Finite Group Databasebeta

← #11748546

Subgroups — #11748546

Order 960.

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

normal subgroups only

This group has 240 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×#6710C211yesmaximal, characteristic, complemented
2C5×#924C211yesmaximal, characteristic, complemented
3C3×#4076C211yesmaximal, characteristic
4C2×#6655C211yesmaximal, characteristic, complemented
5#90989C211yesmaximal, characteristic, complemented
6#90972C211yesmaximal, characteristic, complemented
7#90964C211yesmaximal, characteristic, complemented
8#65338—31nomaximal, Hall
9C22×C3×C4×C5C2211yescharacteristic
10C2×C5×Dic6C2211yescharacteristic
11C2×C3×C22⋊D5—21no—
12C2×C3×D20C2211yescharacteristic
13#6710—22no—
14C2×C3⋊#168C2211yescharacteristic
15C2×C3⋊#168C2211yescharacteristic
16C5×#217—21no—
17C5×C4⋊Dic3C2211yescharacteristic
18C5×Dic3⋊C4—21no—
19C3×#685—21no—
20C3×C4⋊Dic5C2211yescharacteristic
21#6655—22no—
22#5042—51nomaximal, Hall
23C5×C22⋊Q8—31no—
24C2×#688—31no—
25#4076D311yescharacteristic
26C2×#681—31no—
27#3967—31no—
28#3941—31no—
29#3939—31no—
30C23×C3×C5D411yescharacteristic
31C22×C3×D5—21no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5D411yescharacteristic
35C2×C3×C4×C5C2311yescharacteristic
36C2×C5×Dic3—21no—
37C2×C5×Dic3—21no—
38C5×Dic6—21no—
39C5×Dic6—21no—
40C3×C22⋊D5—42no—
41C2×C3×Dic5—21no—
42C3×D20—21no—
43C3×D20—21no—
44C3⋊#168—21no—
45C3⋊#168D412yescomplemented
46C3×#121—51no—
47C2×#214—51no—
48#924D511yescharacteristic, complemented
49C2×#208—51no—
50#832—51no—
51#810—51no—
52#807—51no—
53C2×C5×Q8—31no—
54C22×C4×C5C2×D311yescharacteristic
55C2×C22⋊D5—21no—
56C2×D20C2×D311yescharacteristic
57C5×C4⋊C4—31no—
58C5×C4⋊C4—61no—
59C5×C22⋊C4—61no—
60#688—62no—
61#685—21no—
62C4⋊Dic5C2×D311yescharacteristic
63#681—62no—
64C2×#168—31no—
65C2×#168—31no—
66#468—151noSylow
67C22×C3×C5—21no—
68C22×C3×C5—21no—
69C22×C3×C5—21no—
70C22×C3×C5C2×D411yescharacteristic
71C2×C3×D5—41no—
72C2×C3×D5—41no—
73C2×C3×D5—41no—
74C3×C4×C5—21no—
75C3×C4×C5C2×D411yescharacteristic
76C3×C4×C5#4111yescharacteristic
77C3×Dic5—41no—
78C5×Dic3—41no—
79C5×Dic3—41no—
80C2×C3×D4—51no—
81C2×C3×D4—101no—
82C22×C3×C4C2×D511yescharacteristic
83C2×Dic6C2×D511yescharacteristic
84C3×C4⋊C4—51no—
85C3×C22⋊C4—101no—
86#217—21no—
87#214—102no—
88C4⋊Dic3C2×D511yescharacteristic
89Dic3⋊C4—21no—
90#208—102no—
91C2×C3⋊C8—51no—
92C2×C3⋊C8—51no—
93C23×C5#6711yescharacteristic
94C22×D5—21no—
95C5×Q8—61no—
96C5×Q8—61no—
97C2×C4×C5—21no—
98C2×C4×C5—21no—
99C2×C4×C5—61no—
100C2×C4×C5—61no—
101C2×C4×C5#6711yescharacteristic
102C2×C4×C5C22×D311yescharacteristic
103C22⋊D5—42no—
104C2×Dic5—21no—
105D20—21no—
106D20—21no—
107#168—32no—
108#168—61no—
109C2×SD16—151no—
110C2×M16—151no—
111C22⋊Q8—31no—
112#121—51no—
113#107—151no—
114#103—151no—
115#102—151no—
116C2×C3×C5—41no—
117C2×C3×C5#12111yescharacteristic
