Finite Group Databasebeta

← #11754592

Subgroups — #11754592

Order 960.

660 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 164 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×D15C211yesmaximal, characteristic, complemented
2C2×C5×#235C211yesmaximal, characteristic, complemented
3C3×#4072C211yesmaximal, characteristic, complemented
4#91573C212yesmaximal, complemented
5#91543C212yesmaximal, complemented
6#91466C212yesmaximal, complemented
7C4×#1203C214yesmaximal, complemented
8#91383C212yesmaximal, complemented
9#66162—31nomaximal, Hall
10C23×D15C2211yescharacteristic
11C22×C3×C4×C5C2211yescharacteristic
12C22×Dic15C2211yescharacteristic
13C2×C4×D15—24no—
14C2×C4×D15C2212yes—
15C2×C4×D15C2212yes—
16C2×C5×#67C2212yes—
17C5×#235—24no—
18C2×C5×D12C2211yescharacteristic, complemented
19C2×C4×C5×D3C2212yescomplemented
20C2×C5×Dic6C2211yescharacteristic, complemented
21C2×#1203C2214yes—
22C3×C22⋊Dic5C2212yes—
23C3×C4⋊Dic5C2212yescomplemented
24C3×C4×Dic5C2212yescomplemented
25#6668C2214yescomplemented
26#6667C2214yes—
27(C2×D3)⋊Dic5C2214yescomplemented
28#5524—51nomaximal, Hall
29C2×C5×#41—31no—
30C22×C4×D5—31no—
31#4092—32no—
32#4084—32no—
33#4083—32no—
34#4081—32no—
35C4×C22⋊D5—34no—
36#4072D311yescharacteristic, complemented
37C23×C3×C5C2311yescharacteristic
38C22×D15—22no—
39C22×D15—24no—
40C22×D15C2312yes—
41C22×C5×D3C2312yes—
42C2×C3×C4×C5D414yescomplemented
43C2×C3×C4×C5C2311yescharacteristic
44C2×C3×C4×C5C2311yescharacteristic
45C2×Dic15—22no—
46C2×Dic15C2312yes—
47C4×D15—24no—
48C4×D15—24no—
49C5×#67—24no—
50C2×C5×Dic3C2312yes—
51C5×D12—22no—
52C4×C5×D3—24no—
53C5×Dic6—22no—
54C2×C3×Dic5C2314yes—
55#1203—28no—
56C2×#235D511yescharacteristic, complemented
57C22×C4×D3—51no—
58C3×#117—51no—
59#897—52no—
60#895—52no—
61#886—52no—
62#882—52no—
63C4×D12—54no—
64C23×D5—31no—
65C5×#41—64no—
66C2×C5×Q8—31no—
67C2×C5×D4—32no—
68C2×C5×D4—31no—
69C22×C4×C5—32no—
70C22×C4×C5C2×D311yescharacteristic
71C2×C22⋊D5—34no—
72C22×Dic5—31no—
73C2×C4×D5—32no—
74C2×C4×D5—32no—
75C2×C4×D5—64no—
76C22⋊Dic5—34no—
77C22⋊Dic5C2×D312yes—
78#685—34no—
79C4⋊Dic5C2×D312yescomplemented
80#683—34no—
81C4×Dic5C2×D312yescomplemented
82#525—151noSylow
83C22×C3×C5—22no—
84C22×C3×C5C2×D412yes—
85C22×C3×C5C2411yescharacteristic
86C2×D15—28no—
87C2×D15—22no—
88C2×D15—22no—
89C2×D15#4114yescomplemented
90C2×C5×D3—22no—
91C2×C5×D3—24no—
92C3×C4×C5C2×D412yes—
93C3×C4×C5C2×D412yes—
94Dic15—22no—
95C3×Dic5—24no—
96C5×Dic3—22no—
97C23×D3—51no—
98C22×C3×C4C2×D511yescharacteristic
99C2×#67C2×D512yes—
100C22×Dic3—51no—
101#235—24no—
102C2×D12—54no—
103C2×D12C2×D511yescharacteristic, complemented
104C2×C4×D3—52no—
105C2×C4×D3—52no—
106C2×C4×D3—104no—
107C2×C4×D3C2×D512yescomplemented
108C2×Dic6C2×D511yescharacteristic, complemented
109C3×C4⋊C4—52no—
110C3×C22⋊C4—52no—
111C3×C42—52no—
112(C2×D3)⋊C4—54no—
113(C2×D3)⋊C4—54no—
114C4⋊Dic3—54no—
115C23×C5—32no—
116C23×C5C22×D311yescharacteristic
117C22×D5—32no—
118C22×D5—64no—
119C22×D5—62no—
120C5×Q8—62no—
121C5×D4—64no—
122C5×D4—62no—
123C2×C4×C5—32no—
124C2×C4×C5—64no—
125C2×C4×C5D1214yescomplemented
126C2×C4×C5C22×D311yescharacteristic
127C2×C4×C5C22×D311yescharacteristic
128C22⋊D5—68no—
129C2×Dic5—32no—
130C2×Dic5—62no—
131C2×Dic5C22×D314yes—
132C4×D5—64no—
133C4×D5—64no—
134C2×#41—31no—
135C23×C4—151no—
136#123—152no—
137C22⋊Q8—152no—
138#121—152no—
