Finite Group Databasebeta

← #11748214

Subgroups — #11748214

Order 960.

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

normal subgroups only

This group has 216 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
2#91305C211yesmaximal, characteristic, complemented
3C2×#6653C211yesmaximal, characteristic, complemented
4#91298C211yesmaximal, characteristic, complemented
5#91107C211yesmaximal, characteristic, complemented
6C3×#3955C211yesmaximal, characteristic, complemented
7#90993C211yesmaximal, characteristic, complemented
8#65431—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C5×#235C2211yescharacteristic
11C2×C3×D20C2211yescharacteristic
12C3×C5×M16C2211yescharacteristic
13#6710C2211yescharacteristic
14C2×C5×C3⋊C8C2211yescharacteristic
15C5×ΓL(1,𝔽25)—21no—
16C5×D3×C8—21no—
17C3×#681C2211yescharacteristic
18#6660—21no—
19#6655—21no—
20#6654—21no—
21#6653—21no—
22#6653—21no—
23#6652—21no—
24#4749—51nomaximal, Hall
25C5×#131—31no—
26#4095—31no—
27#4095—31no—
28C2×D40—31no—
29#3955—31no—
30#3955D311yescharacteristic, complemented
31#3951—31no—
32C22×D15—21no—
33C22×C3×D5—21no—
34C2×C3×C4×C5C2311yescharacteristic
35D60—21no—
36D60—21no—
37C5×#67—21no—
38C5×D12D411yescharacteristic
39C4×C5×D3—21no—
40C5×Dic6D411yescharacteristic
41C3×D20—21no—
42C3×D20—21no—
43C3×C5×C8—21no—
44C3⋊#168—21no—
45C3×#168—21no—
46C5×C3⋊C8D411yescharacteristic
47C5×C3⋊C8D411yescharacteristic
48#932—51no—
49C2×#213—51no—
50#908—51no—
51#907D511yescharacteristic, complemented
52C3×#100—51no—
53#823—51no—
54#822—51no—
55C5×#41—31no—
56C2×D20—31no—
57C2×D20C2×D311yescharacteristic
58C5×M16—61no—
59C5×M16C2×D311yescharacteristic
60C2×C5×C8—31no—
61C2×C5×C8—61no—
62#688—61no—
63#688—61no—
64#686—61no—
65#686—61no—
66#681—31no—
67#681C2×D311yescharacteristic
68D40—61no—
69D40—61no—
70#472—151noSylow
71C22×C3×C5#4111yescharacteristic
72C2×D15—41no—
73C2×D15—81no—
74C2×C5×D3—21no—
75C2×C3×D5—41no—
76C2×C3×D5—81no—
77C3×C4×C5C2×D411yescharacteristic
78C3×C4×C5C2×D411yescharacteristic
79C5×Dic3—21no—
80C2×C3×D4—51no—
81#235C2×D511yescharacteristic
82C2×D12—51no—
83C3×M16—51no—
84C3×M16C2×D511yescharacteristic
85#214—101no—
86#213—101no—
87#213—101no—
88#213—101no—
89#208—51no—
90C2×C3⋊C8C2×D511yescharacteristic
91D24—101no—
92#204—101no—
93ΓL(1,𝔽25)—21no—
94D3×C8—21no—
95C22×D5—21no—
96C22×D5—61no—
97C5×Q8—31no—
98C5×D4—31no—
99C5×D4—61no—
100C2×C4×C5—61no—
101C2×C4×C5C22×D311yescharacteristic
102D20—21no—
103D20—21no—
104D20—61no—
105D20—61no—
106C5×C8—21no—
107C5×C8—31no—
108C5×C8—31no—
109#168—21no—
110#168—61no—
111AGL(1,ℤ/8)—151no—
112AGL(1,ℤ/8)—151no—
113C2×D8—151no—
114#131—31no—
115#108—151no—
116#100—51no—
117#100—151no—
118C2×C3×C5—21no—
119C2×C3×C5#12111yescharacteristic
120D15—81no—
121C3×D5—81no—
122C5×D3—41no—
123C23×C3—101no—
124C22×D3—101no—
125C3×D4—101no—
126C3×D4—101no—
127C2×C3×C4C22×D511yescharacteristic
128#67—21no—
129D12—101no—
130D12—101no—
131D12D2011yescharacteristic
132C4×D3—21no—
133Dic6D2011yescharacteristic
134C3×C8—21no—
135C3×C8—101no—
136C3⋊C8—101no—
137C3⋊C8C22⋊D511yescharacteristic
138C3⋊C8C22⋊D511yescharacteristic
139C22×C5—61no—
140C22×C5#23511yescharacteristic
141C2×D5—41no—
142C2×D5—81no—
143C2×D5—121no—
144C2×D5—241no—
145C4×C5—61no—
146C4×C5D3×D411yescharacteristic
147C4×C5D3×D411yescharacteristic
148#41—31no—
149C2×D4—51no—
150C2×D4—151no—
151SD16—301no—
152SD16—301no—
153D8—301no—
154D8—301no—
155D8—301no—
156D8—301no—
157M16—51no—
158M16—61no—
159M16—151no—
160M16D3×D511yescharacteristic
161C2×C8—31no—
162C2×C8—61no—
163C3×C5#47211yescharacteristic, complemented, Hall
164C22×C3—201no—
165C22×C3—401no—
166C22×C3#70911yescharacteristic
167C2×D3—21no—
168C2×D3—201no—
169C2×D3—401no—
170C3×C4C2×D2011yescharacteristic
171C3×C4C2×C22⋊D511yescharacteristic
172Dic3—21no—
173C2×C5—21no—
174C2×C5—121no—
175C2×C5#88411yescharacteristic
176D5—81no—
177D5—241no—
178C23—101no—
179C23—301no—
180Q8—31no—
181D4—31no—
182D4—61no—
183D4—101no—
184D4—101no—
185D4—301no—
186D4—301no—
187C2×C4—61no—
188C2×C4C2×D3×D511yescharacteristic
189C8—21no—
190C8—31no—
191C8—31no—
192C8—101no—
193C8—301no—
194C2×C3—21no—
195C2×C3—401no—
196C2×C3#407611yescharacteristic
197D3—41no—
198D3—401no—
199C5#474911yescharacteristic, complemented, Sylow
200C22—61no—
201C22—201no—
202C22—401no—
203C22—601no—
204C22—1201no—
205C22#677111yescharacteristic
206C4—61no—
207C4D3×D2011yescharacteristic
208C4D3×C22⋊D511yescharacteristic
209C3#6543111yescharacteristic, complemented, Sylow
210C2—21no—
211C2—121no—
212C2—401no—
213C2—1201no—
214C2#9145411yescharacteristic
subgroupG/H
centerC2#91454
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×M16C22
socleC2×C3×C5#121
hypercenterM16D3×D5
hypocenterC3×C5#472
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. #91305C2semidirect
3. C2×#6653C2semidirect
4. #91298C2semidirect
5. #91107C2semidirect
6. C3×#3955C2semidirect
7. #90993C2semidirect
30. #3955D3semidirect
51. #907D5semidirect
163. C3×C5#472semidirect
199. C5#4749semidirect
209. C3#65431semidirect

Maximal subgroups

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

subgroupindex
C5×#9072
#913052
C2×#66532
#912982
#911072
C3×#39552
#909932
#654313
#47495