

Order 1440.

662 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 156 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
1C4×(C3⋊D3)⋊D5C211yesmaximal, characteristic
2Dic6×D15C212yesmaximal, complemented
3C5×#3797C211yesmaximal, characteristic, complemented
4C3⋊D3×Dic10C211yesmaximal, characteristic, complemented
5C3×D15⋊Q8C212yesmaximal, complemented
6#10624039C212yesmaximal, complemented
7#10624038C214yesmaximal, complemented
8#10624022C212yesmaximal
9D3×Q8×D5—32nomaximal
10C2×(C3⋊D3)⋊D5C2211yescharacteristic
11#67180C2211yescharacteristic, complemented
12C4×C5×C3⋊D3C2211yescharacteristic
13C3×C4×D15C2212yes—
14C3×C5×Dic6C2212yescomplemented
15C32×Dic10C2211yescharacteristic, complemented
16#67155C2211yescharacteristic
17#67154C2212yes—
18#67153C2214yescomplemented
19Dic3×D15C2214yes—
20C5×#627C2212yescomplemented
21C5×#624C2212yes—
22#67141C2212yescomplemented
23C3⋊D3×Dic5C2212yes—
24C3×#1204C2214yescomplemented
25C3×#1200C2214yes—
26D32×Q8—51nomaximal, Hall
27Q8×D15—32no—
28C5×D3×Q8—32no—
29C3×Q8×D5—32no—
30C4×D3×D5—32no—
31C4×D3×D5—34no—
32D15⋊Q8—34no—
33D15⋊Q8D312yescomplemented
34D3×Dic10—32no—
35D3×Dic10—34no—
36D3×Dic10—61no—
37D5×Dic6—32no—
38D5×Dic6—34no—
39C2×C5×C3⋊D3C2311yescharacteristic
40C2×C3×D15C2312yes—
41(C3⋊D3)⋊D5Q814yescomplemented
42C32×C4×C5C2311yescharacteristic
43C3⋊Dic15C2312yes—
44C5×C3⋊Dic3C2311yescharacteristic
45C3×Dic15C2312yes—
46C3×C5×Dic3C2314yes—
47C32×Dic5C2312yes—
48C2×Q8×D5—91noHall
49Q8×C3⋊D3—51no—
50C3×D3×Q8—52no—
51C4×D32—51no—
52C4×D32—52no—
53#3797—52no—
54#3797D511yescharacteristic, complemented
55D3×Dic6—52no—
56D3×Dic6—54no—
57C2×D3×D5—32no—
58C3×C5×Q8—32no—
59C4×D15—34no—
60C4×D15C2×D312yes—
61Dic30—32no—
62Dic30—34no—
63Dic30—61no—
64C4×C5×D3—32no—
65C4×C5×D3—34no—
66C4×C5×D3—61no—
67C5×Dic6—34no—
68C5×Dic6C2×D312yescomplemented
69C3×C4×D5—32no—
70C3×C4×D5—34no—
71C3×Dic10—21no—
72C3×Dic10—34no—
73C3×Dic10C2×D312yescomplemented
74#1204—34no—
75#1204—34no—
76#1204—62no—
77#1204C2×D314yescomplemented
78#1200—32no—
79#1200C2×D314yes—
80D3×Dic5—32no—
81D3×Dic5—34no—
82D3×Dic5—62no—
83D5×Dic3—32no—
84D5×Dic3—34no—
85C2×D3×Q8—152no—
86C2×C32×C5C2411yescharacteristic
87C5×C3⋊D3C2×Q812yescomplemented
88C3×D15C2×Q814yescomplemented
89C2×C5×Q8—91no—
90Q8×D5—32no—
91Q8×D5—94no—
92Q8×D5—92no—
93C2×C4×D5—91no—
94C2×C4×D5—92no—
95C2×Dic10—92no—
96C2×Dic10—91no—
97C2×D32—51no—
98C32×Q8—51no—
99C4×C3⋊D3—52no—
100C4×C3⋊D3C2×D511yescharacteristic
101#634—51no—
102#634—52no—
103C3×C4×D3—52no—
104C3×C4×D3—54no—
105C3×Dic6—54no—
106C3×Dic6C2×D512yescomplemented
107#627—54no—
108#627C2×D512yescomplemented
109#624—51no—
110#624C2×D512yes—
111D3×Dic3—52no—
112D3×Dic3—54no—
113C2×D15C22×D312yes—
114C2×C5×D3—32no—
115C2×C5×D3—61no—
116C2×C3×D5—32no—
117D3×D5—38no—
118C3×C4×C5—21no—
119C3×C4×C5—34no—
120C3×C4×C5C22×D312yes—
121Dic15—34no—
122Dic15—62no—
123Dic15C22×D312yes—
124C3×Dic5—22no—
125C3×Dic5—32no—
126C3×Dic5C22×D314yes—
127C5×Dic3—32no—
128C5×Dic3—61no—
129C5×Dic3C22×D314yes—
130C2×C3×Q8—152no—
131D3×Q8—32no—
132D3×Q8—52no—
133D3×Q8—154no—
134D3×Q8—154no—
135D3×Q8—152no—
136D3×Q8—152no—
137D3×Q8—301no—
138C2×C4×D3—152no—
139C2×C4×D3—154no—
140C2×Dic6—154no—
141C2×Dic6—152no—
142C32×C5C22×Q811yescharacteristic, complemented, Hall
143C22×D5—91no—
144C5×Q8—32no—
145C5×Q8—92no—
146C2×C4×C5—92no—
147C2×C4×C5—91no—
148C2×Dic5—91no—
149C2×Dic5—92no—
150C4×D5—32no—
151C4×D5—34no—
152C4×D5—92no—
153C4×D5—94no—
154Dic10—34no—
155Dic10—94no—
156Dic10—91no—
157Dic10—92no—
