Finite Group Databasebeta

← #11754577

Subgroups — #11754577

Order 960.

660 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 168 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
1C22×C4×C5×D3C211yesmaximal, characteristic, complemented
2C2×C3×#709C211yesmaximal, characteristic, complemented
3#91815C211yesmaximal, characteristic, complemented
4#91568C212yesmaximal, complemented
5#91536C212yesmaximal, complemented
6#91456C212yesmaximal, complemented
7C4×#1201C214yesmaximal, complemented
8#91369C212yesmaximal, complemented
9#66125—31nomaximal, Hall
10C23×C5×D3C2211yescharacteristic
11C22×C3×C4×C5C2211yescharacteristic
12C22×C5×Dic3C2211yescharacteristic
13C2×C4×C5×D3—24no—
14C2×C4×C5×D3C2212yes—
15C2×C4×C5×D3C2212yes—
16C2×C3×C22⋊D5C2212yes—
17C3×#709—24no—
18C2×C3×D20C2211yescharacteristic, complemented
19C2×C3×C4×D5C2212yescomplemented
20C2×C3×Dic10C2211yescharacteristic, complemented
21C2×#1201C2214yes—
22#6719C2212yes—
23C4⋊Dic15C2212yescomplemented
24C4×Dic15C2212yescomplemented
25#6669C2214yescomplemented
26(C2×D3)⋊Dic5C2214yes—
27#6665C2214yescomplemented
28#5828—51nomaximal, Hall
29C23×C4×C5—31no—
30C2×#709D311yescharacteristic, complemented
31#4099—32no—
32#4076—32no—
33#4075—32no—
34C4×C22⋊D5—34no—
35#4072—31no—
36#4070—32no—
37C23×C3×C5C2311yescharacteristic
38C22×C5×D3—22no—
39C22×C5×D3—24no—
40C22×C5×D3C2312yes—
41C22×C3×D5C2312yes—
42C2×C3×C4×C5D414yescomplemented
43C2×C3×C4×C5C2311yescharacteristic
44C2×C3×C4×C5C2311yescharacteristic
45C2×Dic15C2314yes—
46C2×C5×Dic3—22no—
47C2×C5×Dic3C2312yes—
48C4×C5×D3—24no—
49C4×C5×D3—24no—
50C3×C22⋊D5—24no—
51C2×C3×Dic5C2312yes—
52C3×D20—22no—
53C3×C4×D5—24no—
54C3×Dic10—22no—
55#1201—28no—
56C2×C3×#41—51no—
57C22×C4×D3D511yescharacteristic, complemented
58#946—52no—
59#938—52no—
60#937—52no—
61#935—52no—
62C4×#67—54no—
63#926—51no—
64C24×C5—31no—
65C22×C4×C5—31no—
66C22×C4×C5—32no—
67C22×C4×C5—32no—
68C22×C4×C5—64no—
69C22×C4×C5C2×D311yescharacteristic
70C2×C22⋊D5—34no—
71C2×C22⋊D5C2×D312yes—
72#709—24no—
73C2×D20C2×D311yescharacteristic, complemented
74C2×C4×D5C2×D312yescomplemented
75C2×Dic10C2×D311yescharacteristic, complemented
76C22⋊Dic5—32no—
77C22⋊Dic5—34no—
78#685—34no—
79C4⋊Dic5—32no—
80#683—34no—
81C4×Dic5—32no—
82#525—151noSylow
83C22×C3×C5—22no—
84C22×C3×C5C2×D412yes—
85C22×C3×C5C2411yescharacteristic
86C2×C5×D3—28no—
87C2×C5×D3—22no—
88C2×C5×D3—22no—
89C2×C5×D3#4114yescomplemented
90C2×C3×D5—22no—
91C2×C3×D5—24no—
92C3×C4×C5C2×D412yes—
93C3×C4×C5C2×D412yes—
94Dic15—24no—
95C3×Dic5—22no—
96C5×Dic3—22no—
97C23×D3C2×D511yescharacteristic
98C3×#41—104no—
99C2×C3×Q8—51no—
100C2×C3×D4—52no—
101C2×C3×D4—51no—
102C22×C3×C4—52no—
103C22×C3×C4C2×D511yescharacteristic
104C2×#67—54no—
105C22×Dic3C2×D511yescharacteristic
106C2×C4×D3—24no—
107C2×C4×D3C2×D512yes—
108C2×C4×D3C2×D512yes—
109#217—52no—
110#217—54no—
111(C2×D3)⋊C4—54no—
112C4⋊Dic3—52no—
113Dic3⋊C4—54no—
114C4×Dic3—52no—
115C23×C5—32no—
116C23×C5—64no—
117C23×C5—62no—
118C23×C5C22×D311yescharacteristic
119C22×D5C22×D312yes—
120C2×C4×C5—32no—
121C2×C4×C5—62no—
122C2×C4×C5—64no—
123C2×C4×C5—64no—
124C2×C4×C5#6714yescomplemented
125C2×C4×C5C22×D311yescharacteristic
126C2×C4×C5C22×D311yescharacteristic
127C22⋊D5—24no—
128C22⋊D5—68no—
129C2×Dic5—34no—
130C2×Dic5C22×D312yes—
131D20—22no—
132C4×D5—24no—
133Dic10—22no—
134C2×#41—51no—
135C23×C4—31no—
136#123—152no—
137C22⋊Q8—152no—
138#121—152no—
139#120—152no—
140C4×D4—154no—
