Finite Group Databasebeta

← #11748128

Subgroups — #11748128

Order 960.

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

normal subgroups only

This group has 316 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, complemented
2C2×#6706C211yesmaximal, characteristic, complemented
3#91450C211yesmaximal, characteristic
4C2×#6660C211yesmaximal, characteristic, complemented
5C5×#816C211yesmaximal, characteristic, complemented
6C3×#3952C211yesmaximal, characteristic, complemented
7#90975C211yesmaximal, characteristic, complemented
8#65095—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C2×Dic30C2211yescharacteristic
11C2×C5×Dic6C2211yescharacteristic
12C2×C3×C4×D5C2211yescharacteristic
13C2×#1204—21no—
14C2×#1202—21no—
15C2×D5×Dic3—21no—
16D5×Dic6—22no—
17D5×Dic6—22no—
18C2×C3×C5×C8C2211yescharacteristic
19#6706—22no—
20C5×C4⋊Dic3C2211yescharacteristic
21C2×C3×#168C2211yescharacteristic
22#6667—21no—
23#6660—22no—
24#4738—51nomaximal, Hall
25C2×Q8×D5—31no—
26C2×#688—31no—
27C2×#677—31no—
28#4041—31no—
29C5×#103—31no—
30#3952D311yescharacteristic, complemented
31#3942—31no—
32C22×D15—21no—
33C22×C3×D5D411yescharacteristic
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15—21no—
36D60—21no—
37D60—21no—
38Dic30—21no—
39Dic30D412yescomplemented
40C2×C5×Dic3—21no—
41C2×C5×Dic3—21no—
42C5×Dic6—21no—
43C5×Dic6D412yescomplemented
44C2×C3×Dic5D411yescharacteristic
45C3×C4×D5—21no—
46C3×C4×D5—21no—
47#1204—24no—
48#1202—42no—
49D5×Dic3—24no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C22×Dic6—51no—
53#930—51no—
54C2×#204—51no—
55C2×#204—51no—
56C3×C22⋊C8—51no—
57#816—51no—
58#816D511yescharacteristic, complemented
59C2×C5×Q8—31no—
60Q8×D5—62no—
61Q8×D5—62no—
62C2×D20—31no—
63C2×D20—61no—
64C2×C4×D5—61no—
65C2×C4×D5C2×D311yescharacteristic
66C2×Dic10—31no—
67C2×Dic10—61no—
68C2×C5×C8C2×D311yescharacteristic
69C5×C4⋊C4—31no—
70#688—62no—
71#685—61no—
72C2×#168C2×D311yescharacteristic
73#677—62no—
74#448—151noSylow
75C22×C3×C5C2×D411yescharacteristic
76C2×D15—41no—
77C2×D15—41no—
78C2×D15—41no—
79C2×C3×D5—21no—
80C2×C3×D5—21no—
81C2×C3×D5SD1612yescomplemented
82C3×C4×C5C2×D411yescharacteristic
83C3×C4×C5C2×D411yescharacteristic
84Dic15—22no—
85C3×Dic5—21no—
86C5×Dic3—22no—
87C5×Dic3—41no—
88C22×C3×C4—51no—
89C2×#67—101no—
90C22×Dic3—101no—
91C2×D12—51no—
92C2×Dic6—51no—
93C2×Dic6—102no—
94C2×Dic6—101no—
95C2×Dic6—102no—
96C2×Dic6C2×D511yescharacteristic
97C2×C3×C8—51no—
98C2×C3×C8C2×D511yescharacteristic
99(C2×D3)⋊C4—101no—
100C4⋊Dic3C2×D511yescharacteristic
101#204—102no—
102#204—102no—
103C22×D5—61no—
104C22×D5D1211yescharacteristic
105C5×Q8—32no—
106C5×Q8—61no—
107C2×C4×C5—61no—
108C2×C4×C5—61no—
109C2×C4×C5C22×D311yescharacteristic
110C2×Dic5—61no—
111C2×Dic5D1211yescharacteristic
112D20—61no—
113D20—61no—
114D20—122no—
115C4×D5—21no—
116C4×D5—21no—
117C4×D5—64no—
118Dic10—32no—
119Dic10—64no—
120Dic10—61no—
121C5×C8—21no—
122#168—21no—
123C22×Q8—151no—
124C2×SD16—151no—
125C2×SD16—151no—
126#121—151no—
127#103—31no—
128#103—151no—
129C22⋊C8—51no—
