Finite Group Databasebeta

← #11755148

Subgroups — #11755148

Order 960.

392 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 120 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
1#91836C211yesmaximal, characteristic
2C5×#944C211yesmaximal, characteristic, complemented
3C3×#4090C211yesmaximal, characteristic, complemented
4#91433C212yesmaximal
5#91424C212yesmaximal, complemented
6#91411C212yesmaximal, complemented
7#91387C212yesmaximal, complemented
8#91382C212yesmaximal, complemented
9#91380C212yesmaximal, complemented
10#66069—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×D60C2211yescharacteristic
13C2×C5×Dic6C2211yescharacteristic
14C2×C3×Dic10C2211yescharacteristic
15C2×#1200C2212yes—
16#6714C2212yes—
17#6714C2212yes—
18C4×Dic15C2211yescharacteristic
19C5×Dic3⋊C4C2212yes—
20C5×Dic3⋊C4C2212yes—
21C4×C5×Dic3C2211yescharacteristic
22C3×#683C2212yes—
23C3×#683C2212yes—
24C3×C4×Dic5C2211yescharacteristic
25Dic3⋊Dic5C2212yes—
26#6669C2212yes—
27#6669C2212yes—
28#6668C2212yes—
29#6667C2212yes—
30#6667C2212yes—
31#6667C2212yes—
32#5735—51nomaximal, Hall
33C5×C4⋊Q8—31no—
34#4093—31no—
35#4092—32no—
36#4090D311yescharacteristic, complemented
37#4044—32no—
38#4042—32no—
39#4040—32no—
40#4035—32no—
41#4022—32no—
42C22×D15C2312yes—
43C3×C5×Q8—41no—
44C2×C3×C4×C5C2311yescharacteristic
45C2×C3×C4×C5C2311yescharacteristic
46C2×C3×C4×C5C2311yescharacteristic
47C2×Dic15C2312yes—
48D60—41no—
49C2×C5×Dic3C2312yes—
50C2×C5×Dic3C2312yes—
51C5×Dic6—41no—
52C2×C3×Dic5C2312yes—
53C2×C3×Dic5C2312yes—
54C3×Dic10—41no—
55#1200—42no—
56C3×C4⋊Q8—51no—
57#947—51no—
58#946—52no—
59#944D511yescharacteristic, complemented
60#898—52no—
61#896—52no—
62#894—52no—
63#889—52no—
64#876—52no—
65C2×C5×Q8—31no—
66C2×C5×Q8C2×D311yescharacteristic
67C2×D20—31no—
68C2×C4×D5—32no—
69C2×Dic10C2×D311yescharacteristic
70C5×C4⋊C4—32no—
71C5×C4⋊C4—32no—
72C42×C5—31no—
73#685—32no—
74#685—32no—
75#685—32no—
76#685—32no—
77#685—32no—
78C4⋊Dic5—32no—
79#683—32no—
80#683—32no—
81#683—32no—
82#683C2×D312yes—
83#683C2×D312yes—
84C4×Dic5—31no—
85C4×Dic5C2×D311yescharacteristic
86#563—151noSylow
87C22×C3×C5C2411yescharacteristic
88C2×D15—22no—
89C2×D15—24no—
90C3×C4×C5—21no—
91C3×C4×C5—21no—
92C3×C4×C5—21no—
93Dic15—22no—
94C3×Dic5—22no—
95C3×Dic5—22no—
96C5×Dic3—22no—
97C5×Dic3—22no—
98C2×C3×Q8—51no—
99C2×C3×Q8C2×D511yescharacteristic
100C2×D12—51no—
101C2×C4×D3—52no—
102C2×Dic6C2×D511yescharacteristic
103C3×C4⋊C4—52no—
104C3×C4⋊C4—52no—
105C3×C42—51no—
106(C2×D3)⋊C4—52no—
107(C2×D3)⋊C4—52no—
108(C2×D3)⋊C4—52no—
109(C2×D3)⋊C4—52no—
110(C2×D3)⋊C4—52no—
111C4⋊Dic3—52no—
112Dic3⋊C4—52no—
113Dic3⋊C4—52no—
114Dic3⋊C4—52no—
115Dic3⋊C4C2×D512yes—
116Dic3⋊C4C2×D512yes—
117C4×Dic3—51no—
118C4×Dic3C2×D511yescharacteristic
119C22×D5—32no—
120C5×Q8—41no—
121C5×Q8—121no—
122C2×C4×C5—32no—
123C2×C4×C5—32no—
