Finite Group Databasebeta

← #11749406

Subgroups — #11749406

Order 960.

304 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×#6773C211yesmaximal, characteristic
2C2×#6717C211yesmaximal, characteristic, complemented
3C2×C5×#216C211yesmaximal, characteristic, complemented
4C3×#4092C211yesmaximal, characteristic, complemented
5#90972C211yesmaximal, characteristic, complemented
6#90968C211yesmaximal, characteristic, complemented
7#90955C211yesmaximal, characteristic, complemented
8#65476—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×D60C2211yescharacteristic
11C2×C5×Dic6C2211yescharacteristic
12C2×C3×C4×D5C2211yescharacteristic
13C2×#1202—21no—
14C2×#1200—21no—
15#6773—22no—
16#6773—22no—
17#6717—22no—
18C2×C3⋊#168C2211yescharacteristic
19C5×#216—22no—
20C2×C5×C3⋊C8C2211yescharacteristic
21C3×#685—21no—
22C3×C4⋊Dic5C2211yescharacteristic
23C3×#683—21no—
24#5047—51nomaximal, Hall
25C2×#713—31no—
26C2×C5×Q16—31no—
27#4092D311yescharacteristic, complemented
28C2×#688—31no—
29#3967—31no—
30#3953—31no—
31#3952—31no—
32C22×D15—21no—
33C22×C3×D5D411yescharacteristic
34C3×C5×Q8—21no—
35C3×C5×Q8—21no—
36C2×C3×C4×C5—21no—
37C2×C3×C4×C5C2311yescharacteristic
38D60—21no—
39D60D412yes—
40C2×C5×Dic3—21no—
41C5×Dic6—21no—
42C5×Dic6D412yes—
43C2×C3×Dic5—21no—
44C2×C3×Dic5D411yescharacteristic
45C3×C4×D5—21no—
46C3×C4×D5—21no—
47#1202—24no—
48#1200—24no—
49C3⋊#168—21no—
50C5×C3⋊C8—21no—
51C2×#235—51no—
52C3×C22⋊Q8—51no—
53C2×#216D511yescharacteristic, complemented
54C2×#215—51no—
55#830—51no—
56#810—51no—
57#809—51no—
58C2×C5×Q8—31no—
59C2×C5×Q8C2×D311yescharacteristic
60#713—62no—
61#713—62no—
62C2×D20—31no—
63C2×D20—61no—
64C2×C4×D5—61no—
65C2×C4×D5C2×D311yescharacteristic
66C5×Q16—62no—
67C2×C5×C8—31no—
68#688—62no—
69#685—21no—
70C4⋊Dic5C2×D311yescharacteristic
71#683—21no—
72C2×#168—31no—
73#452—151noSylow
74C22×C3×C5C2×D411yescharacteristic
75C2×D15—22no—
76C2×D15—41no—
77C2×D15—41no—
78C2×C3×D5—21no—
79C2×C3×D5—21no—
80C2×C3×D5—21no—
81C3×C4×C5—41no—
82C3×C4×C5C2×D411yescharacteristic
83C3×C4×C5C2×D411yescharacteristic
84C3×Dic5—21no—
85C3×Dic5—41no—
86C5×Dic3—22no—
87C2×C3×Q8C2×D511yescharacteristic
88C22×C3×C4—51no—
89C2×#67—101no—
90#235—102no—
91#235—102no—
92C2×D12—51no—
93C2×C4×D3—101no—
94C2×Dic6C2×D511yescharacteristic
95C3×C4⋊C4—51no—
96C3×C4⋊C4—101no—
97C3×C22⋊C4—101no—
98#216—22no—
99#215—102no—
100C2×C3⋊C8—51no—
101C2×C3⋊C8C2×D511yescharacteristic
102C22×D5—61no—
103C22×D5#6711yescharacteristic
104C5×Q8—21no—
105C5×Q8—21no—
106C5×Q8—32no—
107C5×Q8—61no—
108C2×C4×C5—21no—
109C2×C4×C5—61no—
110C2×C4×C5C22×D311yescharacteristic
111C2×Dic5—21no—
112C2×Dic5#6711yescharacteristic
113D20—32no—
114D20—64no—
115D20—61no—
116C4×D5—21no—
117C4×D5—21no—
118C4×D5—64no—
119C5×C8—61no—
120#168—61no—
121C2×#41—151no—
122C2×Q16—31no—
123C2×SD16—151no—
124C22⋊Q8—51no—
125#103—151no—
126#102—151no—