118C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
119C2×C3×C5#13711yescharacteristic
120C3×D5—81no—
121C23×C3—101no—
122C23×C3C22⋊D511yescharacteristic
123C3×D4—101no—
124C3×D4—101no—
125C3×D4—202no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—101no—
129C2×C3×C4C22⋊D511yescharacteristic
130C2×C3×C4C22×D511yescharacteristic
131C2×Dic3—21no—
132C2×Dic3—21no—
133Dic6—21no—
134Dic6—21no—
135C3⋊C8—52no—
136C3⋊C8—101no—
137C22×C5—21no—
138C22×C5—21no—
139C22×C5—21no—
140C22×C5C2×#6711yescharacteristic
141C2×D5—41no—
142C2×D5—41no—
143C2×D5—41no—
144C4×C5—21no—
145C4×C5—121no—
146C4×C5—121no—
147C4×C5D3×D411yescharacteristic
148C4×C5#23711yescharacteristic
149Dic5—41no—
150C2×Q8—31no—
151C2×D4—51no—
152C2×D4—101no—
153C22×C4D3×D511yescharacteristic
154SD16—302no—
155M16—302no—
156C2×C8—151no—
157C2×C8—151no—
158C4⋊C4—31no—
159C4⋊C4—51no—
160C4⋊C4—61no—
161C22⋊C4—61no—
162C22⋊C4—101no—
163C3×C5#46811yescharacteristic, complemented, Hall
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—201no—
168C22×C3—201no—
169C22×C3—201no—
170C22×C3C2×C22⋊D511yescharacteristic
171C3×C4—21no—
172C3×C4—201no—
173C3×C4D4×D511yescharacteristic
174C3×C4#71111yescharacteristic
175Dic3—41no—
176Dic3—41no—
177C2×C5—41no—
178C2×C5#93211yescharacteristic
179C2×C5#93911yescharacteristic
180C2×C5#95111yescharacteristic
181D5—81no—
182C23—101no—
183C23#120111yescharacteristic
184Q8—61no—
185Q8—61no—
186D4—101no—
187D4—101no—
188D4—202no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—61no—
192C2×C4—61no—
193C2×C4—101no—
194C2×C4#120111yescharacteristic
195C2×C4C2×D3×D511yescharacteristic
196C8—152no—
197C8—301no—
198C2×C3—41no—
199C2×C3—401no—
200C2×C3#408511yescharacteristic
201C2×C3#408811yescharacteristic
202C2×C3#409511yescharacteristic
203C5#504211yescharacteristic, complemented, Sylow
204C22—21no—
205C22—21no—
206C22—21no—
207C22—201no—
208C22—201no—
209C22—201no—
210C22C2×#120111yescharacteristic
211C4—21no—
212C4—121no—
213C4—121no—
214C4—201no—
215C4#678011yescharacteristic
216C4#679011yescharacteristic
217C3#6533811yescharacteristic, complemented, Sylow
218C2—41no—
219C2—401no—
220C2#9129811yescharacteristic
221C2#9130711yescharacteristic
222C2#9157111yescharacteristic
subgroupG/H
centerC22C2×#1201
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC22×C3×C4×C5C22
socleC22×C3×C5C2×D4
prime radicalC3×#4076C2
hypercenterC22×C4D3×D5
hypocenterC3×C5#468
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#6710C2semidirect
2. C5×#924C2semidirect
4. C2×#6655C2semidirect
5. #90989C2semidirect
6. #90972C2semidirect
7. #90964C2semidirect
45. C3⋊#168D4semidirect
48. #924D5semidirect
163. C3×C5#468semidirect
203. C5#5042semidirect
217. C3#65338semidirect

Maximal subgroups

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

subgroupindex
C2×#67102
C5×#9242
C3×#40762
C2×#66552
#909892
#909722
#909642
#653383
#50425