Finite Group Databasebeta

← #11748129

Subgroups — #11748129

Order 960.

296 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 70 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×D5×Dic6C211yesmaximal, characteristic
2C2×C5×Dic12C211yesmaximal, characteristic, complemented
3#91359C211yesmaximal, characteristic
4C2×#6663C211yesmaximal, characteristic, complemented
5#91100C211yesmaximal, characteristic, complemented
6C3×#3952C211yesmaximal, characteristic
7#90973C211yesmaximal, characteristic, complemented
8#65475—31nomaximal, Hall
9C2×Dic30C2211yescharacteristic
10C2×C5×Dic6C2211yescharacteristic
11C2×C5×Dic6C2211yescharacteristic
12C2×C3×C4×D5C2211yescharacteristic
13C2×#1204—21no—
14C2×D5×Dic3—21no—
15D5×Dic6—22no—
16D5×Dic6—22no—
17C2×C3×C5×C8C2211yescharacteristic
18C4⋊Dic15C2211yescharacteristic
19C5×Dic12—22no—
20C2×C3×#168C2211yescharacteristic
21#6669—21no—
22#6665—21no—
23#6663—22no—
24#4739—51nomaximal, Hall
25C2×Q8×D5—31no—
26C2×C5×Q16—31no—
27#4092—31no—
28C2×#689—31no—
29#3967—31no—
30#3952D311yescharacteristic
31#3948—31no—
32C22×C3×D5D411yescharacteristic
33C2×C3×C4×C5C2311yescharacteristic
34C2×Dic15—21no—
35C2×Dic15—21no—
36Dic30—21no—
37Dic30D412yes—
38C2×C5×Dic3—21no—
39C2×C5×Dic3—21no—
40C5×Dic6—21no—
41C5×Dic6—21no—
42C5×Dic6—21no—
43C5×Dic6D412yes—
44C2×C3×Dic5D411yescharacteristic
45C3×C4×D5—21no—
46C3×C4×D5—21no—
47#1204—24no—
48D5×Dic3—24no—
49C3×C5×C8—21no—
50C3×#168—21no—
51C22×Dic6—51no—
52#924—51no—
53C2×Dic12—51no—
54C2×Dic12D511yescharacteristic, complemented
55C3×C22⋊C8—51no—
56#816—51no—
57#816—51no—
58C2×C5×Q8—31no—
59C2×C5×Q8—31no—
60Q8×D5—62no—
61Q8×D5—62no—
62C2×C4×D5—61no—
63C2×C4×D5C2×D311yescharacteristic
64C2×Dic10—31no—
65C2×Dic10—61no—
66C5×Q16—62no—
67C2×C5×C8C2×D311yescharacteristic
68#689—62no—
69#685—61no—
70C4⋊Dic5—31no—
71#683—61no—
72C2×#168C2×D311yescharacteristic
73#451—151noSylow
74C22×C3×C5C2×D411yescharacteristic
75C2×C3×D5—21no—
76C2×C3×D5—21no—
77C2×C3×D5Q1612yescomplemented
78C3×C4×C5C2×D411yescharacteristic
79C3×C4×C5C2×D411yescharacteristic
80Dic15—22no—
81Dic15—41no—
82C3×Dic5—21no—
83C5×Dic3—22no—
84C5×Dic3—41no—
85C22×C3×C4—51no—
86C22×Dic3—101no—
87C2×Dic6—51no—
88C2×Dic6—102no—
89C2×Dic6—101no—
90C2×Dic6—102no—
91C2×Dic6C2×D511yescharacteristic
92C2×Dic6C2×D511yescharacteristic
93C2×C3×C8—51no—
94C2×C3×C8C2×D511yescharacteristic
95#217—101no—
96C4⋊Dic3—51no—
97Dic3⋊C4—101no—
98Dic12—22no—
99Dic12—102no—
100C22×D5D1211yescharacteristic
101C5×Q8—32no—
102C5×Q8—61no—
103C5×Q8—61no—
104C5×Q8—61no—
105C2×C4×C5—61no—
106C2×C4×C5—61no—
107C2×C4×C5C22×D311yescharacteristic
108C2×Dic5—61no—
109C2×Dic5—61no—
110C2×Dic5D1211yescharacteristic
111C4×D5—21no—
112C4×D5—21no—
113C4×D5—64no—
114Dic10—32no—
115Dic10—64no—
116Dic10—61no—
117C5×C8—21no—
118#168—21no—
119C22×Q8—151no—
