Finite Group Databasebeta

← #11748221

Subgroups — #11748221

Order 960.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C5×#907C211yesmaximal, characteristic, complemented
2C2×#6658C211yesmaximal, characteristic, complemented
3#91309C211yesmaximal, characteristic, complemented
4#91305C211yesmaximal, characteristic
5#91107C211yesmaximal, characteristic, complemented
6C3×#3956C211yesmaximal, characteristic, complemented
7#90993C211yesmaximal, characteristic, complemented
8#65430—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C5×#235C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C3×C5×M16C2211yescharacteristic
13#6710C2211yescharacteristic
14C2×C5×C3⋊C8C2211yescharacteristic
15C5×ΓL(1,𝔽25)—21no—
16C5×D3×C8—21no—
17C3×#681C2211yescharacteristic
18#6661—21no—
19#6660—21no—
20#6658—21no—
21#6658—21no—
22#6656—21no—
23#6654—21no—
24#4754—51nomaximal, Hall
25C5×#131—31no—
26#4097—31no—
27#4095—31no—
28C2×#677—31no—
29#3956D311yescharacteristic, complemented
30#3955—31no—
31#3951—31no—
32C22×D15—21no—
33C2×C3×C4×C5C2311yescharacteristic
34D60—21no—
35D60—21no—
36C5×#67—21no—
37C5×D12D411yescharacteristic
38C4×C5×D3—21no—
39C5×Dic6D411yescharacteristic
40C2×C3×Dic5—21no—
41C3×Dic10—21no—
42C3×Dic10—21no—
43C3×C5×C8—21no—
44C3⋊#168—21no—
45C3×#168—21no—
46C5×C3⋊C8D411yescharacteristic
47C5×C3⋊C8D411yescharacteristic
48#942—51no—
49C2×#215—51no—
50#908—51no—
51#907D511yescharacteristic, complemented
52C3×#101—51no—
53#823—51no—
54#822—51no—
55C5×#41—31no—
56C2×D20—31no—
57C2×Dic10C2×D311yescharacteristic
58C5×M16—61no—
59C5×M16C2×D311yescharacteristic
60C2×C5×C8—31no—
61C2×C5×C8—61no—
62#689—61no—
63#688—61no—
64#687—61no—
65#686—61no—
66#681—31no—
67#681C2×D311yescharacteristic
68#677—61no—
69#677—61no—
70#471—151noSylow
71C22×C3×C5#4111yescharacteristic
72C2×D15—41no—
73C2×D15—81no—
74C2×C5×D3—21no—
75C3×C4×C5C2×D411yescharacteristic
76C3×C4×C5C2×D411yescharacteristic
77C3×Dic5—41no—
78C5×Dic3—21no—
79C2×C3×Q8—51no—
80#235C2×D511yescharacteristic
81C2×D12—51no—
82C3×M16—51no—
83C3×M16C2×D511yescharacteristic
84#216—101no—
85#215—101no—
86#215—101no—
87#215—101no—
88#208—51no—
89C2×C3⋊C8C2×D511yescharacteristic
90D24—101no—
91#204—101no—
92ΓL(1,𝔽25)—21no—
93D3×C8—21no—
94C22×D5—61no—
95C5×Q8—31no—
96C5×D4—31no—
97C5×D4—61no—
98C2×C4×C5—61no—
99C2×C4×C5C22×D311yescharacteristic
100C2×Dic5—21no—
101D20—61no—
102D20—61no—
103Dic10—21no—
104Dic10—21no—
105C5×C8—21no—
106C5×C8—31no—
107C5×C8—31no—
108#168—21no—
109#168—61no—
110#137—151no—
111AGL(1,ℤ/8)—151no—
112C2×SD16—151no—
113#131—31no—
114#108—151no—
115#101—51no—
116#100—151no—
117C2×C3×C5—21no—
118C2×C3×C5#12111yescharacteristic
119D15—81no—
120C5×D3—41no—
121C22×D3—101no—
122C3×Q8—101no—
123C3×Q8—101no—
124C2×C3×C4—101no—
125C2×C3×C4C22×D511yescharacteristic
126#67—21no—
127D12—101no—
128D12—101no—
129D12D2011yescharacteristic
130C4×D3—21no—
131Dic6D2011yescharacteristic
132C3×C8—21no—
133C3×C8—101no—
134C3⋊C8—101no—
135C3⋊C8C22⋊D511yescharacteristic
136C3⋊C8C22⋊D511yescharacteristic
137C22×C5—61no—
138C22×C5#23511yescharacteristic
139C2×D5—121no—
140C2×D5—241no—
141C4×C5—61no—
142C4×C5D3×D411yescharacteristic
143C4×C5D3×D411yescharacteristic
144Dic5—41no—
145#41—31no—
146C2×Q8—51no—
147C2×D4—151no—
148Q16—301no—
149SD16—301no—
150SD16—301no—
151SD16—301no—
152SD16—301no—
153D8—301no—
154M16—51no—
155M16—61no—
156M16—151no—
157M16D3×D511yescharacteristic
158C2×C8—31no—
159C2×C8—61no—
160C3×C5#47111yescharacteristic, complemented, Hall
161C22×C3#70911yescharacteristic
162C2×D3—21no—
163C2×D3—201no—
164C2×D3—401no—
165C3×C4—201no—
166C3×C4C2×D2011yescharacteristic
167C3×C4C2×C22⋊D511yescharacteristic
168Dic3—21no—
169C2×C5—21no—
170C2×C5—121no—
171C2×C5#88411yescharacteristic
172D5—241no—
173C23—301no—
174Q8—31no—
175Q8—101no—
176Q8—101no—
177D4—31no—
178D4—61no—
179D4—301no—
180D4—301no—
181C2×C4—61no—
182C2×C4—101no—
183C2×C4C2×D3×D511yescharacteristic
184C8—21no—
185C8—31no—
186C8—31no—
187C8—101no—
188C8—301no—
189C2×C3—21no—
190C2×C3#407611yescharacteristic
191D3—41no—
192D3—401no—
193C5#475411yescharacteristic, complemented, Sylow
194C22—61no—
195C22—601no—
196C22—1201no—
197C22#677111yescharacteristic
198C4—61no—
199C4—201no—
200C4D3×D2011yescharacteristic
201C4D3×C22⋊D511yescharacteristic
202C3#6543011yescharacteristic, complemented, Sylow
203C2—21no—
204C2—121no—
205C2—1201no—
206C2#9145411yescharacteristic
subgroupG/H
centerC2#91454
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×M16C22
socleC2×C3×C5#121
prime radical#91305C2
hypercenterM16D3×D5
hypocenterC3×C5#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
1. C5×#907C2semidirect
2. C2×#6658C2semidirect
3. #91309C2semidirect
5. #91107C2semidirect
6. C3×#3956C2semidirect
7. #90993C2semidirect
29. #3956D3semidirect
51. #907D5semidirect
160. C3×C5#471semidirect
193. C5#4754semidirect
202. C3#65430semidirect

Maximal subgroups

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

subgroupindex
C5×#9072
C2×#66582
#913092
#913052
#911072
C3×#39562
#909932
#654303
#47545