Finite Group Databasebeta

← #11751167

Subgroups — #11751167

Order 960.

204 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 69 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×C5×#125C211yesmaximal, characteristic, complemented
2C4×D60C211yesmaximal, characteristic
3#91093C211yesmaximal, characteristic
4#91093C211yesmaximal, characteristic
5#91092C211yesmaximal, characteristic, complemented
6#91091C211yesmaximal, characteristic, complemented
7C4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#65355—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C2×C4×D15—21no—
11C3×C5×C4⋊C4—21no—
12C3×C5×C4⋊C4—21no—
13C3×C5×C4⋊C4C2211yescharacteristic
14C3×C5×C4⋊C4C2211yescharacteristic
15C3×C42×C5C2211yescharacteristic
16#6714—21no—
17C4⋊Dic15C2211yescharacteristic
18C2×C3⋊#168C2211yescharacteristic
19C2×C3⋊#168C2211yescharacteristic
20#5066—51nomaximal, Hall
21C5×#125D311yescharacteristic, complemented
22C4×D20—31no—
23#3941—31no—
24#3941—31no—
25#3940—31no—
26#3939—31no—
27C4⋊#168—31no—
28C22×D15—21no—
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5D411yescharacteristic
32C2×C3×C4×C5D411yescharacteristic
33C2×C3×C4×C5C2311yescharacteristic
34C2×Dic15—21no—
35D60—21no—
36D60Q812yes—
37C4×D15—42no—
38C3⋊#168—21no—
39C3⋊#168—21no—
40C3×#125D511yescharacteristic, complemented
41C4×D12—51no—
42#809—51no—
43#809—51no—
44#808—51no—
45#807—51no—
46C4⋊(C3⋊C8)—51no—
47C2×D20—31no—
48C2×C4×D5—61no—
49C5×C4⋊C4—21no—
50C5×C4⋊C4—21no—
51C5×C4⋊C4C2×D311yescharacteristic
52C5×C4⋊C4C2×D311yescharacteristic
53C42×C5C2×D311yescharacteristic
54#685—61no—
55C4⋊Dic5—31no—
56C2×#168—31no—
57C2×#168—31no—
58#478—151noSylow
59C22×C3×C5C2×D411yescharacteristic
60C2×D15—22no—
61C2×D15—41no—
62C2×D15—41no—
63C3×C4×C5—21no—
64C3×C4×C5—21no—
65C3×C4×C5—41no—
66C3×C4×C5—41no—
67C3×C4×C5C2×Q811yescharacteristic
68C3×C4×C5#4111yescharacteristic
69Dic15—41no—
70C2×D12—51no—
71C2×C4×D3—101no—
72C3×C4⋊C4—21no—
73C3×C4⋊C4—21no—
74C3×C4⋊C4C2×D511yescharacteristic
75C3×C4⋊C4C2×D511yescharacteristic
76C3×C42C2×D511yescharacteristic
77(C2×D3)⋊C4—101no—
78C4⋊Dic3—51no—
79C2×C3⋊C8—51no—
80C2×C3⋊C8—51no—
81C22×D5—61no—
82C2×C4×C5—21no—
83C2×C4×C5—21no—
84C2×C4×C5#6711yescharacteristic
85C2×C4×C5#6711yescharacteristic
86C2×C4×C5C22×D311yescharacteristic
87C2×Dic5—61no—
88D20—32no—
89D20—61no—
90C4×D5—122no—
91#168—61no—
92#168—61no—
93#125D1511yescharacteristic, complemented
94C4×D4—151no—
95#107—151no—
96#106—151no—
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×C3×C4C22⋊D511yescharacteristic
109C2×C3×C4C22×D511yescharacteristic
110C2×Dic3—101no—
111D12—52no—
112D12—101no—
113C4×D3—202no—
114C3⋊C8—101no—
115C3⋊C8—101no—
116C22×C5C2×#6711yescharacteristic
117C2×D5—62no—
118C2×D5—121no—
119C2×D5—121no—
120C4×C5—21no—
121C4×C5—21no—
122C4×C5—41no—
123C4×C5—41no—
124C4×C5D3×Q811yescharacteristic
125C4×C5#23911yescharacteristic
126Dic5—121no—
127C2×D4—151no—
128C22×C4—301no—
129C2×C8—151no—
130C2×C8—151no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—151no—
134C4⋊C4C2×D1511yescharacteristic
135C4⋊C4C2×D1511yescharacteristic
136C22⋊C4—301no—
137C42C2×D1511yescharacteristic
138C3×C5#47811yescharacteristic, complemented, Hall
139C22×C3C2×C22⋊D511yescharacteristic
140C2×D3—102no—
141C2×D3—201no—
142C2×D3—201no—
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—41no—
146C3×C4—41no—
147C3×C4Q8×D511yescharacteristic
148C3×C4#71311yescharacteristic
149Dic3—201no—
150C2×C5#94611yescharacteristic
151C2×C5#94911yescharacteristic
152C2×C5#95011yescharacteristic
153D5—122no—
154C23—301no—
155D4—152no—
156D4—301no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—301no—
160C2×C4—602no—
161C2×C4#122011yescharacteristic
162C2×C4#122011yescharacteristic
163C2×C4C22×D1511yescharacteristic
164C8—301no—
165C8—301no—
166C2×C3#409211yescharacteristic
167C2×C3#409511yescharacteristic
168C2×C3#409611yescharacteristic
169D3—202no—
170C5#506611yescharacteristic, complemented, Sylow
171C22—302no—
172C22—601no—
173C22—601no—
174C22C2×#122011yescharacteristic
175C4—21no—
176C4—21no—
177C4—41no—
178C4—41no—
179C4—601no—
180C4Q8×D1511yescharacteristic
181C4#682111yescharacteristic
182C3#6535511yescharacteristic, complemented, Sylow
183C2—602no—
184C2#9183511yescharacteristic
185C2#9183811yescharacteristic
186C2#9183911yescharacteristic
subgroupG/H
centerC22C2×#1220
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#125C2
socleC22×C3×C5C2×D4
prime radicalC2×D60C22
hypercenter#125D15
hypocenterC3×C5#478
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×C5×#125C2semidirect
5. #91092C2semidirect
6. #91091C2semidirect
7. C4⋊(C3⋊#168)C2semidirect
21. C5×#125D3semidirect
40. C3×#125D5semidirect
93. #125D15semidirect
138. C3×C5#478semidirect
170. C5#5066semidirect
182. C3#65355semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1252
C4×D602
#910932
#910922
#910912
C4⋊(C3⋊#168)2
#653553
#50665