Finite Group Databasebeta

← #13087049

Subgroups — #13087049

Order 1440.

780 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C23×C5×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#67184C211yesmaximal, characteristic, complemented
3C2×#67140C212yesmaximal, complemented
4C32×C22⋊Dic5C211yesmaximal, characteristic, complemented
5#10623771C212yesmaximal, complemented
6#91570—34nomaximal
7C23×C32×C5C2211yescharacteristic
8C22×C3⋊D15C2211yescharacteristic, complemented
9C22×C5×C3⋊D3—22no—
10C22×C5×C3⋊D3—24no—
11C22×C5×C3⋊D3C2212yes—
12#67184—22no—
13C2×C3⋊Dic15C2211yescharacteristic, complemented
14C2×C32×Dic5C2212yescomplemented
15#67140—24no—
16#64091—51nomaximal, Hall
17C23×C5×D3—34no—
18C2×#1220—34no—
19C2×#1203—38no—
20C3×C22⋊Dic5D314yescomplemented
21(C2×D3)⋊Dic5—38no—
22C22×C32×C5—22no—
23C22×C32×C5D412yescomplemented
24C22×C32×C5C2311yescharacteristic
25C2×C3⋊D15—22no—
26C2×C3⋊D15—21no—
27C2×C5×C3⋊D3—28no—
28C2×C5×C3⋊D3—22no—
29C2×C5×C3⋊D3—22no—
30C2×C5×C3⋊D3D414yescomplemented
31C3⋊Dic15—21no—
32C32×Dic5—22no—
33#4099—91noHall
34C23×C3⋊D3D511yescharacteristic, complemented
35C2×#638—51no—
36C2×C4⋊(C3⋊D3)—52no—
37C32×C22⋊C4—51no—
38#3752—52no—
39C23×C3×C5C2×D314yes—
40C22×D15—34no—
41C22×C5×D3—38no—
42C22×C5×D3—616no—
43C22×C5×D3—68no—
44#1220—68no—
45C2×Dic15—34no—
46C2×C3×Dic5C2×D318yescomplemented
47#1203—616no—
48#882—154no—
49C2×C32×C5—22no—
50C2×C32×C5C2×D411yescharacteristic
51C2×C32×C5C2×D412yes—
52C3⋊D15—41no—
53C5×C3⋊D3—24no—
54C24×C5—91no—
55C2×C22⋊D5—91no—
56C2×C22⋊D5—92no—
57C22⋊Dic5—92no—
58C22⋊Dic5C3⋊D311yescharacteristic, complemented
59C23×C32C2×D511yescharacteristic
60C22×C3⋊D3—22no—
61C22×C3⋊D3—24no—
62C22×C3⋊D3—51no—
63C22×C3⋊D3C2×D512yes—
64C2×C32×C4—52no—
65#638—102no—
66C2×C3⋊Dic3—51no—
67C4⋊(C3⋊D3)—104no—
68C22×C3×C5—28no—
69C22×C3×C5D1218yescomplemented
70C22×C3×C5C22×D314yes—
71C2×D15—64no—
72C2×D15—68no—
73C2×C5×D3—316no—
74C2×C5×D3—632no—
75C2×C5×D3—68no—
76C2×C5×D3—68no—
77Dic15—64no—
78C3×Dic5—28no—
79C23×D3—34no—
80C2×#67—154no—
81C2×D12—158no—
82C3×C22⋊C4—54no—
83(C2×D3)⋊C4—158no—
84C32×C5#12011yescharacteristic, complemented, Hall
85C23×C5—92no—
86C23×C5—184no—
87C23×C5—182no—
88C23×C5C2×C3⋊D311yescharacteristic
89C22×D5—91no—
90C22⋊D5—184no—
91C22⋊D5—182no—
92C2×Dic5—91no—
93C2×Dic5C2×C3⋊D312yescomplemented
94C22×C32—22no—
95C22×C32C22⋊D512yescomplemented
96C22×C32C22×D511yescharacteristic
97C2×C3⋊D3—28no—
98C2×C3⋊D3—22no—
99C2×C3⋊D3—22no—
100C2×C3⋊D3—102no—
101C2×C3⋊D3—101no—
102C2×C3⋊D3C22⋊D514yescomplemented
103C32×C4—102no—
104C3⋊Dic3—101no—
105#120—451noSylow
106C2×C3×C5—28no—
107C2×C3×C5C2×D1214yes—
