Finite Group Databasebeta

← #11747907

Subgroups — #11747907

Order 960.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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×#6706C211yesmaximal, characteristic, complemented
2C2×C3×#676C211yesmaximal, characteristic, complemented
3#91450C211yesmaximal, characteristic
4#91360C211yesmaximal, characteristic, complemented
5C5×#818C211yesmaximal, characteristic, complemented
6#90975C211yesmaximal, characteristic, complemented
7#90969C211yesmaximal, characteristic, complemented
8#65175—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C2×Dic30C2211yescharacteristic
11C2×C3×C4×D5C2211yescharacteristic
12C2×#1202—21no—
13C2×C3×C5×C8C2211yescharacteristic
14#6706—22no—
15C5×C4⋊Dic3C2211yescharacteristic
16C5×C4⋊Dic3C2211yescharacteristic
17C2×C3×#168C2211yescharacteristic
18C3×#676—22no—
19Dic3⋊Dic5—21no—
20#6667—21no—
21#6665—21no—
22#5134—51nomaximal, Hall
23C2×#677—31no—
24C2×#676D311yescharacteristic, complemented
25#4043—31no—
26#4041—31no—
27C5×#107—31no—
28#3942—31no—
29#3941—31no—
30C22×D15—21no—
31C22×C3×D5D411yescharacteristic
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15—21no—
34D60—21no—
35D60—21no—
36Dic30—21no—
37Dic30—21no—
38C2×C5×Dic3—21no—
39C2×C5×Dic3—21no—
40C2×C3×Dic5D411yescharacteristic
41C3×C4×D5—21no—
42C3×C4×D5—21no—
43#1202—42no—
44C3×C5×C8D412yescomplemented
45C3×#168—21no—
46C2×C3×M16—51no—
47#930—51no—
48#924—51no—
49C2×#204—51no—
50#821—51no—
51#818D511yescharacteristic, complemented
52#816—51no—
53C2×D20—31no—
54C2×D20—61no—
55C2×C4×D5C2×D311yescharacteristic
56C2×Dic10—31no—
57C2×C5×C8C2×D311yescharacteristic
58C5×C4⋊C4—31no—
59C5×C4⋊C4—31no—
60#685—61no—
61#685—61no—
62C4⋊Dic5—61no—
63C2×#168C2×D311yescharacteristic
64#677—62no—
65#676—22no—
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×C5C2×D411yescharacteristic
75C3×C4×C5#4111yescharacteristic
76Dic15—41no—
77C3×Dic5—21no—
78C5×Dic3—41no—
79C5×Dic3—41no—
80C22×C3×C4—51no—
81C2×#67—101no—
82C2×D12—51no—
83C2×Dic6—51no—
84C3×M16—102no—
85C2×C3×C8—51no—
86C2×C3×C8C2×D511yescharacteristic
87#217—101no—
88(C2×D3)⋊C4—101no—
89C4⋊Dic3C2×D511yescharacteristic
90C4⋊Dic3C2×D511yescharacteristic
91Dic3⋊C4—101no—
92#204—102no—
93C22×D5—61no—
94C22×D5D1211yescharacteristic
95C2×C4×C5—61no—
96C2×C4×C5—61no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—61no—
99C2×Dic5D1211yescharacteristic
100D20—61no—
101D20—61no—
102D20—122no—
103C4×D5—21no—
104C4×D5—21no—
105Dic10—61no—
106Dic10—61no—
107C5×C8#6712yescomplemented
108#168—21no—
109C2×SD16—151no—
110C2×M16—51no—
111C22⋊Q8—151no—
112#121—151no—
113#107—31no—
114#103—151no—
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—
123C2×C3×C4—51no—
124C2×C3×C4—101no—
125C2×C3×C4—101no—
126C2×C3×C4C22×D511yescharacteristic
127#67—202no—
128C2×Dic3—21no—
129C2×Dic3—21no—
130C2×Dic3—101no—
131D12—101no—
132D12—101no—
133Dic6—101no—
134Dic6—101no—
135C3×C8—101no—
136C3×C8D2012yescomplemented
137C22×C5C2×D1211yescharacteristic
138C2×D5—21no—
139C2×D5—21no—
140C2×D5—21no—
141C2×D5—121no—
142C2×D5—121no—
143C2×D5—121no—
144C4×C5—121no—
145C4×C5—121no—
146C4×C5#23511yescharacteristic
147C4×C5C2×#6711yescharacteristic
148Dic5—21no—
149Dic5—121no—
150C2×Q8—151no—
151C2×D4—151no—
152C2×D4—301no—
153C22×C4—51no—
154SD16—302no—
155M16—102no—
156C2×C8—51no—
157C2×C8D3×D511yescharacteristic
158C4⋊C4—31no—
159C4⋊C4—31no—
160C4⋊C4—301no—
161C22⋊C4—301no—
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—101no—
172C3×C4C2×D2011yescharacteristic
173C3×C4#71311yescharacteristic
174Dic3—41no—
175Dic3—41no—
176Dic3—201no—
177C2×C5#90811yescharacteristic
178C2×C5#90911yescharacteristic
179C2×C5#93011yescharacteristic
180D5—41no—
181D5—241no—
182C23—51no—
183C23—301no—
184Q8—301no—
185Q8—301no—
186D4—301no—
187D4—301no—
188D4—602no—
189C2×C4—51no—
190C2×C4—61no—
191C2×C4—61no—
192C2×C4—101no—
193C2×C4—101no—
194C2×C4—301no—
195C2×C4C2×D3×D511yescharacteristic
196C8—101no—
197C8#120212yescomplemented
198C2×C3—201no—
199C2×C3#404111yescharacteristic
200C2×C3#405711yescharacteristic
201C2×C3#406411yescharacteristic
202D3—401no—
203C5#513411yescharacteristic, complemented, Sylow
204C22—101no—
205C22—101no—
206C22—101no—
207C22—601no—
208C22—601no—
209C22—601no—
210C22D5×D1211yescharacteristic
211C4—101no—
212C4—121no—
213C4—121no—
214C4—601no—
215C4#677311yescharacteristic
216C4C2×#120211yescharacteristic
217C3#6517511yescharacteristic, complemented, Sylow
218C2—201no—
219C2—1201no—
220C2#9125011yescharacteristic
221C2#9126111yescharacteristic
222C2#9145011yescharacteristic
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#468
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×#6706C2semidirect
2. C2×C3×#676C2semidirect
4. #91360C2semidirect
5. C5×#818C2semidirect
6. #90975C2semidirect
7. #90969C2semidirect
24. C2×#676D3semidirect
44. C3×C5×C8D4semidirect
51. #818D5semidirect
107. C5×C8#67semidirect
136. C3×C8D20semidirect
163. C3×C5#468semidirect
197. C8#1202semidirect
203. C5#5134semidirect
217. C3#65175semidirect

Maximal subgroups

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

subgroupindex
C2×#67062
C2×C3×#6762
#914502
#913602
C5×#8182
#909752
#909692
#651753
#51345