Finite Group Databasebeta

← #11749332

Subgroups — #11749332

Order 960.

180 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 68 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×Q8×Dic5C211yesmaximal, characteristic
2#91388C211yesmaximal, characteristic
3#91119C211yesmaximal, characteristic
4C5×#835C211yesmaximal, characteristic
5#90989C211yesmaximal, characteristic
6#90987C211yesmaximal, characteristic
7#90982C211yesmaximal, characteristic
8#65088—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C4⋊Dic15C2211yescharacteristic
11C2×C3⋊#168C2211yescharacteristic
12C5×C4⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊C8C2211yescharacteristic
14C3×C4⋊Dic5—21no—
15C3×C4⋊Dic5C2211yescharacteristic
16C3×C4×Dic5—21no—
17C3×C4×Dic5C2211yescharacteristic
18Dic3⋊Dic5—21no—
19#6669—21no—
20#5022—51nomaximal, Hall
21Q8×Dic5D311yescharacteristic
22#4036—31no—
23C5×#103—31no—
24#3967—31no—
25#3949—31no—
26#3946—31no—
27#3939—31no—
28C3×C5×Q8—21no—
29C3×C5×Q8Q812yes—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C2×C5×Dic3—21no—
34C2×C3×Dic5—21no—
35C2×C3×Dic5D411yescharacteristic
36C2×C3×Dic5D411yescharacteristic
37C3⋊#168—21no—
38C5×C3⋊C8—21no—
39C3×C4×Q8—51no—
40#870—51no—
41#835—51no—
42#835D511yescharacteristic
43#808—51no—
44#807—51no—
45C4⋊(C3⋊C8)—51no—
46C2×C5×Q8C2×D311yescharacteristic
47C2×C5×C8—31no—
48C5×C4⋊C4—31no—
49C4⋊Dic5—21no—
50C4⋊Dic5—31no—
51C4⋊Dic5—61no—
52C4⋊Dic5C2×D311yescharacteristic
53#683—61no—
54C4×Dic5—21no—
55C4×Dic5C2×D311yescharacteristic
56C2×#168—31no—
57#479—151noSylow
58C22×C3×C5C2×D411yescharacteristic
59C3×C4×C5—22no—
60C3×C4×C5C2×Q811yescharacteristic
61C3×C4×C5#4111yescharacteristic
62Dic15—41no—
63C3×Dic5—21no—
64C3×Dic5—21no—
65C3×Dic5—41no—
66C5×Dic3—41no—
67C2×C3×Q8C2×D511yescharacteristic
68C3×C4⋊C4—51no—
69C3×C4⋊C4—101no—
70C3×C42—51no—
71C3×C42—101no—
72C4⋊Dic3—51no—
73C4⋊Dic3C2×D511yescharacteristic
74Dic3⋊C4—101no—
75Dic3⋊C4—101no—
76C2×C3⋊C8—51no—
77C2×C3⋊C8C2×D511yescharacteristic
78C5×Q8—21no—
79C5×Q8Dic612yes—
80C2×C4×C5—21no—
81C2×C4×C5—61no—
82C2×C4×C5C22×D311yescharacteristic
83C2×Dic5—21no—
84C2×Dic5—61no—
85C2×Dic5#6711yescharacteristic
86C2×Dic5#6711yescharacteristic
87C5×C8—61no—
88#168—61no—
89#125—151no—
90C4×Q8—51no—
91#107—151no—
92#106—151no—
93C4⋊C8—151no—
94#103—31no—
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—51no—
103C2×C3×C4—51no—
104C2×C3×C4—101no—
105C2×C3×C4C22×D511yescharacteristic
106C2×Dic3—21no—
107C2×Dic3—101no—
108C3⋊C8—21no—
109C3⋊C8—101no—
110C22×C5C2×#6711yescharacteristic
111C4×C5—22no—
112C4×C5—121no—
113C4×C5C2×Dic611yescharacteristic
114C4×C5#23511yescharacteristic
115Dic5—21no—
116Dic5—21no—
117Dic5—41no—
118Dic5—121no—
119C2×Q8D3×D511yescharacteristic
120C2×C8—31no—
121C2×C8—151no—
122C4⋊C4—31no—
123C4⋊C4—51no—
124C4⋊C4—101no—
125C4⋊C4—151no—
126C4⋊C4—301no—
127C4⋊C4—301no—
128C42—51no—
129C42—101no—
130C3×C5#47911yescharacteristic, complemented, Hall
131C22×C3D4×D511yescharacteristic
132C3×C4—22no—
133C3×C4—101no—
134C3×C4—101no—
135C3×C4—201no—
136C3×C4C2×Dic1011yescharacteristic
137C3×C4#71111yescharacteristic
138Dic3—41no—
139Dic3—201no—
140C2×C5#92411yescharacteristic
141C2×C5#94211yescharacteristic
142C2×C5#95011yescharacteristic
143Q8—21no—
144Q8#120412yes—
145C2×C4—21no—
146C2×C4—51no—
147C2×C4—51no—
148C2×C4—61no—
149C2×C4—101no—
150C2×C4—301no—
151C2×C4C2×D3×D511yescharacteristic
152C8—61no—
153C8—301no—
154C2×C3#402411yescharacteristic
155C2×C3#406211yescharacteristic
156C2×C3#406411yescharacteristic
157C5#502211yescharacteristic, complemented, Sylow
158C22D5×#6711yescharacteristic
159C4—22no—
160C4—101no—
161C4—101no—
162C4—121no—
163C4—201no—
164C4—601no—
165C4#678211yescharacteristic
166C4C2×#120411yescharacteristic
167C3#6508811yescharacteristic, complemented, Sylow
168C2#9151411yescharacteristic
169C2#9151511yescharacteristic
170C2#9157411yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socle, prime radicalC22×C3×C5C2×D4
hypercenterC2×Q8D3×D5
hypocenterC3×C5#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
130. C3×C5#479semidirect
157. C5#5022semidirect
167. C3#65088semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic52
#913882
#911192
C5×#8352
#909892
#909872
#909822
#650883
#50225