Finite Group Databasebeta

← #11751110

Subgroups — #11751110

Order 960.

204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C3×C4×C5×D4C211yesmaximal, characteristic
2#91759C211yesmaximal, characteristic, complemented
3#91116C211yesmaximal, characteristic
4#91116C211yesmaximal, characteristic
5#91092C211yesmaximal, characteristic, complemented
6#91091C211yesmaximal, characteristic, complemented
7C4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#65298—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10C22×C3×C4×C5—21no—
11C3×C5×C4⋊C4C2211yescharacteristic
12C3×C5×C22⋊C4—21no—
13C3×C42×C5C2211yescharacteristic
14C4⋊Dic15C2211yescharacteristic
15C4⋊Dic15C2211yescharacteristic
16#6712—21no—
17#6712—21no—
18C2×C3⋊#168C2211yescharacteristic
19C2×C3⋊#168C2211yescharacteristic
20#5009—51nomaximal, Hall
21C4×C5×D4D311yescharacteristic
22#4016—31no—
23#3964—31no—
24#3964—31no—
25#3940—31no—
26#3939—31no—
27C4⋊#168—31no—
28C23×C3×C5—21no—
29C3×C5×D4—21no—
30C3×C5×D4Q812yes—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5—42no—
33C2×C3×C4×C5D411yescharacteristic
34C2×C3×C4×C5D411yescharacteristic
35C2×C3×C4×C5C2311yescharacteristic
36C2×Dic15—21no—
37C2×Dic15—21no—
38C3⋊#168—21no—
39C3⋊#168—21no—
40C3×C4×D4D511yescharacteristic
41#870—51no—
42#832—51no—
43#832—51no—
44#808—51no—
45#807—51no—
46C4⋊(C3⋊C8)—51no—
47C2×C5×D4C2×D311yescharacteristic
48C22×C4×C5—21no—
49C5×C4⋊C4C2×D311yescharacteristic
50C5×C22⋊C4—21no—
51C42×C5C2×D311yescharacteristic
52C4⋊Dic5—31no—
53C4⋊Dic5—31no—
54#683—61no—
55#683—61no—
56C2×#168—31no—
57C2×#168—31no—
58#478—151noSylow
59C22×C3×C5—22no—
60C22×C3×C5—41no—
61C22×C3×C5—41no—
62C22×C3×C5C2×D411yescharacteristic
63C3×C4×C5—21no—
64C3×C4×C5—21no—
65C3×C4×C5—41no—
66C3×C4×C5C2×Q811yescharacteristic
67C3×C4×C5#4111yescharacteristic
68Dic15—41no—
69Dic15—41no—
70C2×C3×D4C2×D511yescharacteristic
71C22×C3×C4—21no—
72C3×C4⋊C4C2×D511yescharacteristic
73C3×C22⋊C4—21no—
74C3×C42C2×D511yescharacteristic
75C4⋊Dic3—51no—
76C4⋊Dic3—51no—
77Dic3⋊C4—101no—
78Dic3⋊C4—101no—
79C2×C3⋊C8—51no—
80C2×C3⋊C8—51no—
81C23×C5—21no—
82C5×D4—21no—
83C5×D4Dic612yes—
84C2×C4×C5—21no—
85C2×C4×C5—42no—
86C2×C4×C5#6711yescharacteristic
87C2×C4×C5#6711yescharacteristic
88C2×C4×C5C22×D311yescharacteristic
89C2×Dic5—61no—
90C2×Dic5—61no—
91#168—61no—
92#168—61no—
93#125—151no—
94C4×D4D1511yescharacteristic
95#107—151no—
96#106—151no—
97C4⋊C8—151no—
98#102—151no—
99#102—151no—
100C2×C3×C5—42no—
101C2×C3×C5C22⋊Q811yescharacteristic
102C2×C3×C5#13511yescharacteristic
103C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
104C23×C3—21no—
105C3×D4—21no—
106C3×D4Dic1012yes—
107C2×C3×C4—21no—
108C2×C3×C4—42no—
109C2×C3×C4C22⋊D511yescharacteristic
110C2×C3×C4C22⋊D511yescharacteristic
111C2×C3×C4C22×D511yescharacteristic
112C2×Dic3—101no—
113C2×Dic3—101no—
114C3⋊C8—101no—
115C3⋊C8—101no—
116C22×C5—22no—
117C22×C5—41no—
118C22×C5—41no—
119C22×C5C2×#6711yescharacteristic
120C4×C5—21no—
121C4×C5—21no—
122C4×C5—41no—
123C4×C5C2×Dic611yescharacteristic
124C4×C5#23511yescharacteristic
125Dic5—121no—
126Dic5—121no—
127C2×D4C2×D1511yescharacteristic
128C22×C4—21no—
129C2×C8—151no—
130C2×C8—151no—
131C4⋊C4—151no—
132C4⋊C4—151no—
133C4⋊C4—301no—
134C4⋊C4—301no—
135C4⋊C4C2×D1511yescharacteristic
136C22⋊C4—21no—
137C42C2×D1511yescharacteristic
138C3×C5#47811yescharacteristic, complemented, Hall
139C22×C3—22no—
140C22×C3—41no—
141C22×C3—41no—
142C22×C3C2×C22⋊D511yescharacteristic
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—41no—
146C3×C4C2×Dic1011yescharacteristic
147C3×C4#70911yescharacteristic
148Dic3—201no—
149Dic3—201no—
150C2×C5—42no—
151C2×C5#92411yescharacteristic
152C2×C5#93211yescharacteristic
153C2×C5#95011yescharacteristic
154C23—21no—
155D4—21no—
156D4Dic3012yes—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—301no—
160C2×C4—301no—
161C2×C4#122011yescharacteristic
162C2×C4#122011yescharacteristic
163C2×C4C22×D1511yescharacteristic
164C8—301no—
165C8—301no—
166C2×C3—42no—
167C2×C3#407011yescharacteristic
168C2×C3#407811yescharacteristic
169C2×C3#409611yescharacteristic
170C5#500911yescharacteristic, complemented, Sylow
171C22—22no—
172C22—41no—
173C22—41no—
174C22C2×#122011yescharacteristic
175C4—21no—
176C4—21no—
177C4—41no—
178C4—601no—
179C4—601no—
180C4C2×Dic3011yescharacteristic
181C4#681711yescharacteristic
182C3#6529811yescharacteristic, complemented, Sylow
183C2—42no—
184C2#9181311yescharacteristic
185C2#9182111yescharacteristic
186C2#9183911yescharacteristic
subgroupG/H
centerC22C2×#1220
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C4×C5×D4C2
socleC22×C3×C5C2×D4
prime radicalC2×C3×C5×D4C22
hypercenterC4×D4D15
hypocenterC3×C5#478
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #91759C2semidirect
5. #91092C2semidirect
6. #91091C2semidirect
7. C4⋊(C3⋊#168)C2semidirect
138. C3×C5#478semidirect
170. C5#5009semidirect
182. C3#65298semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C5×D42
#917592
#911162
#910922
#910912
C4⋊(C3⋊#168)2
#652983
#50095