Finite Group Databasebeta

← #11755215

Subgroups — #11755215

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#91833C211yesmaximal, characteristic, complemented
2C5×#944C211yesmaximal, characteristic, complemented
3C3×#4093C211yesmaximal, characteristic
4#91431C212yesmaximal, complemented
5#91421C212yesmaximal, complemented
6#91407C212yesmaximal
7#91378C212yesmaximal, complemented
8#91366C212yesmaximal, complemented
9#91363C212yesmaximal, complemented
10#66069—31nomaximal, Hall
11C2×C3×C5×Q8C2211yescharacteristic
12C2×Dic30C2211yescharacteristic
13C2×C5×Dic6C2211yescharacteristic
14C2×C3×D20C2211yescharacteristic
15C2×D5×Dic3C2212yes—
16#6712C2212yes—
17#6712C2212yes—
18C4×Dic15C2211yescharacteristic
19C5×Dic3⋊C4C2212yes—
20C5×Dic3⋊C4C2212yes—
21C4×C5×Dic3C2211yescharacteristic
22C3×#685C2212yes—
23C3×#685C2212yes—
24C3×C4×Dic5C2211yescharacteristic
25Dic3⋊Dic5C2212yes—
26#6669C2212yes—
27#6668C2212yes—
28#6668C2212yes—
29#6665C2212yes—
30#6665C2212yes—
31#6665C2212yes—
32#5672—51nomaximal, Hall
33C5×C4⋊Q8—31no—
34#4093D311yescharacteristic
35#4092—32no—
36#4090—31no—
37#4044—32no—
38#4042—32no—
39#4040—32no—
40#4035—32no—
41#4022—32no—
42C22×C3×D5C2312yes—
43C3×C5×Q8—41no—
44C2×C3×C4×C5C2311yescharacteristic
45C2×C3×C4×C5C2311yescharacteristic
46C2×C3×C4×C5C2311yescharacteristic
47C2×Dic15C2312yes—
48C2×Dic15C2312yes—
49Dic30—41no—
50C2×C5×Dic3C2312yes—
51C2×C5×Dic3C2312yes—
52C5×Dic6—41no—
53C2×C3×Dic5C2312yes—
54C3×D20—41no—
55D5×Dic3—42no—
56C3×#124—51no—
57#944—51no—
58#944D511yescharacteristic, complemented
59#935—52no—
60#879—52no—
61#879—52no—
62#878—52no—
63#878—52no—
64#870—52no—
65C2×C5×Q8—31no—
66C2×C5×Q8C2×D311yescharacteristic
67C2×D20C2×D311yescharacteristic
68C2×C4×D5—32no—
69C2×Dic10—31no—
70C5×C4⋊C4—32no—
71C5×C4⋊C4—32no—
72C42×C5—31no—
73#685—32no—
74#685—32no—
75#685—32no—
76#685C2×D312yes—
77#685C2×D312yes—
78C4⋊Dic5—32no—
79#683—32no—
80#683—32no—
81#683—32no—
82#683—32no—
83#683—32no—
84C4×Dic5—31no—
85C4×Dic5C2×D311yescharacteristic
86#563—151noSylow
87C22×C3×C5C2411yescharacteristic
88C2×C3×D5—22no—
89C2×C3×D5—24no—
90C3×C4×C5—21no—
91C3×C4×C5—21no—
92C3×C4×C5—21no—
93Dic15—22no—
94Dic15—22no—
95C3×Dic5—22no—
96C5×Dic3—22no—
97C5×Dic3—22no—
98C2×C3×Q8C2×D511yescharacteristic
99C2×C3×D4—51no—
100C22×Dic3—52no—
101C2×Dic6—51no—
102C2×Dic6C2×D511yescharacteristic
103C3×C22⋊C4—52no—
104C3×C22⋊C4—52no—
105C3×C42—51no—
106#217—52no—
107#217—52no—
108#217—52no—
109C4⋊Dic3—52no—
110C4⋊Dic3—52no—
111Dic3⋊C4—52no—
112Dic3⋊C4—52no—
113Dic3⋊C4—52no—
114Dic3⋊C4—52no—
115Dic3⋊C4C2×D512yes—
116Dic3⋊C4C2×D512yes—
117C4×Dic3—51no—
118C4×Dic3C2×D511yescharacteristic
119C22×D5C22×D312yes—