139#120—152no—
140C4×D4—154no—
141#117—51no—
142C2×C3×C5—22no—
143C2×C3×C5C22×D411yescharacteristic
144C2×C3×C5C2×#4112yes—
145D15—24no—
146C5×D3—42no—
147C23×C3C22×D511yescharacteristic
148C22×D3—52no—
149C22×D3—104no—
150C22×D3—102no—
151C22×D3C22×D512yes—
152C2×C3×C4—54no—
153C2×C3×C4C22⋊D514yescomplemented
154C2×C3×C4C22×D511yescharacteristic
155C2×C3×C4C22×D511yescharacteristic
156#67—24no—
157C2×Dic3—52no—
158C2×Dic3—102no—
159C2×Dic3C22×D512yes—
160D12—22no—
161D12—108no—
162C4×D3—24no—
163C4×D3—104no—
164C4×D3—104no—
165Dic6—22no—
166C22×C5—22no—
167C22×C5—62no—
168C22×C5—64no—
169C22×C5C2×D1212yes—
170C22×C5C23×D311yescharacteristic
171C2×D5—34no—
172C2×D5—68no—
173C2×D5—62no—
174C2×D5—62no—
175C4×C5—62no—
176C4×C5C2×D1212yes—
177C4×C5C2×D1212yes—
178Dic5—24no—
179Dic5—62no—
180C24—151no—
181#41—64no—
182C2×Q8—31no—
183C2×D4—32no—
184C2×D4—31no—
185C2×D4—154no—
186C22×C4—32no—
187C22×C4—151no—
188C22×C4—152no—
189C22×C4—152no—
190C22×C4—304no—
191C22×C4D3×D511yescharacteristic
192C4⋊C4—52no—
193C4⋊C4—154no—
194C22⋊C4—52no—
195C22⋊C4—154no—
196C22⋊C4—154no—
197C42—52no—
198C3×C5#52511yescharacteristic, complemented, Hall
199C22×C3—22no—
200C22×C3C2×C22⋊D512yes—
201C22×C3C23×D511yescharacteristic
202C2×D3—24no—
203C2×D3—22no—
204C2×D3—54no—
205C2×D3—108no—
206C2×D3—102no—
207C2×D3—102no—
208C3×C4—104no—
209C3×C4C2×C22⋊D512yes—
210C3×C4C2×C22⋊D512yes—
211Dic3—22no—
212Dic3—102no—
213C2×C5—22no—
214C2×C5—122no—
215C2×C5C22×D1211yescharacteristic
216C2×C5D3×#4112yes—
217D5—64no—
218C23—32no—
219C23—152no—
220C23—304no—
221C23—302no—
222C23C2×D3×D511yescharacteristic
223Q8—62no—
224D4—64no—
225D4—62no—
226D4—308no—
227C2×C4—32no—
228C2×C4—54no—
229C2×C4—64no—
230C2×C4—152no—
231C2×C4—302no—
232C2×C4—304no—
233C2×C4—304no—
234C2×C4#120314yescomplemented
235C2×C4C2×D3×D511yescharacteristic
236C2×C4C2×D3×D511yescharacteristic
237C2×C3—22no—
238C2×C3D5×#4112yes—
239C2×C3C22×C22⋊D511yescharacteristic
240D3—42no—
241D3—104no—
242C5#552411yescharacteristic, complemented, Sylow
243C22—22no—
244C22—64no—
245C22—62no—
246C22—154no—
247C22—308no—
248C22—302no—
249C22—302no—
250C22C2×#120312yes—
251C22C22×D3×D511yescharacteristic
252C4—62no—
253C4—104no—
254C4—302no—
255C4C2×#120312yes—
256C4C2×#120312yes—
257C3#6616211yescharacteristic, complemented, Sylow
258C2—22no—
259C2—122no—
260C2—304no—
261C2#9201612yes—
262C2C22×#120311yescharacteristic
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×D15C2semidirect
2. C2×C5×#235C2semidirect
3. C3×#4072C2semidirect
4. #91573C2semidirect
5. #91543C2semidirect
6. #91466C2semidirect
7. C4×#1203C2semidirect
8. #91383C2semidirect
18. C2×C5×D12C22semidirect
19. C2×C4×C5×D3C22semidirect
20. C2×C5×Dic6C22semidirect
23. C3×C4⋊Dic5C22semidirect
24. C3×C4×Dic5C22semidirect
25. #6668C22semidirect
27. (C2×D3)⋊Dic5C22semidirect
36. #4072D3semidirect
42. C2×C3×C4×C5D4semidirect
56. C2×#235D5semidirect
79. C4⋊Dic5C2×D3semidirect
81. C4×Dic5C2×D3semidirect
89. C2×D15#41semidirect
103. C2×D12C2×D5semidirect
107. C2×C4×D3C2×D5semidirect
108. C2×Dic6C2×D5semidirect
125. C2×C4×C5D12semidirect
153. C2×C3×C4C22⋊D5semidirect
198. C3×C5#525semidirect
234. C2×C4#1203semidirect
242. C5#5524semidirect
257. C3#66162semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D152
C2×C5×#2352
C3×#40722
#915732
#915432
#914662
C4×#12032
#913832
#661623
#55245