Finite Group Databasebeta

← #11749273

Subgroups — #11749273

Order 960.

240 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 62 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×#6717C211yesmaximal, characteristic, complemented
2C3×#4092C211yesmaximal, characteristic, complemented
3#91450C211yesmaximal, characteristic
4C2×#6649C211yesmaximal, characteristic, complemented
5C5×#835C211yesmaximal, characteristic, complemented
6#90989C211yesmaximal, characteristic, complemented
7#90968C211yesmaximal, characteristic, complemented
8#65101—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×D60C2211yescharacteristic
11C2×C3×C4×D5C2211yescharacteristic
12C2×#1202—21no—
13#6717—22no—
14C2×C3⋊#168C2211yescharacteristic
15C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#685—21no—
18C3×C4⋊Dic5C2211yescharacteristic
19C3×#683—21no—
20#6667—21no—
21#6649—22no—
22#5049—51nomaximal, Hall
23#4092D311yescharacteristic, complemented
24C2×#688—31no—
25C2×#676—31no—
26#4041—31no—
27C5×#103—31no—
28#3953—31no—
29#3939—31no—
30C22×D15—21no—
31C22×C3×D5D411yescharacteristic
32C3×C5×Q8—21no—
33C3×C5×Q8—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36D60—21no—
37D60—21no—
38C2×C5×Dic3—21no—
39C2×C3×Dic5—21no—
40C2×C3×Dic5D411yescharacteristic
41C3×C4×D5—21no—
42C3×C4×D5—21no—
43#1202—42no—
44C3⋊#168D412yescomplemented
45C5×C3⋊C8—21no—
46C3×C22⋊Q8—51no—
47C2×#215—51no—
48#930—51no—
49C2×#208—51no—
50#835D511yescharacteristic, complemented
51#809—51no—
52#807—51no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×D20—31no—
55C2×D20—61no—
56C2×C4×D5C2×D311yescharacteristic
57C2×C5×C8—31no—
58C5×C4⋊C4—31no—
59#688—62no—
60#685—21no—
61#685—61no—
62C4⋊Dic5C2×D311yescharacteristic
63#683—21no—
64C2×#168—31no—
65#676—62no—
66#468—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×D15—41no—
69C2×D15—41no—
70C2×D15—41no—
71C2×C3×D5—21no—
72C2×C3×D5—21no—
73C2×C3×D5—21no—
74C3×C4×C5—41no—
75C3×C4×C5C2×D411yescharacteristic
76C3×C4×C5#4111yescharacteristic
77C3×Dic5—21no—
78C3×Dic5—41no—
79C5×Dic3—41no—
80C2×C3×Q8C2×D511yescharacteristic
81C22×C3×C4—51no—
82C2×#67—101no—
83C2×D12—51no—
84C3×C4⋊C4—51no—
85C3×C4⋊C4—101no—
86C3×C22⋊C4—101no—
87#215—102no—
88(C2×D3)⋊C4—101no—
89C4⋊Dic3C2×D511yescharacteristic
90#208—102no—
91C2×C3⋊C8—51no—
92C2×C3⋊C8C2×D511yescharacteristic
93C22×D5—61no—
94C22×D5#6711yescharacteristic
95C5×Q8—21no—
96C5×Q8—21no—
97C2×C4×C5—21no—
98C2×C4×C5—61no—
99C2×C4×C5C22×D311yescharacteristic
100C2×Dic5—21no—
101C2×Dic5#6711yescharacteristic
102D20—61no—
103D20—61no—
104D20—122no—
105C4×D5—21no—
106C4×D5—21no—
107C5×C8—61no—
108#168—32no—
109C2×SD16—151no—
110C2×M16—151no—
111C22⋊Q8—51no—
112#121—151no—
113#107—151no—
114#103—31no—
115#102—151no—
116C2×C3×C5#12111yescharacteristic
117C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
118C2×C3×C5#13711yescharacteristic
119D15—81no—
120C3×D5—41no—
121C23×C3—51no—
122C22×D3—101no—
123C3×Q8—21no—
124C3×Q8—21no—
125C2×C3×C4—21no—
126C2×C3×C4—51no—
127C2×C3×C4—101no—
128C2×C3×C4—101no—
129C2×C3×C4—101no—
130C2×C3×C4C22×D511yescharacteristic
131#67—202no—
132C2×Dic3—21no—
133D12—101no—
134D12—101no—
135C3⋊C8—21no—
136C3⋊C8—52no—
137C22×C5C2×#6711yescharacteristic
138C2×D5—21no—
139C2×D5—21no—
140C2×D5—21no—
141C2×D5—121no—
142C2×D5—121no—
143C2×D5—121no—
144C4×C5—41no—
145C4×C5—121no—
146C4×C5D3×D411yescharacteristic
147C4×C5#23711yescharacteristic
148Dic5—21no—
149Dic5—41no—
150C2×Q8D3×D511yescharacteristic
151C2×D4—151no—
152C2×D4—301no—
153C22×C4—51no—
154SD16—302no—
155M16—302no—
156C2×C8—31no—
157C2×C8—151no—
158C4⋊C4—31no—
159C4⋊C4—51no—
160C4⋊C4—101no—
161C22⋊C4—101no—
162C22⋊C4—301no—
163C3×C5#46811yescharacteristic, complemented, Hall
164C22×C3—101no—
165C22×C3—101no—
166C22×C3—101no—
167C22×C3D4×D511yescharacteristic
168C2×D3—201no—
169C2×D3—201no—
170C2×D3—201no—
171C3×C4—41no—
172C3×C4—101no—
173C3×C4—201no—
174C3×C4#70911yescharacteristic
175C3×C4D4×D511yescharacteristic
176Dic3—41no—
177C2×C5#93911yescharacteristic
178C2×C5#94211yescharacteristic
179C2×C5#94911yescharacteristic
180D5—41no—
181D5—241no—
182C23—51no—
183C23—301no—
184Q8—21no—
185Q8—21no—
186D4—301no—
187D4—301no—
188D4—602no—
189C2×C4—21no—
190C2×C4—51no—
191C2×C4—61no—
192C2×C4—101no—
193C2×C4—101no—
194C2×C4—101no—
195C2×C4C2×D3×D511yescharacteristic
196C8—61no—
197C8—152no—
198C2×C3—201no—
199C2×C3#403011yescharacteristic
200C2×C3#406011yescharacteristic
201C2×C3#406411yescharacteristic
202D3—401no—
203C5#504911yescharacteristic, complemented, Sylow
204C22—101no—
205C22—101no—
206C22—101no—
207C22—601no—
208C22—601no—
209C22—601no—
210C22D5×#6711yescharacteristic
211C4—41no—
212C4—101no—
213C4—121no—
214C4—201no—
215C4#677911yescharacteristic
216C4#679011yescharacteristic
217C3#6510111yescharacteristic, complemented, Sylow
218C2—201no—
219C2—1201no—
220C2#9150211yescharacteristic
221C2#9151511yescharacteristic
222C2#9155011yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radical#91450C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#468
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
1. C2×#6717C2semidirect
2. C3×#4092C2semidirect
4. C2×#6649C2semidirect
5. C5×#835C2semidirect
6. #90989C2semidirect
7. #90968C2semidirect
23. #4092D3semidirect
44. C3⋊#168D4semidirect
50. #835D5semidirect
163. C3×C5#468semidirect
203. C5#5049semidirect
217. C3#65101semidirect

Maximal subgroups

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

subgroupindex
C2×#67172
C3×#40922
#914502
C2×#66492
C5×#8352
#909892
#909682
#651013
#50495