141#117—151no—
142C2×C3×C5—22no—
143C2×C3×C5C22×D411yescharacteristic
144C2×C3×C5C2×#4112yes—
145C3×D5—42no—
146C5×D3—24no—
147C23×C3—52no—
148C23×C3C22×D511yescharacteristic
149C22×D3—22no—
150C22×D3—24no—
151C22×D3C22×D512yes—
152C3×Q8—102no—
153C3×D4—104no—
154C3×D4—102no—
155C2×C3×C4—52no—
156C2×C3×C4—104no—
157C2×C3×C4C22⋊D514yescomplemented
158C2×C3×C4C22×D511yescharacteristic
159C2×C3×C4C22×D511yescharacteristic
160#67—108no—
161C2×Dic3—22no—
162C2×Dic3—54no—
163C2×Dic3C22×D512yes—
164C4×D3—24no—
165C4×D3—24no—
166C22×C5—22no—
167C22×C5—34no—
168C22×C5—68no—
169C22×C5—62no—
170C22×C5—62no—
171C22×C5C2×#6712yes—
172C22×C5C23×D311yescharacteristic
173C2×D5—24no—
174C2×D5—22no—
175C4×C5—62no—
176C4×C5C2×#6712yes—
177C4×C5C2×#6712yes—
178Dic5—22no—
179Dic5—64no—
180C24—31no—
181#41—104no—
182C2×Q8—51no—
183C2×D4—52no—
184C2×D4—51no—
185C2×D4—154no—
186C22×C4—31no—
187C22×C4—32no—
188C22×C4—32no—
189C22×C4—52no—
190C22×C4—64no—
191C22×C4D3×D511yescharacteristic
192C4⋊C4—154no—
193C4⋊C4—152no—
194C22⋊C4—154no—
195C22⋊C4—154no—
196C22⋊C4—152no—
197C42—152no—
198C3×C5#52511yescharacteristic, complemented, Hall
199C22×C3—22no—
200C22×C3—104no—
201C22×C3—102no—
202C22×C3C2×C22⋊D512yes—
203C22×C3C23×D511yescharacteristic
204C2×D3—28no—
205C2×D3—22no—
206C2×D3—22no—
207C2×D3#70914yescomplemented
208C3×C4—102no—
209C3×C4C2×C22⋊D512yes—
210C3×C4C2×C22⋊D512yes—
211Dic3—22no—
212Dic3—104no—
213C2×C5—22no—
214C2×C5—64no—
215C2×C5D3×#4112yes—
216C2×C5C22×#6711yescharacteristic
217D5—42no—
218C23—32no—
219C23—52no—
220C23—64no—
221C23—62no—
222C23C2×D3×D511yescharacteristic
223Q8—102no—
224D4—104no—
225D4—102no—
226D4—308no—
227C2×C4—32no—
228C2×C4—52no—
229C2×C4—62no—
230C2×C4—64no—
231C2×C4—64no—
232C2×C4—104no—
233C2×C4—154no—
234C2×C4#120114yescomplemented
235C2×C4C2×D3×D511yescharacteristic
236C2×C4C2×D3×D511yescharacteristic
237C2×C3—22no—
238C2×C3—202no—
239C2×C3C2×#70912yes—
240C2×C3C22×C22⋊D511yescharacteristic
241D3—24no—
242C5#582811yescharacteristic, complemented, Sylow
243C22—22no—
244C22—34no—
245C22—68no—
246C22—62no—
247C22—62no—
248C22—104no—
249C22—102no—
250C22C2×#120112yes—
251C22C22×D3×D511yescharacteristic
252C4—62no—
253C4—102no—
254C4—304no—
255C4C2×#120112yes—
256C4C2×#120112yes—
257C3#6612511yescharacteristic, complemented, Sylow
258C2—22no—
259C2—64no—
260C2—202no—
261C2D3×#70912yes—
262C2C22×#120111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FrattiniC22C22×D3×D5
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#525
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×D3C2semidirect
2. C2×C3×#709C2semidirect
3. #91815C2semidirect
4. #91568C2semidirect
5. #91536C2semidirect
6. #91456C2semidirect
7. C4×#1201C2semidirect
8. #91369C2semidirect
18. C2×C3×D20C22semidirect
19. C2×C3×C4×D5C22semidirect
20. C2×C3×Dic10C22semidirect
23. C4⋊Dic15C22semidirect
24. C4×Dic15C22semidirect
25. #6669C22semidirect
27. #6665C22semidirect
30. C2×#709D3semidirect
42. C2×C3×C4×C5D4semidirect
57. C22×C4×D3D5semidirect
73. C2×D20C2×D3semidirect
74. C2×C4×D5C2×D3semidirect
75. C2×Dic10C2×D3semidirect
89. C2×C5×D3#41semidirect
124. C2×C4×C5#67semidirect
157. C2×C3×C4C22⋊D5semidirect
198. C3×C5#525semidirect
207. C2×D3#709semidirect
234. C2×C4#1201semidirect
242. C5#5828semidirect
257. C3#66125semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×D32
C2×C3×#7092
#918152
#915682
#915362
#914562
C4×#12012
#913692
#661253
#58285