Finite Group Databasebeta

← #11749134

Subgroups — #11749134

Order 960.

208 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 54 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#91821C211yesmaximal, characteristic
2C2×C5×#214C211yesmaximal, characteristic, complemented
3#91321C211yesmaximal, characteristic, complemented
4#91291C211yesmaximal, characteristic, complemented
5C3×#3965C211yesmaximal, characteristic, complemented
6#90993C211yesmaximal, characteristic, complemented
7#90962C211yesmaximal, characteristic, complemented
8#65466—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10#6817C2211yescharacteristic
11C2×C5×Dic6C2211yescharacteristic
12#6716—21no—
13#6715—21no—
14#6710C2211yescharacteristic
15C5×#214—21no—
16C5×#214—21no—
17C2×C5×C3⋊C8C2211yescharacteristic
18C3×#681C2211yescharacteristic
19C3×#681C2211yescharacteristic
20#6663—21no—
21#6660—21no—
22#6651—21no—
23#6648—21no—
24#4748—51nomaximal, Hall
25C2×C5×SD16—31no—
26#4088—31no—
27#4078—31no—
28#4047—31no—
29#3968—31no—
30#3965D311yescharacteristic, complemented
31#3951—31no—
32C23×C3×C5—21no—
33C3×C5×D4—21no—
34C3×C5×D4—21no—
35C2×C3×C4×C5C2311yescharacteristic
36#1220—21no—
37D60D411yescharacteristic
38C4×D15—21no—
39Dic30D411yescharacteristic
40C2×C5×Dic3—21no—
41C5×Dic6—21no—
42C5×Dic6—21no—
43C3⋊#168—21no—
44C3×#168—21no—
45C3×#168—21no—
46C5×C3⋊C8D411yescharacteristic
47C5×C3⋊C8D411yescharacteristic
48C2×#214D511yescharacteristic, complemented
49#932—51no—
50#909—51no—
51#907—51no—
52C3×#100—51no—
53#824—51no—
54#822—51no—
55C2×C5×Q8—31no—
56C2×C5×D4C2×D311yescharacteristic
57#709—31no—
58C5×SD16—61no—
59C5×SD16—61no—
60C2×C5×C8—31no—
61#689—61no—
62#688—61no—
63#687—61no—
64#686—61no—
65#681—31no—
66#681C2×D311yescharacteristic
67#681C2×D311yescharacteristic
68#676—61no—
69C8×D5—61no—
70#471—151noSylow
71C22×C3×C5—41no—
72C22×C3×C5—81no—
73C22×C3×C5#4111yescharacteristic
74C2×D15—21no—
75C3×C4×C5C2×D411yescharacteristic
76C3×C4×C5C2×D411yescharacteristic
77Dic15—21no—
78C5×Dic3—41no—
79C2×C3×D4C2×D511yescharacteristic
80#235—51no—
81C2×Dic6C2×D511yescharacteristic
82C3×M16—51no—
83C3×M16—51no—
84#214—21no—
85#214—21no—
86#214—101no—
87#213—101no—
88#208—51no—
89C2×C3⋊C8C2×D511yescharacteristic
90Dic12—101no—
91#204—101no—
92ΓL(1,𝔽25)—101no—
93D3×C8—101no—
94C23×C5—21no—
95C5×Q8—61no—
96C5×Q8—61no—
97C5×D4—21no—
98C5×D4—21no—
99C2×C4×C5—61no—
100C2×C4×C5C22×D311yescharacteristic
101C22⋊D5—61no—
102D20—31no—
103C4×D5—61no—
104Dic10—31no—
105C5×C8—31no—
106C5×C8—31no—
107#168—21no—
108#168—21no—
109#168—61no—
110#137—151no—
111AGL(1,ℤ/8)—151no—
112C2×SD16—31no—
113#131—151no—
114#108—151no—
115#101—151no—
116#100—51no—
117C2×C3×C5—21no—
118C2×C3×C5—81no—
119C2×C3×C5#12111yescharacteristic
120D15—41no—
121C23×C3—21no—
122C3×D4—21no—
123C3×D4—21no—
124C2×C3×C4C22×D511yescharacteristic
125#67—101no—
126C2×Dic3—21no—
127D12—51no—
128C4×D3—101no—
129Dic6—21no—
130Dic6—21no—
131Dic6—51no—
132C3×C8—101no—
133C3×C8—101no—
134C3⋊C8—101no—
135C3⋊C8C22⋊D511yescharacteristic
136C3⋊C8C22⋊D511yescharacteristic
137C22×C5—41no—
138C22×C5—81no—
139C22×C5#23511yescharacteristic
140C2×D5—61no—
141C4×C5—121no—
142C4×C5D3×D411yescharacteristic
143C4×C5D3×D411yescharacteristic
144Dic5—61no—
145#41—151no—
146C2×Q8—31no—
147C2×D4D3×D511yescharacteristic
148Q16—301no—
149SD16—61no—
150SD16—61no—
151SD16—301no—
152SD16—301no—
153D8—301no—
154M16—51no—
155M16—51no—
156M16—151no—
157M16—301no—
158C2×C8—31no—
159C2×C8—301no—
160C3×C5#47111yescharacteristic, complemented, Hall
161C22×C3—41no—
162C22×C3—81no—
163C22×C3#71111yescharacteristic
164C2×D3—101no—
165C3×C4D4×D511yescharacteristic
166C3×C4C2×C22⋊D511yescharacteristic
167Dic3—41no—
168Dic3—101no—
169C2×C5—21no—
170C2×C5—81no—
171C2×C5#88411yescharacteristic
172D5—121no—
173C23—21no—
174Q8—61no—
175Q8—61no—
176Q8—151no—
177D4—21no—
178D4—21no—
179D4—151no—
180D4—301no—
181C2×C4—61no—
182C2×C4—301no—
183C2×C4C2×D3×D511yescharacteristic
184C8—31no—
185C8—31no—
186C8—101no—
187C8—101no—
188C8—301no—
189C2×C3—21no—
190C2×C3—81no—
191C2×C3#408411yescharacteristic
192D3—201no—
193C5#474811yescharacteristic, complemented, Sylow
194C22—41no—
195C22—81no—
196C22—301no—
197C22#678211yescharacteristic
198C4—121no—
199C4—301no—
200C4D3×C22⋊D511yescharacteristic
201C4#679011yescharacteristic
202C3#6546611yescharacteristic, complemented, Sylow
203C2—21no—
204C2—81no—
205C2—601no—
206C2#9155711yescharacteristic
subgroupG/H
centerC2#91557
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×D4C22
socleC2×C3×C5#121
prime radical#91821C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#214C2semidirect
3. #91321C2semidirect
4. #91291C2semidirect
5. C3×#3965C2semidirect
6. #90993C2semidirect
7. #90962C2semidirect
30. #3965D3semidirect
48. C2×#214D5semidirect
160. C3×C5#471semidirect
193. C5#4748semidirect
202. C3#65466semidirect

Maximal subgroups

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

subgroupindex
#918212
C2×C5×#2142
#913212
#912912
C3×#39652
#909932
#909622
#654663
#47485