Finite Group Databasebeta

← #11747239

Subgroups — #11747239

Order 960.

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

normal subgroups only

This group has 216 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
1C3×#4034C211yesmaximal, characteristic, complemented
2Dic5×D12C211yesmaximal, characteristic
3#91092C211yesmaximal, characteristic, complemented
4C5×#809C211yesmaximal, characteristic
5#90987C211yesmaximal, characteristic, complemented
6#90982C211yesmaximal, characteristic, complemented
7#90966C211yesmaximal, characteristic
8#65050—31nomaximal, Hall
9C2×C5×D12C2211yescharacteristic
10C2×C3×Dic10—21no—
11C2×D3×Dic5—21no—
12C3×C5×C4⋊C4C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×C4⋊Dic5C2211yescharacteristic
17C3×#683—21no—
18C3×C4×Dic5C2211yescharacteristic
19(C2×D3)⋊Dic5—21no—
20#5084—51nomaximal, Hall
21D4×Dic5—31no—
22#4034D311yescharacteristic, complemented
23C5×#102—31no—
24#3964—31no—
25#3949—31no—
26#3946—31no—
27#3940—31no—
28C22×C5×D3—21no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5C2311yescharacteristic
31C2×Dic15—21no—
32C5×D12—21no—
33C5×D12Q812yescomplemented
34C2×C3×Dic5—21no—
35C2×C3×Dic5D411yescharacteristic
36C2×C3×Dic5D411yescharacteristic
37C3×Dic10—42no—
38D3×Dic5—42no—
39C3⋊#168—21no—
40C5×C3⋊C8—21no—
41C3×C4⋊Q8—51no—
42C4×D12—51no—
43#809—51no—
44#809D511yescharacteristic
45#808—51no—
46#808—51no—
47C4⋊(C3⋊C8)—51no—
48C2×C5×D4—31no—
49C22×Dic5—61no—
50C2×Dic10—21no—
51C2×C5×C8—31no—
52C5×C4⋊C4C2×D311yescharacteristic
53C22⋊Dic5—61no—
54C4⋊Dic5—31no—
55C4⋊Dic5C2×D311yescharacteristic
56#683—21no—
57C4×Dic5C2×D311yescharacteristic
58C2×#168—31no—
59#476—151noSylow
60C22×C3×C5C2×D411yescharacteristic
61C2×C5×D3—22no—
62C2×C5×D3—41no—
63C2×C5×D3—41no—
64C3×C4×C5—41no—
65C3×C4×C5C2×Q811yescharacteristic
66C3×C4×C5#4111yescharacteristic
67Dic15—41no—
68C3×Dic5—21no—
69C3×Dic5—41no—
70C3×Dic5SD1612yes—
71C2×C3×Q8—101no—
72C2×D12C2×D511yescharacteristic
73C2×C4×D3—101no—
74C3×C4⋊C4—51no—
75C3×C4⋊C4—101no—
76C3×C4⋊C4C2×D511yescharacteristic
77C3×C42—51no—
78(C2×D3)⋊C4—101no—
79C4⋊Dic3—51no—
80C2×C3⋊C8—51no—
81C2×C3⋊C8C2×D511yescharacteristic
82C23×C5—61no—
83C5×D4—32no—
84C5×D4—61no—
85C2×C4×C5—21no—
86C2×C4×C5C22×D311yescharacteristic
87C2×Dic5—21no—
88C2×Dic5—61no—
89C2×Dic5—122no—
90C2×Dic5#6711yescharacteristic
91C2×Dic5#6711yescharacteristic
92Dic10—42no—
93C5×C8—61no—
94#168—61no—
95C4⋊Q8—51no—
96C4×D4—151no—
97#106—151no—
98#106—151no—
99C4⋊C8—151no—
100#102—31no—
101#102—151no—
102C2×C3×C5C22⋊Q811yescharacteristic
103C2×C3×C5C2×SD1611yescharacteristic
104C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
105C5×D3—42no—
106C22×D3—21no—
107C3×Q8—202no—
108C2×C3×C4—21no—
109C2×C3×C4—51no—
110C2×C3×C4—51no—
111C2×C3×C4—101no—
112C2×C3×C4C22×D511yescharacteristic
113C2×Dic3—101no—
114D12—21no—
115D12Dic1012yescomplemented
116C4×D3—202no—
117C3⋊C8—21no—
118C3⋊C8—101no—
119C22×C5—62no—
120C22×C5—121no—
121C22×C5—121no—
122C22×C5C2×#6711yescharacteristic
123C4×C5—41no—
124C4×C5D3×Q811yescharacteristic
125C4×C5#23911yescharacteristic
126Dic5—21no—
127Dic5—41no—
128Dic5—121no—
129Dic5#21512yes—
130C2×Q8—101no—
131C2×D4—31no—
132C22×C4—301no—
133C2×C8—31no—
134C2×C8—151no—
135C4⋊C4—51no—
136C4⋊C4—101no—
137C4⋊C4—151no—
138C4⋊C4D3×D511yescharacteristic
139C22⋊C4—301no—
140C42—51no—
141C3×C5#47611yescharacteristic, complemented, Hall
142C22×C3D4×D511yescharacteristic
143C2×D3—22no—
144C2×D3—41no—
145C2×D3—41no—
146C3×C4—41no—
147C3×C4—52no—
148C3×C4—101no—
149C3×C4—201no—
150C3×C4C2×Dic1011yescharacteristic
151C3×C4#71111yescharacteristic
152Dic3—201no—
153C2×C5—122no—
154C2×C5#93211yescharacteristic
155C2×C5C2×#21511yescharacteristic
156C2×C5#94611yescharacteristic
157C23—61no—
158Q8—202no—
159D4—32no—
160D4—61no—
161C2×C4—21no—
162C2×C4—51no—
163C2×C4—51no—
164C2×C4—101no—
165C2×C4—301no—
166C2×C4—602no—
167C2×C4C2×D3×D511yescharacteristic
168C8—61no—
169C8—301no—
170C2×C3#402411yescharacteristic
171C2×C3#405711yescharacteristic
172C2×C3D5×SD1611yescharacteristic
173D3—42no—
174C5#508411yescharacteristic, complemented, Sylow
175C22—62no—
176C22—121no—
177C22—121no—
178C22D5×#6711yescharacteristic
179C4—41no—
180C4—52no—
181C4—101no—
182C4—201no—
183C4—601no—
184C4D3×Dic1011yescharacteristic
185C4#676811yescharacteristic
186C3#6505011yescharacteristic, complemented, Sylow
187C2—122no—
188C2#9141011yescharacteristic
189C2#9148911yescharacteristic
190C2D5×#21511yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC2×C5×D12C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#476
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#4034C2semidirect
3. #91092C2semidirect
5. #90987C2semidirect
6. #90982C2semidirect
22. #4034D3semidirect
33. C5×D12Q8semidirect
115. D12Dic10semidirect
141. C3×C5#476semidirect
174. C5#5084semidirect
186. C3#65050semidirect

Maximal subgroups

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

subgroupindex
C3×#40342
Dic5×D122
#910922
C5×#8092
#909872
#909822
#909662
#650503
#50845