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×Dic5—32no—
129C2×Dic5C22×D312yes—
130D20—41no—
131C4×D5—122no—
132Dic10—121no—
133C4⋊Q8—31no—
134C4⋊Q8—151no—
135#126—152no—
136#126—152no—
137#125—152no—
138#124—51no—
139#123—152no—
140C22⋊Q8—152no—
141C22⋊Q8—152no—
142C2×C3×C5H(5,𝔽2)11yescharacteristic
143C2×C3×C52−1+412yes—
144C3×D5—42no—
145C23×C3—52no—
146C3×Q8—41no—
147C3×D4—201no—
148C2×C3×C4—52no—
149C2×C3×C4C22×D511yescharacteristic
150C2×C3×C4C22×D511yescharacteristic
151C2×C3×C4C22×D511yescharacteristic
152C2×Dic3—52no—
153C2×Dic3—52no—
154C2×Dic3—202no—
155C2×Dic3C22×D512yes—
156C2×Dic3C22×D512yes—
157Dic6—41no—
158Dic6—201no—
159C22×C5C23×D311yescharacteristic
160C2×D5—22no—
161C2×D5—24no—
162C4×C5—21no—
163C4×C5—21no—
164C4×C5—21no—
165C4×C5—62no—
166C4×C5—62no—
167Dic5—22no—
168Dic5—62no—
169Dic5—62no—
170C2×Q8—31no—
171C2×Q8—151no—
172C2×Q8D3×D511yescharacteristic
173C2×D4—51no—
174C22×C4—152no—
175C4⋊C4—32no—
176C4⋊C4—32no—
177C4⋊C4—152no—
178C4⋊C4—152no—
179C4⋊C4—152no—
180C4⋊C4—152no—
181C4⋊C4—152no—
182C4⋊C4—152no—
183C22⋊C4—52no—
184C22⋊C4—52no—
185C22⋊C4—152no—
186C22⋊C4—152no—
187C22⋊C4—152no—
188C42—31no—
189C42—51no—
190C42—151no—
191C3×C5#56311yescharacteristic, complemented, Hall
192C22×C3—102no—
193C22×C3—104no—
194C22×C3C23×D511yescharacteristic
195C3×C4—21no—
196C3×C4—21no—
197C3×C4—21no—
198C3×C4—102no—
199Dic3—22no—
200Dic3—22no—
201Dic3—102no—
202Dic3—102no—
203C2×C5#100411yescharacteristic
204C2×C5#101012yes—
205D5—42no—
206C23—52no—
207Q8—41no—
208Q8—121no—
209Q8—601no—
210D4—201no—
211C2×C4—32no—
212C2×C4—32no—
213C2×C4—52no—
214C2×C4—152no—
215C2×C4—152no—
216C2×C4—602no—
217C2×C4C2×D3×D511yescharacteristic
218C2×C4C2×D3×D511yescharacteristic
219C2×C4C2×D3×D511yescharacteristic
220C2×C3—202no—
221C2×C3#414411yescharacteristic
222C2×C3#414712yes—
223C5#567211yescharacteristic, complemented, Sylow
224C22—104no—
225C22—102no—
226C22C22×D3×D511yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—62no—
231C4—62no—
232C4—102no—
233C4—302no—
234C4—302no—
235C3#6606911yescharacteristic, complemented, Sylow
236C2—202no—
237C2#9202812yes—
238C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radicalC2×C3×D20C22
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
1. #91833C2semidirect
2. C5×#944C2semidirect
4. #91431C2semidirect
5. #91421C2semidirect
7. #91378C2semidirect
8. #91366C2semidirect
9. #91363C2semidirect
58. #944D5semidirect
191. C3×C5#563semidirect
223. C5#5672semidirect
235. C3#66069semidirect

Maximal subgroups

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

subgroupindex
#918332
C5×#9442
C3×#40932
#914312
#914212
#914072
#913782
#913662
#913632
#660693
#56725