Finite Group Databasebeta

← #11750972

Subgroups — #11750972

Order 960.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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#91782C211yesmaximal, characteristic
2#91779C211yesmaximal, characteristic, complemented
3C3×C5×#106C211yesmaximal, characteristic, complemented
4#91105C211yesmaximal, characteristic
5#91098C211yesmaximal, characteristic, complemented
6#91093C211yesmaximal, characteristic
7#91091C211yesmaximal, characteristic, complemented
8#65160—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C2×C4×D15—21no—
11C2×C3×C5×C8C2211yescharacteristic
12C3×C5×C4⋊C4C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14#6714—21no—
15C4⋊Dic15—21no—
16C4⋊Dic15C2211yescharacteristic
17#6712—21no—
18C4×Dic15C2211yescharacteristic
19C2×C3⋊#168C2211yescharacteristic
20#4871—51nomaximal, Hall
21#4039—31no—
22#4036—31no—
23C5×#106D311yescharacteristic, complemented
24#3953—31no—
25#3946—31no—
26#3941—31no—
27#3939—31no—
28C22×D15—21no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C2×Dic15D411yescharacteristic
34C2×Dic15D411yescharacteristic
35D60—21no—
36D60Q812yes—
37C4×D15—42no—
38C3×C5×C8—21no—
39C3⋊#168—21no—
40#893—51no—
41#890—51no—
42C3×#106D511yescharacteristic, complemented
43#821—51no—
44Dic3⋊C8—51no—
45#809—51no—
46#807—51no—
47C2×D20—31no—
48C2×C4×D5—61no—
49C2×C5×C8C2×D311yescharacteristic
50C5×C4⋊C4C2×D311yescharacteristic
51C5×C4⋊C4C2×D311yescharacteristic
52#685—61no—
53C4⋊Dic5—31no—
54C4⋊Dic5—61no—
55#683—61no—
56C4×Dic5—31no—
57C2×#168—31no—
58#478—151noSylow
59C22×C3×C5C2×D411yescharacteristic
60C2×D15—22no—
61C2×D15—41no—
62C2×D15—41no—
63C3×C4×C5—41no—
64C3×C4×C5—41no—
65C3×C4×C5C2×Q811yescharacteristic
66C3×C4×C5#4111yescharacteristic
67Dic15—21no—
68Dic15—21no—
69Dic15—41no—
70C2×D12—51no—
71C2×C4×D3—101no—
72C2×C3×C8C2×D511yescharacteristic
73C3×C4⋊C4C2×D511yescharacteristic
74C3×C4⋊C4C2×D511yescharacteristic
75(C2×D3)⋊C4—101no—
76C4⋊Dic3—51no—
77C4⋊Dic3—101no—
78Dic3⋊C4—101no—
79C4×Dic3—51no—
80C2×C3⋊C8—51no—
81C22×D5—61no—
82C2×C4×C5—21no—
83C2×C4×C5—21no—
84C2×C4×C5C22×D311yescharacteristic
85C2×Dic5—31no—
86C2×Dic5—31no—
87C2×Dic5—61no—
88D20—32no—
89D20—61no—
90C4×D5—122no—
91C5×C8—21no—
92#168—61no—
93#125—151no—
94C4×D4—151no—
95#107—151no—
96#106D1511yescharacteristic, complemented
97C4⋊C8—151no—
98#102—151no—
99#102—151no—
100C2×C3×C5C22⋊Q811yescharacteristic
101C2×C3×C5#13511yescharacteristic
102C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
103D15—42no—
104C22×D3—101no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4C22×D511yescharacteristic
108C2×Dic3—51no—
109C2×Dic3—51no—
110C2×Dic3—101no—
111D12—52no—
112D12—101no—
113C4×D3—202no—
114C3×C8—21no—
115C3⋊C8—101no—
116C22×C5D3×D411yescharacteristic
117C2×D5—62no—
118C2×D5—121no—
119C2×D5—121no—
120C4×C5—41no—
121C4×C5—41no—
122C4×C5#23511yescharacteristic
123C4×C5D3×Q811yescharacteristic
124Dic5—61no—
125Dic5—61no—
126Dic5—121no—
127C2×D4—151no—
128C22×C4—301no—
129C2×C8—151no—
130C2×C8C2×D1511yescharacteristic
131C4⋊C4—151no—
132C4⋊C4—301no—
133C4⋊C4—301no—
134C4⋊C4C2×D1511yescharacteristic
135C4⋊C4C2×D1511yescharacteristic
136C22⋊C4—301no—
137C42—151no—
138C3×C5#47811yescharacteristic, complemented, Hall
139C22×C3D4×D511yescharacteristic
140C2×D3—102no—
141C2×D3—201no—
142C2×D3—201no—
143C3×C4—41no—
144C3×C4—41no—
145C3×C4#70911yescharacteristic
146C3×C4Q8×D511yescharacteristic
147Dic3—101no—
148Dic3—101no—
149Dic3—201no—
150C2×C5#89611yescharacteristic
151C2×C5#91411yescharacteristic
152C2×C5#91611yescharacteristic
153D5—122no—
154C23—301no—
155D4—152no—
156D4—301no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—151no—
160C2×C4—151no—
161C2×C4—301no—
162C2×C4—602no—
163C2×C4C22×D1511yescharacteristic
164C8—21no—
165C8—301no—
166C2×C3#404211yescharacteristic
167C2×C3#406011yescharacteristic
168C2×C3#406211yescharacteristic
169D3—202no—
170C5#487111yescharacteristic, complemented, Sylow
171C22—302no—
172C22—601no—
173C22—601no—
174C22D4×D1511yescharacteristic
175C4—41no—
176C4—41no—
177C4—301no—
178C4—301no—
179C4—601no—
180C4#681711yescharacteristic
181C4Q8×D1511yescharacteristic
182C3#6516011yescharacteristic, complemented, Sylow
183C2—602no—
184C2#9178511yescharacteristic
185C2#9180311yescharacteristic
186C2#9180511yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#106C2
socleC22×C3×C5C2×D4
prime radicalC2×D60C22
hypercenter#106D15
hypocenterC3×C5#478
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #91779C2semidirect
3. C3×C5×#106C2semidirect
5. #91098C2semidirect
7. #91091C2semidirect
23. C5×#106D3semidirect
42. C3×#106D5semidirect
96. #106D15semidirect
138. C3×C5#478semidirect
170. C5#4871semidirect
182. C3#65160semidirect

Maximal subgroups

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

subgroupindex
#917822
#917792
C3×C5×#1062
#911052
#910982
#910932
#910912
#651603
#48715