130C2×C3×C5#12011yescharacteristic
131C2×C3×C5C2×SD1611yescharacteristic
132C2×C3×C5#13711yescharacteristic
133D15—81no—
134C3×D5—22no—
135C23×C3—51no—
136C22×D3—101no—
137C2×C3×C4—51no—
138C2×C3×C4—101no—
139C2×C3×C4—101no—
140C2×C3×C4C22×D511yescharacteristic
141#67—202no—
142C2×Dic3—21no—
143C2×Dic3—21no—
144C2×Dic3—104no—
145C2×Dic3—101no—
146D12—101no—
147D12—101no—
148Dic6—21no—
149Dic6—52no—
150Dic6—104no—
151Dic6—101no—
152Dic6D2012yescomplemented
153C3×C8—21no—
154C3×C8—101no—
155C22×C5C2×D1211yescharacteristic
156C2×D5—21no—
157C2×D5—21no—
158C2×D5—121no—
159C2×D5—121no—
160C2×D5—121no—
161C2×D5#20412yescomplemented
162C4×C5—62no—
163C4×C5—121no—
164C4×C5D3×D411yescharacteristic
165C4×C5D3×D411yescharacteristic
166Dic5—21no—
167Dic5—62no—
168C2×Q8—31no—
169C2×Q8—151no—
170C2×Q8—301no—
171C2×Q8—302no—
172C2×Q8—302no—
173C2×D4—151no—
174C2×D4—301no—
175C22×C4—51no—
176C22×C4—301no—
177SD16—302no—
178SD16—302no—
179C2×C8—51no—
180C2×C8D3×D511yescharacteristic
181C4⋊C4—31no—
182C22⋊C4—301no—
183C3×C5#44811yescharacteristic, complemented, Hall
184C22×C3—52no—
185C22×C3—101no—
186C22×C3—101no—
187C22×C3D4×D511yescharacteristic
188C2×D3—201no—
189C2×D3—201no—
190C2×D3—201no—
191C3×C4—101no—
192C3×C4C2×D2011yescharacteristic
193C3×C4D4×D511yescharacteristic
194Dic3—22no—
195Dic3—41no—
196Dic3—102no—
197C2×C5#88211yescharacteristic
198C2×C5C2×#20411yescharacteristic
199C2×C5#90911yescharacteristic
200D5—22no—
201D5—241no—
202C23—51no—
203C23—301no—
204Q8—32no—
205Q8—61no—
206Q8—152no—
207Q8—304no—
208Q8—301no—
209D4—301no—
210D4—301no—
211D4—602no—
212C2×C4—51no—
213C2×C4—61no—
214C2×C4—61no—
215C2×C4—101no—
216C2×C4—101no—
217C2×C4—304no—
218C2×C4—301no—
219C2×C4C2×D3×D511yescharacteristic
220C8—21no—
221C8—101no—
222C2×C3—102no—
223C2×C3#402811yescharacteristic
224C2×C3D5×SD1611yescharacteristic
225C2×C3#406411yescharacteristic
226D3—401no—
227C5#473811yescharacteristic, complemented, Sylow
228C22—52no—
229C22—101no—
230C22—101no—
231C22—601no—
232C22—601no—
233C22—601no—
234C22D5×D1211yescharacteristic
235C4—62no—
236C4—101no—
237C4—121no—
238C4—302no—
239C4D3×D2011yescharacteristic
240C4#679011yescharacteristic
241C3#6509511yescharacteristic, complemented, Sylow
242C2—102no—
243C2—1201no—
244C2D5×#20411yescharacteristic
245C2#9126111yescharacteristic
246C2#9147611yescharacteristic
subgroupG/H
centerC22D5×D12
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radical#91450C2
hypercenterC2×C8D3×D5
hypocenterC3×C5#448
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
1. C2×D5×Dic6C2semidirect
2. C2×#6706C2semidirect
4. C2×#6660C2semidirect
5. C5×#816C2semidirect
6. C3×#3952C2semidirect
7. #90975C2semidirect
30. #3952D3semidirect
39. Dic30D4semidirect
43. C5×Dic6D4semidirect
58. #816D5semidirect
81. C2×C3×D5SD16semidirect
152. Dic6D20semidirect
161. C2×D5#204semidirect
183. C3×C5#448semidirect
227. C5#4738semidirect
241. C3#65095semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic62
C2×#67062
#914502
C2×#66602
C5×#8162
C3×#39522
#909752
#650953
#47385