108C2×C3×C5D3×D418yes—
109D15—124no—
110C5×D3—616no—
111C23×C3D3×D514yes—
112C22×D3—38no—
113C22×D3—616no—
114C22×D3—68no—
115C22×D3—154no—
116C2×C3×C4—58no—
117#67—308no—
118C2×Dic3—154no—
119D12—3016no—
120C22×C5—22no—
121C22×C5—94no—
122C22×C5—188no—
123C22×C5—182no—
124C22×C5—182no—
125C22×C5C4⋊(C3⋊D3)12yescomplemented
126C22×C5C22×C3⋊D311yescharacteristic
127C2×D5—181no—
128C2×D5—182no—
129Dic5—22no—
130Dic5—181no—
131C2×C32—22no—
132C2×C32C2×C22⋊D511yescharacteristic
133C2×C32C2×C22⋊D512yes—
134C3⋊D3—24no—
135C3⋊D3—201no—
136C24—91no—
137C2×D4—452no—
138C2×D4—451no—
139C22⋊C4—51no—
140C22⋊C4—452no—
141C3×C5#88214yescomplemented
142C22×C3—28no—
143C22×C3#120318yescomplemented
144C22×C3C2×D3×D514yes—
145C2×D3—316no—
146C2×D3—632no—
147C2×D3—68no—
148C2×D3—68no—
149C2×D3—304no—
150C2×D3—308no—
151C3×C4—108no—
152Dic3—304no—
153C2×C5—22no—
154C2×C5—184no—
155C2×C5C2×C4⋊(C3⋊D3)11yescharacteristic
156C2×C5D4×C3⋊D312yes—
157D5—361no—
158C32#409911yescharacteristic, complemented, Sylow
159C23—92no—
160C23—184no—
161C23—182no—
162C23—451no—
163C23D5×C3⋊D311yescharacteristic
164D4—904no—
165D4—902no—
166C2×C4—52no—
167C2×C4—451no—
168C2×C3—28no—
169C2×C3C2×#120314yes—
170C2×C3D3×C22⋊D518yes—
171D3—616no—
172D3—604no—
173C5#6409111yescharacteristic, complemented, Sylow
174C22—22no—
175C22—94no—
176C22—188no—
177C22—182no—
178C22—182no—
179C22—901no—
180C22—902no—
181C22#6714012yescomplemented
182C22C2×D5×C3⋊D311yescharacteristic
183C4—102no—
184C4—901no—
185C3#9157014yescomplemented
186C2—22no—
187C2—184no—
188C2—1801no—
189C2C2×#6714011yescharacteristic
190C2C3⋊D3×C22⋊D512yes—
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C23
FittingC23×C32×C5C22
hypercenterC23D5×C3⋊D3
hypocenterC32×C5#120
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×C5×C3⋊D3C2semidirect
2. C2×#67184C2semidirect
3. C2×#67140C2semidirect
4. C32×C22⋊Dic5C2semidirect
5. #10623771C2semidirect
8. C22×C3⋊D15C22semidirect
13. C2×C3⋊Dic15C22semidirect
14. C2×C32×Dic5C22semidirect
20. C3×C22⋊Dic5D3semidirect
23. C22×C32×C5D4semidirect
30. C2×C5×C3⋊D3D4semidirect
34. C23×C3⋊D3D5semidirect
46. C2×C3×Dic5C2×D3semidirect
58. C22⋊Dic5C3⋊D3semidirect
69. C22×C3×C5D12semidirect
84. C32×C5#120semidirect
93. C2×Dic5C2×C3⋊D3semidirect
95. C22×C32C22⋊D5semidirect
102. C2×C3⋊D3C22⋊D5semidirect
125. C22×C5C4⋊(C3⋊D3)semidirect
141. C3×C5#882semidirect
143. C22×C3#1203semidirect
158. C32#4099semidirect
173. C5#64091semidirect
181. C22#67140semidirect
185. C3#91570semidirect

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C2×#671842
C2×#671402
C32×C22⋊Dic52
#106237712
#915703
#640915