124C2×C4×C5C22×D311yescharacteristic
125C2×C4×C5C22×D311yescharacteristic
126C2×C4×C5C22×D311yescharacteristic
127C2×Dic5—32no—
128C2×Dic5C22×D312yes—
129C2×Dic5C22×D312yes—
130D20—121no—
131C4×D5—122no—
132Dic10—41no—
133C4⋊Q8—31no—
134C4⋊Q8—51no—
135#126—152no—
136#126—152no—
137#125—152no—
138#124—151no—
139#123—152no—
140C22⋊Q8—152no—
141C22⋊Q8—152no—
142C2×C3×C5H(5,𝔽2)11yescharacteristic
143C2×C3×C52−1+412yes—
144D15—42no—
145C22×D3—52no—
146C3×Q8—41no—
147C3×Q8—201no—
148C2×C3×C4—52no—
149C2×C3×C4—52no—
150C2×C3×C4C22×D511yescharacteristic
151C2×C3×C4C22×D511yescharacteristic
152C2×C3×C4C22×D511yescharacteristic
153C2×Dic3—52no—
154C2×Dic3C22×D512yes—
155C2×Dic3C22×D512yes—
156D12—201no—
157C4×D3—202no—
158Dic6—41no—
159C22×C5C23×D311yescharacteristic
160C2×D5—62no—
161C2×D5—64no—
162C4×C5—21no—
163C4×C5—21no—
164C4×C5—21no—
165C4×C5—62no—
166C4×C5—62no—
167Dic5—22no—
168Dic5—22no—
169Dic5—62no—
170C2×Q8—31no—
171C2×Q8—51no—
172C2×Q8D3×D511yescharacteristic
173C2×D4—151no—
174C22×C4—152no—
175C4⋊C4—32no—
176C4⋊C4—32no—
177C4⋊C4—52no—
178C4⋊C4—52no—
179C4⋊C4—152no—
180C4⋊C4—152no—
181C4⋊C4—152no—
182C4⋊C4—152no—
183C22⋊C4—152no—
184C22⋊C4—152no—
185C22⋊C4—152no—
186C22⋊C4—152no—
187C22⋊C4—152no—
188C42—31no—
189C42—51no—
190C42—151no—
191C3×C5#56311yescharacteristic, complemented, Hall
192C22×C3C23×D511yescharacteristic
193C2×D3—102no—
194C2×D3—104no—
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—102no—
199C3×C4—102no—
200Dic3—22no—
201Dic3—22no—
202Dic3—102no—
203C2×C5#100411yescharacteristic
204C2×C5#100712yes—
205D5—122no—
206C23—152no—
207Q8—41no—
208Q8—121no—
209Q8—201no—
210D4—601no—
211C2×C4—32no—
212C2×C4—32no—
213C2×C4—52no—
214C2×C4—52no—
215C2×C4—152no—
216C2×C4—602no—
217C2×C4C2×D3×D511yescharacteristic
218C2×C4C2×D3×D511yescharacteristic
219C2×C4C2×D3×D511yescharacteristic
220C2×C3#414411yescharacteristic
221C2×C3#414712yes—
222D3—202no—
223C5#573511yescharacteristic, complemented, Sylow
224C22—304no—
225C22—302no—
226C22C22×D3×D511yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—62no—
231C4—62no—
232C4—102no—
233C4—102no—
234C4—302no—
235C3#6606911yescharacteristic, complemented, Sylow
236C2—602no—
237C2#9202912yes—
238C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radicalC2×D60C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#563
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#944C2semidirect
3. C3×#4090C2semidirect
5. #91424C2semidirect
6. #91411C2semidirect
7. #91387C2semidirect
8. #91382C2semidirect
9. #91380C2semidirect
36. #4090D3semidirect
59. #944D5semidirect
191. C3×C5#563semidirect
223. C5#5735semidirect
235. C3#66069semidirect

Maximal subgroups

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

subgroupindex
#918362
C5×#9442
C3×#40902
#914332
#914242
#914112
#913872
#913822
#913802
#660693
#57355