Finite Group Databasebeta

← #11751123

Subgroups — #11751123

Order 960.

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

normal subgroups only

This group has 180 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×Q8C211yesmaximal, characteristic
2#91759C211yesmaximal, characteristic
3#91119C211yesmaximal, characteristic
4#91119C211yesmaximal, characteristic
5#91092C211yesmaximal, characteristic
6#91091C211yesmaximal, characteristic
7C4⋊(C3⋊#168)C211yesmaximal, characteristic
8#65311—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C3×C5×C4⋊C4—21no—
11C3×C5×C4⋊C4C2211yescharacteristic
12C3×C42×C5—21no—
13C3×C42×C5C2211yescharacteristic
14C4⋊Dic15C2211yescharacteristic
15C4⋊Dic15C2211yescharacteristic
16#6712—21no—
17#6712—21no—
18C2×C3⋊#168C2211yescharacteristic
19C2×C3⋊#168C2211yescharacteristic
20#5022—51nomaximal, Hall
21C4×C5×Q8D311yescharacteristic
22#4016—31no—
23#3967—31no—
24#3967—31no—
25#3940—31no—
26#3939—31no—
27C4⋊#168—31no—
28C3×C5×Q8—21no—
29C3×C5×Q8Q812yes—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5D411yescharacteristic
33C2×C3×C4×C5D411yescharacteristic
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15—21no—
36C2×Dic15—21no—
37C3⋊#168—21no—
38C3⋊#168—21no—
39C3×C4×Q8D511yescharacteristic
40#870—51no—
41#835—51no—
42#835—51no—
43#808—51no—
44#807—51no—
45C4⋊(C3⋊C8)—51no—
46C2×C5×Q8C2×D311yescharacteristic
47C5×C4⋊C4—21no—
48C5×C4⋊C4C2×D311yescharacteristic
49C42×C5—21no—
50C42×C5C2×D311yescharacteristic
51C4⋊Dic5—31no—
52C4⋊Dic5—31no—
53#683—61no—
54#683—61no—
55C2×#168—31no—
56C2×#168—31no—
57#479—151noSylow
58C22×C3×C5C2×D411yescharacteristic
59C3×C4×C5—22no—
60C3×C4×C5—21no—
61C3×C4×C5—21no—
62C3×C4×C5—41no—
63C3×C4×C5C2×Q811yescharacteristic
64C3×C4×C5#4111yescharacteristic
65Dic15—41no—
66Dic15—41no—
67C2×C3×Q8C2×D511yescharacteristic
68C3×C4⋊C4—21no—
69C3×C4⋊C4C2×D511yescharacteristic
70C3×C42—21no—
71C3×C42C2×D511yescharacteristic
72C4⋊Dic3—51no—
73C4⋊Dic3—51no—
74Dic3⋊C4—101no—
75Dic3⋊C4—101no—
76C2×C3⋊C8—51no—
77C2×C3⋊C8—51no—
78C5×Q8—21no—
79C5×Q8Dic612yes—
80C2×C4×C5—21no—
81C2×C4×C5—21no—
82C2×C4×C5#6711yescharacteristic
83C2×C4×C5#6711yescharacteristic
84C2×C4×C5C22×D311yescharacteristic
85C2×Dic5—61no—
86C2×Dic5—61no—
87#168—61no—
88#168—61no—
89#125—151no—
90C4×Q8D1511yescharacteristic
91#107—151no—
92#106—151no—
93C4⋊C8—151no—
94#103—151no—
95#103—151no—
96C2×C3×C5C22⋊Q811yescharacteristic
97C2×C3×C5#13511yescharacteristic
98C2×C3×C5#13711yescharacteristic
99C3×Q8—21no—
100C3×Q8Dic1012yes—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4C22⋊D511yescharacteristic
104C2×C3×C4C22⋊D511yescharacteristic
105C2×C3×C4C22×D511yescharacteristic
106C2×Dic3—101no—
107C2×Dic3—101no—
108C3⋊C8—101no—
109C3⋊C8—101no—
110C22×C5C2×#6711yescharacteristic
111C4×C5—22no—
112C4×C5—21no—
113C4×C5—21no—
114C4×C5—41no—
115C4×C5C2×Dic611yescharacteristic
116C4×C5#23511yescharacteristic
117Dic5—121no—
118Dic5—121no—
119C2×Q8C2×D1511yescharacteristic
120C2×C8—151no—
121C2×C8—151no—
122C4⋊C4—21no—
123C4⋊C4—151no—
124C4⋊C4—151no—
125C4⋊C4—301no—
126C4⋊C4—301no—
127C4⋊C4C2×D1511yescharacteristic
128C42—21no—
129C42C2×D1511yescharacteristic
130C3×C5#47911yescharacteristic, complemented, Hall
131C22×C3C2×C22⋊D511yescharacteristic
132C3×C4—21no—
133C3×C4—22no—
134C3×C4—21no—
135C3×C4—41no—
136C3×C4C2×Dic1011yescharacteristic
137C3×C4#70911yescharacteristic
138Dic3—201no—
139Dic3—201no—
140C2×C5#92411yescharacteristic
141C2×C5#94211yescharacteristic
142C2×C5#95011yescharacteristic
143Q8—21no—
144Q8Dic3012yes—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—301no—
148C2×C4—301no—
149C2×C4#122011yescharacteristic
150C2×C4#122011yescharacteristic
151C2×C4C22×D1511yescharacteristic
152C8—301no—
153C8—301no—
154C2×C3#407011yescharacteristic
155C2×C3#408811yescharacteristic
156C2×C3#409611yescharacteristic
157C5#502211yescharacteristic, complemented, Sylow
158C22C2×#122011yescharacteristic
159C4—22no—
160C4—21no—
161C4—21no—
162C4—41no—
163C4—601no—
164C4—601no—
165C4C2×Dic3011yescharacteristic
166C4#681711yescharacteristic
167C3#6531111yescharacteristic, complemented, Sylow
168C2#9181311yescharacteristic
169C2#9183111yescharacteristic
170C2#9183911yescharacteristic
subgroupG/H
centerC22C2×#1220
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C4×C5×Q8C2
socle, prime radicalC22×C3×C5C2×D4
hypercenterC4×Q8D15
hypocenterC3×C5#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
130. C3×C5#479semidirect
157. C5#5022semidirect
167. C3#65311semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C5×Q82
#917592
#911192
#910922
#910912
C4⋊(C3⋊#168)2
#653113
#50225