Finite Group Databasebeta

← #11750984

Subgroups — #11750984

Order 960.

268 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×D120C211yesmaximal, characteristic, complemented
2C2×C8×D15C211yesmaximal, characteristic, complemented
3#91784C212yesmaximal, complemented
4C3×C5×#107C211yesmaximal, characteristic, complemented
5#91093C212yesmaximal, complemented
6#65172—31nomaximal, Hall
7C2×D60—22no—
8C2×D60C2212yes—
9C2×C4×D15C2211yescharacteristic
10C2×C3×C5×C8C2211yescharacteristic
11C3×C5×C4⋊C4C2212yes—
12#6714—22no—
13C2×C3⋊#168C2211yescharacteristic
14D120—22no—
15C8×D15—22no—
16#4883—51nomaximal, Hall
17C2×D40—31no—
18C2×C8×D5—31no—
19#4041—32no—
20C5×#107D311yescharacteristic, complemented
21#3941—32no—
22C22×D15—22no—
23C22×D15D411yescharacteristic
24C2×C3×C4×C5—22no—
25C2×C3×C4×C5C2311yescharacteristic
26C2×Dic15D411yescharacteristic
27D60—22no—
28D60—22no—
29D60—44no—
30C4×D15—21no—
31C4×D15—21no—
32C3×C5×C8D412yescomplemented
33C3⋊#168—21no—
34C2×D24—51no—
35C2×D3×C8—51no—
36#895—52no—
37C3×#107D511yescharacteristic, complemented
38#809—52no—
39C2×D20—32no—
40C2×D20—62no—
41C2×C4×D5—31no—
42C2×C5×C8C2×D311yescharacteristic
43C5×C4⋊C4C2×D312yes—
44#685—62no—
45C2×#168—31no—
46D40—62no—
47C8×D5—62no—
48#466—151noSylow
49C22×C3×C5C2×D411yescharacteristic
50C2×D15—21no—
51C2×D15—21no—
52C2×D15—42no—
53C2×D15—42no—
54C2×D15—42no—
55C2×D15D812yescomplemented
56C3×C4×C5—42no—
57C3×C4×C5C2×D411yescharacteristic
58C3×C4×C5#4111yescharacteristic
59Dic15—21no—
60C2×D12—52no—
61C2×D12—102no—
62C2×C4×D3—51no—
63C2×C3×C8C2×D511yescharacteristic
64C3×C4⋊C4C2×D512yes—
65(C2×D3)⋊C4—102no—
66C2×C3⋊C8—51no—
67D24—102no—
68D3×C8—102no—
69C22×D5—31no—
70C22×D5—62no—
71C2×C4×C5—22no—
72C2×C4×C5C22×D311yescharacteristic
73C2×Dic5—31no—
74D20—62no—
75D20—62no—
76D20—124no—
77C4×D5—61no—
78C4×D5—61no—
79C5×C8D1212yescomplemented
80#168—61no—
81C2×D8—151no—
82C22×C8—151no—
83#121—152no—
84#107D1511yescharacteristic, complemented
85#102—152no—
86C2×C3×C5#12111yescharacteristic
87C2×C3×C5C2×D811yescharacteristic
88C2×C3×C5#13511yescharacteristic
89D15—22no—
90D15—82no—
91C22×D3—51no—
92C22×D3—102no—
93C2×C3×C4—22no—
94C2×C3×C4C22×D511yescharacteristic
95C2×Dic3—51no—
96D12—102no—
97D12—102no—
98D12—204no—
99C4×D3—101no—
100C4×D3—101no—
101C3×C8D2012yescomplemented
102C3⋊C8—101no—
103C22×C5D3×D411yescharacteristic
104C2×D5—32no—
105C2×D5—61no—
106C2×D5—61no—
107C2×D5—122no—
108C2×D5—122no—
109C2×D5—122no—
110C4×C5—42no—
111C4×C5C2×D1211yescharacteristic
112C4×C5#23911yescharacteristic
113Dic5—61no—
114C2×D4—152no—
115C2×D4—302no—
116C22×C4—151no—
117D8—302no—
118C2×C8—151no—
119C2×C8—302no—
120C2×C8C2×D1511yescharacteristic
121C4⋊C4C2×D1512yes—
122C22⋊C4—302no—
123C3×C5#46611yescharacteristic, complemented, Hall
124C22×C3D4×D511yescharacteristic
125C2×D3—52no—
126C2×D3—101no—
127C2×D3—101no—
128C2×D3—202no—
129C2×D3—202no—
130C2×D3—202no—
131C3×C4—42no—
132C3×C4C2×D2011yescharacteristic
133C3×C4#71311yescharacteristic
134Dic3—101no—
135C2×C5#89511yescharacteristic
136C2×C5D3×D811yescharacteristic
137C2×C5#91911yescharacteristic
138D5—62no—
139D5—242no—
140C23—151no—
141C23—302no—
142D4—302no—
143D4—302no—
144D4—604no—
145C2×C4—22no—
146C2×C4—151no—
147C2×C4—301no—
148C2×C4—301no—
149C2×C4C22×D1511yescharacteristic
150C8—301no—
151C8D6012yescomplemented
152C2×C3#404111yescharacteristic
153C2×C3D5×D811yescharacteristic
154C2×C3#406511yescharacteristic
155D3—102no—
156D3—402no—
157C5#488311yescharacteristic, complemented, Sylow
158C22—152no—
159C22—301no—
160C22—301no—
161C22—602no—
162C22—602no—
163C22—602no—
164C22D4×D1511yescharacteristic
165C4—42no—
166C4—301no—
167C4C2×D6011yescharacteristic
168C4#682111yescharacteristic
169C3#6517211yescharacteristic, complemented, Sylow
170C2—302no—
171C2—1202no—
172C2#9178411yescharacteristic
173C2D8×D1511yescharacteristic
174C2#9180811yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#107C2
socleC22×C3×C5C2×D4
hypercenter#107D15
hypocenterC3×C5#466
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×D120C2semidirect
2. C2×C8×D15C2semidirect
3. #91784C2semidirect
4. C3×C5×#107C2semidirect
5. #91093C2semidirect
20. C5×#107D3semidirect
32. C3×C5×C8D4semidirect
37. C3×#107D5semidirect
55. C2×D15D8semidirect
79. C5×C8D12semidirect
84. #107D15semidirect
101. C3×C8D20semidirect
123. C3×C5#466semidirect
151. C8D60semidirect
157. C5#4883semidirect
169. C3#65172semidirect

Maximal subgroups

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

subgroupindex
C2×D1202
C2×C8×D152
#917842
C3×C5×#1072
#910932
#651723
#48835