Finite Group Databasebeta

← #11751069

Subgroups — #11751069

Order 960.

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

normal subgroups only

This group has 228 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
1C2×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2#91819C211yesmaximal, characteristic
3#91114C211yesmaximal, characteristic, complemented
4#91093C212yesmaximal, complemented
5#91092C212yesmaximal, complemented
6#65257—31nomaximal, Hall
7C22×C3×C4×C5—21no—
8C22×C3×C4×C5C2211yescharacteristic
9C2×#1220—21no—
10C2×D60C2211yescharacteristic
11C3×C5×C4⋊C4—21no—
12C3×C5×C4⋊C4C2212yes—
13#6714—21no—
14C4⋊Dic15C2211yescharacteristic
15C2×C3⋊#168C2212yes—
16#4968—51nomaximal, Hall
17C2×C5×C4⋊C4D311yescharacteristic, complemented
18#4076—31no—
19C22⋊#168—31no—
20#3941—32no—
21#3940—32no—
22C23×C3×C5D411yescharacteristic
23C22×D15—21no—
24C2×C3×C4×C5—22no—
25C2×C3×C4×C5—22no—
26C2×C3×C4×C5—42no—
27C2×C3×C4×C5D411yescharacteristic
28C2×C3×C4×C5C2311yescharacteristic
29#1220—42no—
30C2×Dic15—21no—
31D60—22no—
32C3⋊#168—22no—
33C2×C3×C4⋊C4D511yescharacteristic, complemented
34#930—51no—
35#830—51no—
36#809—52no—
37#808—52no—
38C22×C4×C5—21no—
39C22×C4×C5C2×D311yescharacteristic
40C2×C22⋊D5—61no—
41C2×D20—31no—
42C5×C4⋊C4—21no—
43C5×C4⋊C4C2×D312yes—
44#685—61no—
45C4⋊Dic5—31no—
46C2×#168—32no—
47#481—151noSylow
48C22×C3×C5—21no—
49C22×C3×C5—21no—
50C22×C3×C5SD1612yes—
51C22×C3×C5C2×D411yescharacteristic
52C2×D15—41no—
53C2×D15—41no—
54C2×D15—41no—
55C3×C4×C5—21no—
56C3×C4×C5—42no—
57C3×C4×C5#4112yes—
58Dic15—41no—
59C22×C3×C4—21no—
60C22×C3×C4C2×D511yescharacteristic
61C2×#67—101no—
62C2×D12—51no—
63C3×C4⋊C4—21no—
64C3×C4⋊C4C2×D512yes—
65(C2×D3)⋊C4—101no—
66C4⋊Dic3—51no—
67C2×C3⋊C8—52no—
68C23×C5#6711yescharacteristic
69C22×D5—61no—
70C2×C4×C5—22no—
71C2×C4×C5—22no—
72C2×C4×C5—42no—
73C2×C4×C5#6711yescharacteristic
74C2×C4×C5C22×D311yescharacteristic
75C22⋊D5—122no—
76C2×Dic5—61no—
77D20—62no—
78#168—62no—
79#121—151no—
80C2×C4⋊C4D1511yescharacteristic, complemented
81#106—152no—
82#102—152no—
83C22⋊C8—151no—
84C2×C3×C5—22no—
85C2×C3×C5#12311yescharacteristic
86C2×C3×C5C2×SD1611yescharacteristic
87C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
88D15—81no—
89C23×C3C22⋊D511yescharacteristic
90C22×D3—101no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—42no—
94C2×C3×C4C22⋊D511yescharacteristic
95C2×C3×C4C22×D511yescharacteristic
96#67—202no—
97C2×Dic3—101no—
98D12—102no—
99C3⋊C8—102no—
100C22×C5—21no—
101C22×C5—21no—
102C22×C5#21512yes—
103C22×C5C2×#6711yescharacteristic
104C2×D5—121no—
105C2×D5—121no—
106C2×D5—121no—
107C4×C5—21no—
108C4×C5—42no—
109C4×C5#23512yes—
110Dic5—121no—
111C2×D4—151no—
112C2×D4—301no—
113C22×C4—21no—
114C22×C4C2×D1511yescharacteristic
115C2×C8—152no—
116C4⋊C4—21no—
117C4⋊C4—151no—
118C4⋊C4C2×D1512yes—
119C22⋊C4—301no—
120C3×C5#48111yescharacteristic, complemented, Hall
121C22×C3—21no—
122C22×C3—21no—
123C22×C3#68812yes—
124C22×C3C2×C22⋊D511yescharacteristic
125C2×D3—201no—
126C2×D3—201no—
127C2×D3—201no—
128C3×C4—21no—
129C3×C4—42no—
130C3×C4#70912yes—
131Dic3—201no—
132C2×C5—22no—
133C2×C5#92911yescharacteristic
134C2×C5#93211yescharacteristic
135C2×C5C2×#21511yescharacteristic
136D5—241no—
137C23—301no—
138C23#122011yescharacteristic
139D4—302no—
140D4—602no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—301no—
145C2×C4#122011yescharacteristic
146C2×C4C22×D1511yescharacteristic
147C8—302no—
148C2×C3—22no—
149C2×C3#407511yescharacteristic
150C2×C3#407811yescharacteristic
151C2×C3C2×#68811yescharacteristic
152D3—401no—
153C5#496811yescharacteristic, complemented, Sylow
154C22—21no—
155C22—21no—
156C22—601no—
157C22—601no—
158C22—601no—
159C22#671712yes—
160C22C2×#122011yescharacteristic
161C4—21no—
162C4—42no—
163C4—601no—
164C4#681712yes—
165C3#6525711yescharacteristic, complemented, Sylow
166C2—22no—
167C2—1201no—
168C2#9181811yescharacteristic
169C2#9182111yescharacteristic
170C2C2×#671711yescharacteristic
subgroupG/H
centerC22C2×#1220
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC2×C3×C5×C4⋊C4C2
socleC22×C3×C5C2×D4
prime radical#91819C2
hypercenterC2×C4⋊C4D15
hypocenterC3×C5#481
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C4⋊C4C2semidirect
3. #91114C2semidirect
4. #91093C2semidirect
5. #91092C2semidirect
17. C2×C5×C4⋊C4D3semidirect
33. C2×C3×C4⋊C4D5semidirect
80. C2×C4⋊C4D15semidirect
120. C3×C5#481semidirect
153. C5#4968semidirect
165. C3#65257semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×C4⋊C42
#918192
#911142
#910932
#910922
#652573
#49685