Finite Group Databasebeta

← #11750991

Subgroups — #11750991

Order 960.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#91782C211yesmaximal, characteristic
2#91777C211yesmaximal, characteristic, complemented
3C3×C5×#107C211yesmaximal, characteristic, complemented
4#91105C211yesmaximal, characteristic
5#91098C211yesmaximal, characteristic, complemented
6#91093C211yesmaximal, characteristic
7#91091C211yesmaximal, characteristic, complemented
8#65179—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C2×C4×D15—21no—
11C2×Dic30—21no—
12C2×C3×C5×C8C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14C3×C5×C4⋊C4C2211yescharacteristic
15#6714—21no—
16C4⋊Dic15C2211yescharacteristic
17#6712—21no—
18C4×Dic15C2211yescharacteristic
19C2×C3⋊#168C2211yescharacteristic
20#4890—51nomaximal, Hall
21#4039—31no—
22#4034—31no—
23C5×#107D311yescharacteristic, complemented
24#3953—31no—
25#3946—31no—
26#3941—31no—
27#3939—31no—
28C22×D15—21no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C2×Dic15D411yescharacteristic
34C2×Dic15D411yescharacteristic
35D60—21no—
36D60Q812yescomplemented
37C4×D15—42no—
38Dic30—42no—
39C3×C5×C8—21no—
40C3⋊#168—21no—
41#893—51no—
42#888—51no—
43C3×#107D511yescharacteristic, complemented
44#821—51no—
45Dic3⋊C8—51no—
46#809—51no—
47#807—51no—
48C2×D20—31no—
49C2×C4×D5—61no—
50C2×Dic10—61no—
51C2×C5×C8C2×D311yescharacteristic
52C5×C4⋊C4C2×D311yescharacteristic
53C5×C4⋊C4C2×D311yescharacteristic
54#685—61no—
55C4⋊Dic5—31no—
56#683—61no—
57C4×Dic5—31no—
58C2×#168—31no—
59#474—151noSylow
60C22×C3×C5C2×D411yescharacteristic
61C2×D15—22no—
62C2×D15—41no—
63C2×D15—41no—
64C3×C4×C5—41no—
65C3×C4×C5—41no—
66C3×C4×C5C2×Q811yescharacteristic
67C3×C4×C5#4111yescharacteristic
68Dic15—21no—
69Dic15—41no—
70Dic15D812yes—
71C2×D12—51no—
72C2×C4×D3—101no—
73C2×Dic6—101no—
74C2×C3×C8C2×D511yescharacteristic
75C3×C4⋊C4C2×D511yescharacteristic
76C3×C4⋊C4C2×D511yescharacteristic
77(C2×D3)⋊C4—101no—
78C4⋊Dic3—51no—
79Dic3⋊C4—101no—
80C4×Dic3—51no—
81C2×C3⋊C8—51no—
82C22×D5—61no—
83C2×C4×C5—21no—
84C2×C4×C5—21no—
85C2×C4×C5C22×D311yescharacteristic
86C2×Dic5—31no—
87C2×Dic5—31no—
88C2×Dic5—61no—
89D20—32no—
90D20—61no—
91C4×D5—122no—
92Dic10—122no—
93C5×C8—21no—
94#168—61no—
95C4⋊Q8—151no—
96C4×D4—151no—
97#107—151no—
98#107D1511yescharacteristic, complemented
99C4⋊C8—151no—
100#102—151no—
101#102—151no—
102C2×C3×C5C22⋊Q811yescharacteristic
103C2×C3×C5C2×D811yescharacteristic
104C2×C3×C5#13711yescharacteristic
105D15—42no—
106C22×D3—101no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4C22×D511yescharacteristic
110C2×Dic3—51no—
111C2×Dic3—51no—
112C2×Dic3—101no—
113D12—52no—
114D12—101no—
115C4×D3—202no—
116Dic6—202no—
117C3×C8—21no—
118C3⋊C8—101no—
119C22×C5D3×D411yescharacteristic
120C2×D5—62no—
121C2×D5—121no—
122C2×D5—121no—
123C4×C5—41no—
124C4×C5—41no—
125C4×C5#23511yescharacteristic
126C4×C5D3×Q811yescharacteristic
127Dic5—32no—
128Dic5—61no—
129Dic5—121no—
130C2×Q8—301no—
131C2×D4—151no—
132C22×C4—301no—
133C2×C8—151no—
134C2×C8C2×D1511yescharacteristic
135C4⋊C4—151no—
136C4⋊C4—301no—
137C4⋊C4C2×D1511yescharacteristic
138C4⋊C4C2×D1511yescharacteristic
139C22⋊C4—301no—
140C42—151no—
141C3×C5#47411yescharacteristic, complemented, Hall
142C22×C3D4×D511yescharacteristic
143C2×D3—102no—
144C2×D3—201no—
145C2×D3—201no—
146C3×C4—41no—
147C3×C4—41no—
148C3×C4#70911yescharacteristic
149C3×C4Q8×D511yescharacteristic
150Dic3—52no—
151Dic3—101no—
152Dic3—201no—
153C2×C5#89611yescharacteristic
154C2×C5D3×D811yescharacteristic
155C2×C5#91811yescharacteristic
156D5—122no—
157C23—301no—
158Q8—602no—
159D4—152no—
160D4—301no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—151no—
164C2×C4—151no—
165C2×C4—301no—
166C2×C4—602no—
167C2×C4C22×D1511yescharacteristic
168C8—21no—
169C8—301no—
170C2×C3#404211yescharacteristic
171C2×C3D5×D811yescharacteristic
172C2×C3#406411yescharacteristic
173D3—202no—
174C5#489011yescharacteristic, complemented, Sylow
175C22—302no—
176C22—601no—
177C22—601no—
178C22D4×D1511yescharacteristic
179C4—41no—
180C4—41no—
181C4—152no—
182C4—301no—
183C4—601no—
184C4#681711yescharacteristic
185C4Q8×D1511yescharacteristic
186C3#6517911yescharacteristic, complemented, Sylow
187C2—602no—
188C2#9178511yescharacteristic
189C2D8×D1511yescharacteristic
190C2#9180711yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#107C2
socleC22×C3×C5C2×D4
prime radicalC2×D60C22
hypercenter#107D15
hypocenterC3×C5#474
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #91777C2semidirect
3. C3×C5×#107C2semidirect
5. #91098C2semidirect
7. #91091C2semidirect
23. C5×#107D3semidirect
36. D60Q8semidirect
43. C3×#107D5semidirect
98. #107D15semidirect
141. C3×C5#474semidirect
174. C5#4890semidirect
186. C3#65179semidirect

Maximal subgroups

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

subgroupindex
#917822
#917772
C3×C5×#1072
#911052
#910982
#910932
#910912
#651793
#48905