Finite Group Databasebeta

← #11747784

Subgroups — #11747784

Order 960.

204 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 64 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
1Dic3×D20C211yesmaximal, characteristic
2#91381C211yesmaximal, characteristic, complemented
3#91101C211yesmaximal, characteristic, complemented
4C5×Dic3⋊C8C211yesmaximal, characteristic, complemented
5C3×#3953C211yesmaximal, characteristic
6#90990C211yesmaximal, characteristic, complemented
7#90965C211yesmaximal, characteristic
8#65136—31nomaximal, Hall
9C2×C3×D20C2211yescharacteristic
10C2×D5×Dic3—21no—
11C2×C3×C5×C8C2211yescharacteristic
12C4⋊Dic15C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14C4×C5×Dic3C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×C4⋊Dic5C2211yescharacteristic
17#6669—21no—
18#6668—21no—
19#6665—21no—
20#4763—51nomaximal, Hall
21C4×D20—31no—
22#4016—31no—
23C5×C4⋊C8—31no—
24#3953—31no—
25#3953D311yescharacteristic
26#3950—31no—
27#3949—31no—
28C22×C3×D5—21no—
29C2×C3×C4×C5C2311yescharacteristic
30C2×Dic15—21no—
31C2×Dic15—21no—
32C2×C5×Dic3D411yescharacteristic
33C2×C5×Dic3D411yescharacteristic
34C2×C3×Dic5—21no—
35C3×D20—21no—
36C3×D20Q812yes—
37D5×Dic3—42no—
38C3×C5×C8—21no—
39C5×C3⋊C8—21no—
40D4×Dic3—51no—
41#890—51no—
42C3×#102—51no—
43#832—51no—
44#817—51no—
45Dic3⋊C8D511yescharacteristic, complemented
46#807—51no—
47C2×D20C2×D311yescharacteristic
48C2×C4×D5—61no—
49C2×C5×C8—31no—
50C2×C5×C8C2×D311yescharacteristic
51C42×C5—31no—
52#685—61no—
53C4⋊Dic5—31no—
54C4⋊Dic5—31no—
55C4⋊Dic5C2×D311yescharacteristic
56#683—61no—
57#683—61no—
58#478—151noSylow
59C22×C3×C5C2×D411yescharacteristic
60C2×C3×D5—22no—
61C2×C3×D5—41no—
62C2×C3×D5—41no—
63C3×C4×C5C2×Q811yescharacteristic
64C3×C4×C5#4111yescharacteristic
65Dic15—41no—
66Dic15—41no—
67C3×Dic5—41no—
68C5×Dic3—21no—
69C5×Dic3—21no—
70C2×C3×D4—51no—
71C22×Dic3—101no—
72C2×C3×C8C2×D511yescharacteristic
73C3×C4⋊C4—51no—
74#217—101no—
75C4⋊Dic3—51no—
76C4⋊Dic3—51no—
77C4⋊Dic3—101no—
78Dic3⋊C4—101no—
79C4×Dic3C2×D511yescharacteristic
80C2×C3⋊C8C2×D511yescharacteristic
81C22×D5—21no—
82C2×C4×C5—31no—
83C2×C4×C5—31no—
84C2×C4×C5C22×D311yescharacteristic
85C2×Dic5—21no—
86C2×Dic5—61no—
87C2×Dic5—61no—
88D20—21no—
89D20Dic612yes—
90C4×D5—122no—
91C5×C8—21no—
92C5×C8—61no—
93#125—151no—
94C4×D4—151no—
95#107—151no—
96#106—151no—
97C4⋊C8—31no—
98#102—51no—
99#102—151no—
100C2×C3×C5C22⋊Q811yescharacteristic
101C2×C3×C5#13511yescharacteristic
102C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
103C3×D5—42no—
104C23×C3—101no—
105C3×D4—52no—
106C3×D4—101no—
107C2×C3×C4—101no—
108C2×C3×C4C22×D511yescharacteristic
109C2×Dic3—101no—
110C2×Dic3—101no—
111C2×Dic3—202no—
112C2×Dic3D2011yescharacteristic
113C2×Dic3D2011yescharacteristic
114C3×C8—21no—
115C3⋊C8—21no—
116C22×C5D3×D411yescharacteristic
117C2×D5—22no—
118C2×D5—41no—
119C2×D5—41no—
120C4×C5—61no—
121C4×C5—61no—
122C4×C5C2×Dic611yescharacteristic
123C4×C5#23711yescharacteristic
124Dic5—41no—
125Dic5—121no—
126Dic5—121no—
127C2×D4—51no—
128C22×C4—301no—
129C2×C8—31no—
130C2×C8D3×D511yescharacteristic
131C4⋊C4—51no—
132C4⋊C4—151no—
133C4⋊C4—151no—
134C4⋊C4—301no—
135C4⋊C4—301no—
136C22⋊C4—301no—
137C42—31no—
138C3×C5#47811yescharacteristic, complemented, Hall
139C22×C3—102no—
140C22×C3—201no—
141C22×C3—201no—
142C22×C3C2×D2011yescharacteristic
143C3×C4—201no—
144C3×C4#71111yescharacteristic
145C3×C4Q8×D511yescharacteristic
146Dic3—21no—
147Dic3—21no—
148Dic3—201no—
149Dic3—201no—
150C2×C5#87811yescharacteristic
151C2×C5#91111yescharacteristic
152C2×C5#91611yescharacteristic
153D5—42no—
154C23—101no—
155D4—52no—
156D4—101no—
157C2×C4—31no—
158C2×C4—31no—
159C2×C4—101no—
160C2×C4—301no—
161C2×C4—301no—
162C2×C4—602no—
163C2×C4C2×D3×D511yescharacteristic
164C8—21no—
165C8—61no—
166C2×C3—202no—
167C2×C3#404311yescharacteristic
168C2×C3#405011yescharacteristic
169C2×C3#405411yescharacteristic
170C5#476311yescharacteristic, complemented, Sylow
171C22—102no—
172C22—201no—
173C22—201no—
174C22D3×D2011yescharacteristic
175C4—61no—
176C4—61no—
177C4—201no—
178C4—601no—
179C4—601no—
180C4D5×Dic611yescharacteristic
181C4#678011yescharacteristic
182C3#6513611yescharacteristic, complemented, Sylow
183C2—202no—
184C2#9125411yescharacteristic
185C2#9127211yescharacteristic
186C2#9142211yescharacteristic
subgroupG/H
centerC22D3×D20
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radicalC2×C3×D20C22
hypercenterC2×C8D3×D5
hypocenterC3×C5#478
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #91381C2semidirect
3. #91101C2semidirect
4. C5×Dic3⋊C8C2semidirect
6. #90990C2semidirect
45. Dic3⋊C8D5semidirect
138. C3×C5#478semidirect
170. C5#4763semidirect
182. C3#65136semidirect

Maximal subgroups

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

subgroupindex
Dic3×D202
#913812
#911012
C5×Dic3⋊C82
C3×#39532
#909902
#909652
#651363
#47635