120C2×Q16—31no—
121C2×Q16—151no—
122C22⋊Q8—151no—
123#103—151no—
124#103—151no—
125C22⋊C8—51no—
126C2×C3×C5#12011yescharacteristic
127C2×C3×C5C2×Q1611yescharacteristic
128C2×C3×C5#13711yescharacteristic
129C3×D5—22no—
130C23×C3—51no—
131C2×C3×C4—51no—
132C2×C3×C4—101no—
133C2×C3×C4—101no—
134C2×C3×C4C22×D511yescharacteristic
135C2×Dic3—21no—
136C2×Dic3—21no—
137C2×Dic3—104no—
138C2×Dic3—101no—
139C2×Dic3—101no—
140Dic6—21no—
141Dic6—21no—
142Dic6—21no—
143Dic6—52no—
144Dic6—104no—
145Dic6—101no—
146Dic6C22⋊D512yes—
147C3×C8—21no—
148C3×C8—101no—
149C22×C5C2×D1211yescharacteristic
150C2×D5—21no—
151C2×D5—21no—
152C2×D5Dic1212yescomplemented
153C4×C5—62no—
154C4×C5—121no—
155C4×C5D3×D411yescharacteristic
156C4×C5D3×D411yescharacteristic
157Dic5—21no—
158Dic5—62no—
159Dic5—121no—
160C2×Q8—31no—
161C2×Q8—31no—
162C2×Q8—151no—
163C2×Q8—301no—
164C2×Q8—302no—
165C2×Q8—302no—
166C22×C4—51no—
167C22×C4—301no—
168Q16—62no—
169Q16—302no—
170C2×C8—51no—
171C2×C8D3×D511yescharacteristic
172C4⋊C4—151no—
173C4⋊C4—301no—
174C22⋊C4—301no—
175C3×C5#45111yescharacteristic, complemented, Hall
176C22×C3—52no—
177C22×C3—101no—
178C22×C3—101no—
179C22×C3D4×D511yescharacteristic
180C3×C4—101no—
181C3×C4D4×D511yescharacteristic
182C3×C4C2×C22⋊D511yescharacteristic
183Dic3—22no—
184Dic3—41no—
185Dic3—102no—
186Dic3—201no—
187C2×C5#88211yescharacteristic
188C2×C5C2×Dic1211yescharacteristic
189C2×C5#90911yescharacteristic
190D5—22no—
191C23—51no—
192Q8—32no—
193Q8—61no—
194Q8—61no—
195Q8—61no—
196Q8—152no—
197Q8—304no—
198Q8—301no—
199C2×C4—51no—
200C2×C4—61no—
201C2×C4—61no—
202C2×C4—101no—
203C2×C4—101no—
204C2×C4—304no—
205C2×C4—301no—
206C2×C4—301no—
207C2×C4C2×D3×D511yescharacteristic
208C8—21no—
209C8—101no—
210C2×C3—102no—
211C2×C3D5×Q1611yescharacteristic
212C2×C3#406411yescharacteristic
213C2×C3#408311yescharacteristic
214C5#473911yescharacteristic, complemented, Sylow
215C22—52no—
216C22—101no—
217C22—101no—
218C22D5×D1211yescharacteristic
219C4—62no—
220C4—101no—
221C4—121no—
222C4—302no—
223C4—601no—
224C4#677711yescharacteristic
225C4D3×C22⋊D511yescharacteristic
226C3#6547511yescharacteristic, complemented, Sylow
227C2—102no—
228C2D5×Dic1211yescharacteristic
229C2#9126111yescharacteristic
230C2#9147511yescharacteristic
subgroupG/H
centerC22D5×D12
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radicalC22×C3×D5D4
hypercenterC2×C8D3×D5
hypocenterC3×C5#451
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C5×Dic12C2semidirect
4. C2×#6663C2semidirect
5. #91100C2semidirect
7. #90973C2semidirect
54. C2×Dic12D5semidirect
77. C2×C3×D5Q16semidirect
152. C2×D5Dic12semidirect
175. C3×C5#451semidirect
214. C5#4739semidirect
226. C3#65475semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic62
C2×C5×Dic122
#913592
C2×#66632
#911002
C3×#39522
#909732
#654753
#47395