Finite Group Databasebeta

← #11750986

Subgroups — #11750986

Order 960.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#91784C211yesmaximal, characteristic
2#91781C211yesmaximal, characteristic, complemented
3C3×C5×#107C211yesmaximal, characteristic, complemented
4#91105C211yesmaximal, characteristic, complemented
5#91104C211yesmaximal, characteristic, complemented
6#91093C211yesmaximal, characteristic, complemented
7#91092C211yesmaximal, characteristic, complemented
8#65174—31nomaximal, Hall
9C2×D60—21no—
10C2×D60C2211yescharacteristic
11C2×C4×D15C2211yescharacteristic
12C2×C3×C5×C8C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14C3×C5×C4⋊C4C2211yescharacteristic
15#6714—21no—
16#6714—21no—
17C4⋊Dic15C2211yescharacteristic
18C4×Dic15—21no—
19C2×C3⋊#168C2211yescharacteristic
20#4885—51nomaximal, Hall
21#4041—31no—
22#4038—31no—
23C5×#107D311yescharacteristic, complemented
24#3953—31no—
25#3952—31no—
26#3941—31no—
27#3940—31no—
28C22×D15—21no—
29C22×D15D411yescharacteristic
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15—21no—
34C2×Dic15D411yescharacteristic
35D60—21no—
36D60—21no—
37D60—42no—
38C4×D15—21no—
39C4×D15—21no—
40C3×C5×C8—21no—
41C3⋊#168—21no—
42#895—51no—
43#892—51no—
44C3×#107D511yescharacteristic, complemented
45#821—51no—
46(C2×D3)⋊C8—51no—
47#809—51no—
48#808—51no—
49C2×D20—31no—
50C2×D20—61no—
51C2×C4×D5—31no—
52C2×C5×C8C2×D311yescharacteristic
53C5×C4⋊C4C2×D311yescharacteristic
54C5×C4⋊C4C2×D311yescharacteristic
55#685—61no—
56#685—61no—
57C4⋊Dic5—31no—
58C4×Dic5—61no—
59C2×#168—31no—
60#482—151noSylow
61C22×C3×C5C2×D411yescharacteristic
62C2×D15—21no—
63C2×D15—21no—
64C2×D15—21no—
65C2×D15—41no—
66C2×D15—41no—
67C2×D15—41no—
68C3×C4×C5—41no—
69C3×C4×C5—41no—
70C3×C4×C5#4111yescharacteristic
71C3×C4×C5#4111yescharacteristic
72Dic15—21no—
73Dic15—41no—
74C2×D12—51no—
75C2×D12—101no—
76C2×C4×D3—51no—
77C2×C3×C8C2×D511yescharacteristic
78C3×C4⋊C4C2×D511yescharacteristic
79C3×C4⋊C4C2×D511yescharacteristic
80(C2×D3)⋊C4—101no—
81(C2×D3)⋊C4—101no—
82C4⋊Dic3—51no—
83C4×Dic3—101no—
84C2×C3⋊C8—51no—
85C22×D5—31no—
86C22×D5—61no—
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5C22×D311yescharacteristic
90C2×Dic5—31no—
91C2×Dic5—61no—
92D20—61no—
93D20—61no—
94D20—122no—
95C4×D5—61no—
96C4×D5—61no—
97C5×C8—21no—
98#168—61no—
99#121—151no—
100#117—151no—
101#107D1511yescharacteristic, complemented
102#106—151no—
103#102—151no—
104#102—151no—
105C22⋊C8—151no—
106C2×C3×C5#12311yescharacteristic
107C2×C3×C5#13511yescharacteristic
108C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
109D15—41no—
110D15—81no—
111C22×D3—51no—
112C22×D3—101no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4C22×D511yescharacteristic
116C2×Dic3—51no—
117C2×Dic3—101no—
118D12—101no—
119D12—101no—
120D12—202no—
121C4×D3—101no—
122C4×D3—101no—
123C3×C8—21no—
124C3⋊C8—101no—
125C22×C5D3×D411yescharacteristic
126C2×D5—61no—
127C2×D5—61no—
128C2×D5—61no—
129C2×D5—121no—
130C2×D5—121no—
131C2×D5—121no—
132C4×C5—41no—
133C4×C5—41no—
134C4×C5#23511yescharacteristic
135C4×C5#23911yescharacteristic
136Dic5—61no—
137Dic5—121no—
138C2×D4—151no—
139C2×D4—301no—
140C22×C4—151no—
141C2×C8—151no—
142C2×C8C2×D1511yescharacteristic
143C4⋊C4—151no—
144C4⋊C4C2×D1511yescharacteristic
145C4⋊C4C2×D1511yescharacteristic
146C22⋊C4—301no—
147C22⋊C4—301no—
148C42—301no—
149C3×C5#48211yescharacteristic, complemented, Hall
150C22×C3D4×D511yescharacteristic
151C2×D3—101no—
152C2×D3—101no—
153C2×D3—101no—
154C2×D3—201no—
155C2×D3—201no—
156C2×D3—201no—
157C3×C4—41no—
158C3×C4—41no—
159C3×C4#70911yescharacteristic
160C3×C4#71311yescharacteristic
161Dic3—101no—
162Dic3—201no—
163C2×C5#89411yescharacteristic
164C2×C5#91111yescharacteristic
165C2×C5#91911yescharacteristic
166D5—121no—
167D5—241no—
168C23—151no—
169C23—301no—
170D4—301no—
171D4—301no—
172D4—602no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—151no—
176C2×C4—301no—
177C2×C4—301no—
178C2×C4—301no—
179C2×C4C22×D1511yescharacteristic
180C8—21no—
181C8—301no—
182C2×C3#404011yescharacteristic
183C2×C3#405711yescharacteristic
184C2×C3#406511yescharacteristic
185D3—201no—
186D3—401no—
187C5#488511yescharacteristic, complemented, Sylow
188C22—301no—
189C22—301no—
190C22—301no—
191C22—601no—
192C22—601no—
193C22—601no—
194C22D4×D1511yescharacteristic
195C4—41no—
196C4—41no—
197C4—301no—
198C4—601no—
199C4#681711yescharacteristic
200C4#682111yescharacteristic
201C3#6517411yescharacteristic, complemented, Sylow
202C2—601no—
203C2—1201no—
204C2#9178311yescharacteristic
205C2#9180011yescharacteristic
206C2#9180811yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#107C2
socleC22×C3×C5C2×D4
prime radical#91784C2
hypercenter#107D15
hypocenterC3×C5#482
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. #91781C2semidirect
3. C3×C5×#107C2semidirect
4. #91105C2semidirect
5. #91104C2semidirect
6. #91093C2semidirect
7. #91092C2semidirect
23. C5×#107D3semidirect
44. C3×#107D5semidirect
101. #107D15semidirect
149. C3×C5#482semidirect
187. C5#4885semidirect
201. C3#65174semidirect

Maximal subgroups

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

subgroupindex
#917842
#917812
C3×C5×#1072
#911052
#911042
#910932
#910922
#651743
#48855