158Dic10D3211yescharacteristic, complemented
159C2×C3⋊D3C22×D511yescharacteristic
160C2×C3×D3—52no—
161D32—54no—
162C32×C4—52no—
163C32×C4C22×D511yescharacteristic
164C3⋊Dic3—52no—
165C3⋊Dic3C22×D511yescharacteristic
166C3×Dic3—52no—
167C3×Dic3C22×D514yes—
168C22×Q8—451noSylow
169C2×C3×C5—21no—
170C2×C3×C5C23×D312yes—
171D15D3×Q814yescomplemented
172C3×D5—34no—
173C5×D3—34no—
174C5×D3—62no—
175C22×D3—152no—
176C3×Q8—32no—
177C3×Q8—52no—
178C3×Q8—101no—
179C3×Q8—154no—
180C2×C3×C4—154no—
181C2×C3×C4—152no—
182C2×Dic3—152no—
183C2×Dic3—154no—
184C4×D3—32no—
185C4×D3—34no—
186C4×D3—52no—
187C4×D3—54no—
188C4×D3—61no—
189C4×D3—152no—
190C4×D3—152no—
191C4×D3—154no—
192C4×D3—154no—
193C4×D3—302no—
194Dic6—34no—
195Dic6—54no—
196Dic6—154no—
197Dic6—154no—
198Dic6—152no—
199Dic6—154no—
200Dic6—302no—
201Dic6—301no—
202Dic6D3×D512yescomplemented
203C22×C5—91no—
204C2×D5—32no—
205C2×D5—94no—
206C4×C5—34no—
207C4×C5—91no—
208C4×C5C2×D3211yescharacteristic
209Dic5—32no—
210Dic5—92no—
211Dic5C2×D3212yes—
212C2×C32C23×D511yescharacteristic
213C3⋊D3Q8×D512yescomplemented
214C3×D3—54no—
215C2×Q8—91no—
216C2×Q8—152no—
217C2×Q8—451no—
218C2×Q8—452no—
219C2×Q8—452no—
220C2×Q8—454no—
221C22×C4—452no—
222C22×C4—451no—
223C3×C5—21no—
224C3×C5C2×D3×Q812yescomplemented
225C22×C3—152no—
226C2×D3—32no—
227C2×D3—52no—
228C2×D3—61no—
229C2×D3—158no—
230C3×C4—21no—
231C3×C4—34no—
232C3×C4—54no—
233C3×C4—102no—
234C3×C4—152no—
235C3×C4C2×D3×D512yes—
236Dic3—32no—
237Dic3—52no—
238Dic3—61no—
239Dic3—154no—
240Dic3—302no—
241Dic3C2×D3×D514yes—
242C2×C5—92no—
243C2×C5C22×D3211yescharacteristic
244D5—34no—
245C32C2×Q8×D511yescharacteristic, complemented, Sylow
246C23—451no—
247Q8—32no—
248Q8—51no—
249Q8—92no—
250Q8—154no—
251Q8—454no—
252Q8—452no—
253Q8—451no—
254C2×C4—92no—
255C2×C4—91no—
256C2×C4—154no—
257C2×C4—152no—
258C2×C4—454no—
259C2×C4—452no—
260C2×C4—452no—
261C2×C4—451no—
262C2×C3—21no—
263C2×C3—154no—
264C2×C3C22×D3×D512yes—
265D3—34no—
266D3—54no—
267D3—62no—
268C5D32×Q811yescharacteristic, complemented, Sylow
269C22—91no—
270C22—152no—
271C22—454no—
272C4—34no—
273C4—52no—
274C4—91no—
275C4—152no—
276C4—452no—
277C4D32×D511yescharacteristic
278C3—21no—
279C3D3×Q8×D512yescomplemented
280C2—92no—
281C2—154no—
282C2C2×D32×D511yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×D5
commutator, socle, cosocleC2×C32×C5C24
FittingC32×C4×C5C23
prime radicalC2×(C3⋊D3)⋊D5C22
hypercenterC4D32×D5
hypocenterC32×C5C22×Q8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. Dic6×D15C2semidirect
3. C5×#3797C2semidirect
4. C3⋊D3×Dic10C2semidirect
5. C3×D15⋊Q8C2semidirect
6. #10624039C2semidirect
7. #10624038C2semidirect
11. #67180C22semidirect
14. C3×C5×Dic6C22semidirect
15. C32×Dic10C22semidirect
18. #67153C22semidirect
20. C5×#627C22semidirect
22. #67141C22semidirect
24. C3×#1204C22semidirect
33. D15⋊Q8D3semidirect
41. (C3⋊D3)⋊D5Q8semidirect
54. #3797D5semidirect
68. C5×Dic6C2×D3semidirect
73. C3×Dic10C2×D3semidirect
77. #1204C2×D3semidirect
87. C5×C3⋊D3C2×Q8semidirect
88. C3×D15C2×Q8semidirect
106. C3×Dic6C2×D5semidirect
108. #627C2×D5semidirect
142. C32×C5C22×Q8semidirect
158. Dic10D32semidirect
171. D15D3×Q8semidirect
202. Dic6D3×D5semidirect
213. C3⋊D3Q8×D5semidirect
224. C3×C5C2×D3×Q8semidirect
245. C32C2×Q8×D5semidirect
268. C5D32×Q8semidirect
279. C3D3×Q8×D5semidirect

Maximal subgroups

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

subgroupindex
C4×(C3⋊D3)⋊D52
Dic6×D152
C5×#37972
C3⋊D3×Dic102
C3×D15⋊Q82
#106240392
#106240382
#106240222
D3×Q8×D53
D32×Q85