127C22⋊C8—151no—
128C2×C3×C5#12011yescharacteristic
129C2×C3×C5#13511yescharacteristic
130C2×C3×C5#13711yescharacteristic
131D15—42no—
132C3×D5—41no—
133C23×C3—51no—
134C22×D3—101no—
135C3×Q8—21no—
136C3×Q8—21no—
137C2×C3×C4—21no—
138C2×C3×C4—51no—
139C2×C3×C4—101no—
140C2×C3×C4—101no—
141C2×C3×C4—101no—
142C2×C3×C4C22×D511yescharacteristic
143#67—104no—
144C2×Dic3—21no—
145D12—52no—
146D12—101no—
147C4×D3—104no—
148Dic6—21no—
149Dic6C22⋊D512yes—
150C3⋊C8—21no—
151C3⋊C8—101no—
152C22×C5C2×#6711yescharacteristic
153C2×D5—21no—
154C2×D5—21no—
155C2×D5—21no—
156C2×D5—62no—
157C2×D5—121no—
158C2×D5—121no—
159C4×C5—41no—
160C4×C5—62no—
161C4×C5D3×D411yescharacteristic
162C4×C5D3×D411yescharacteristic
163Dic5—21no—
164Dic5—41no—
165#41—302no—
166#41—302no—
167C2×Q8—31no—
168C2×Q8D3×D511yescharacteristic
169C2×D4—151no—
170C2×D4—301no—
171C22×C4—51no—
172C22×C4—301no—
173Q16—62no—
174SD16—302no—
175C2×C8—31no—
176C2×C8—151no—
177C4⋊C4—51no—
178C4⋊C4—101no—
179C22⋊C4—101no—
180C3×C5#45211yescharacteristic, complemented, Hall
181C22×C3—101no—
182C22×C3—101no—
183C22×C3—101no—
184C22×C3D4×D511yescharacteristic
185C2×D3—102no—
186C2×D3—201no—
187C2×D3—201no—
188C3×C4—41no—
189C3×C4—101no—
190C3×C4—201no—
191C3×C4D4×D511yescharacteristic
192C3×C4C2×C22⋊D511yescharacteristic
193Dic3—22no—
194C2×C5#93711yescharacteristic
195C2×C5#94211yescharacteristic
196C2×C5#95011yescharacteristic
197D5—41no—
198D5—122no—
199C23—51no—
200C23—301no—
201Q8—21no—
202Q8—21no—
203Q8—32no—
204Q8—61no—
205D4—152no—
206D4—304no—
207D4—301no—
208C2×C4—21no—
209C2×C4—51no—
210C2×C4—61no—
211C2×C4—101no—
212C2×C4—101no—
213C2×C4—101no—
214C2×C4—304no—
215C2×C4C2×D3×D511yescharacteristic
216C8—61no—
217C8—301no—
218C2×C3—201no—
219C2×C3#406411yescharacteristic
220C2×C3#406511yescharacteristic
221C2×C3#408311yescharacteristic
222D3—202no—
223C5#504711yescharacteristic, complemented, Sylow
224C22—101no—
225C22—101no—
226C22—101no—
227C22—302no—
228C22—601no—
229C22—601no—
230C22D5×#6711yescharacteristic
231C4—41no—
232C4—62no—
233C4—101no—
234C4—201no—
235C4D3×C22⋊D511yescharacteristic
236C4#679011yescharacteristic
237C3#6547611yescharacteristic, complemented, Sylow
238C2—201no—
239C2—602no—
240C2#9151511yescharacteristic
241C2#9151611yescharacteristic
242C2#9157711yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC2×#6773C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#452
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#6717C2semidirect
3. C2×C5×#216C2semidirect
4. C3×#4092C2semidirect
5. #90972C2semidirect
6. #90968C2semidirect
7. #90955C2semidirect
27. #4092D3semidirect
53. C2×#216D5semidirect
180. C3×C5#452semidirect
223. C5#5047semidirect
237. C3#65476semidirect

Maximal subgroups

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

subgroupindex
C2×#67732
C2×#67172
C2×C5×#2162
C3×#40922
#909722
#909682
#909552
#654763
#50475