Finite Group Databasebeta

← #13087041

Subgroups — #13087041

Order 1440.

780 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 152 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×C32×D5C211yesmaximal, characteristic, complemented
2C2×C5×#638C211yesmaximal, characteristic, complemented
3C2×#67138C212yesmaximal, complemented
4#10623913C211yesmaximal, characteristic, complemented
5#10623770C212yesmaximal, complemented
6#91563—34nomaximal
7C23×C32×C5C2211yescharacteristic
8C22×C5×C3⋊D3C2211yescharacteristic, complemented
9C22×C32×D5—22no—
10C22×C32×D5—24no—
11C22×C32×D5C2212yes—
12C2×C3⋊Dic15C2212yescomplemented
13C5×#638—22no—
14C2×C5×C3⋊Dic3C2211yescharacteristic, complemented
15#67138—24no—
16#64162—51nomaximal, Hall
17C23×C3×D5D314yescomplemented
18C2×C5×#67—34no—
19C2×#1201—38no—
20#6719—34no—
21#6665—38no—
22C22×C32×C5—22no—
23C22×C32×C5D412yescomplemented
24C22×C32×C5C2311yescharacteristic
25C2×C5×C3⋊D3—22no—
26C2×C5×C3⋊D3—21no—
27C2×C32×D5—28no—
28C2×C32×D5—22no—
29C2×C32×D5—22no—
30C2×C32×D5D414yescomplemented
31C3⋊Dic15—22no—
32C5×C3⋊Dic3—21no—
33#4083—91noHall
34C24×C32—51no—
35C2×#638—52no—
36C2×#638D511yescharacteristic, complemented
37#3757—51no—
38#3757—52no—
39C23×C3×C5C2×D314yes—
40C22×C5×D3—34no—
41C22×C3×D5—28no—
42C22×C3×D5—216no—
43C22×C3×D5C2×D318yes—
44C2×Dic15—38no—
45C5×#67—68no—
46C2×C5×Dic3—34no—
47#1201—616no—
48#953—154no—
49C2×C32×C5—22no—
50C2×C32×C5C2×D412yes—
51C2×C32×C5C2×D411yescharacteristic
52C5×C3⋊D3—41no—
53C32×D5—24no—
54C23×D5C3⋊D311yescharacteristic, complemented
55C2×C5×D4—91no—
56C2×C22⋊D5—92no—
57C22⋊Dic5—91no—
58#685—92no—
59C23×C32—52no—
60C23×C32—104no—
61C23×C32—102no—
62C23×C32C2×D511yescharacteristic
63C22×C3⋊D3C2×D511yescharacteristic, complemented
64#638—22no—
65#638—104no—
66C2×C3⋊Dic3—52no—
67C2×C3⋊Dic3C2×D511yescharacteristic, complemented
68C22×C3×C5—28no—
69C22×C3×C5#6718yescomplemented
70C22×C3×C5C22×D314yes—
71C2×C5×D3—68no—
72C2×C5×D3—64no—
73C2×C3×D5—232no—
74C2×C3×D5—28no—
75C2×C3×D5—28no—
76C2×C3×D5#67116yescomplemented
77Dic15—68no—
78C5×Dic3—64no—
79C24×C3—54no—
80C2×#67—34no—
81C2×#67—158no—
82#217—158no—
83#217—154no—
84C32×C5#12011yescharacteristic, complemented, Hall
85C23×C5—91no—
86C23×C5C2×C3⋊D311yescharacteristic
87C22×D5—22no—
88C22×D5—24no—
89C22×D5C2×C3⋊D312yes—
90C5×D4—182no—
91C2×C4×C5—91no—
92C22⋊D5—184no—
93C2×Dic5—92no—
94C22×C32—22no—
95C22×C32—54no—
96C22×C32—108no—
97C22×C32—102no—
98C22×C32—102no—
99C22×C32C22⋊D512yescomplemented
100C22×C32C22×D511yescharacteristic
101C2×C3⋊D3—22no—
102C2×C3⋊D3—21no—
103C3⋊Dic3—21no—
104C3⋊Dic3—102no—
105#120—451noSylow
106C2×C3×C5—28no—
107C2×C3×C5C2×#6714yes—
108C2×C3×C5C2×#6718yes—
109C3×D5—216no—
110C5×D3—124no—
111C23×C3—58no—
112C23×C3—1016no—
113C23×C3—108no—
114C23×C3D3×D514yes—
115C22×D3—34no—
116#67—68no—
117#67—3016no—
118C2×Dic3—34no—
119C2×Dic3—158no—
120C22×C5—22no—
121C22×C5—182no—
122C22×C5—181no—
123C22×C5#63812yescomplemented
124C22×C5C22×C3⋊D311yescharacteristic
125C2×D5—28no—
126C2×D5—22no—
127C2×D5—22no—
128C2×D5#63814yescomplemented
129C4×C5—181no—
130Dic5—182no—
131C2×C32—22no—
132C2×C32—104no—
133C2×C32D4×D512yes—
134C2×C32C2×C22⋊D511yescharacteristic
135C3⋊D3—41no—
136C24—51no—
137C2×D4—91no—
138C2×D4—452no—
139C22⋊C4—452no—
140C22⋊C4—451no—
141C3×C5#95314yescomplemented
142C22×C3—28no—
143C22×C3—516no—
144C22×C3—1032no—
145C22×C3—108no—
146C22×C3—108no—
147C22×C3#120118yescomplemented
148C22×C3C2×D3×D514yes—
149C2×D3—64no—
150C2×D3—68no—
151Dic3—64no—
152Dic3—308no—
153C2×C5—22no—
154C2×C5—361no—
155C2×C5C2×#63811yescharacteristic
156C2×C5C2×#63812yes—
157D5—24no—
158C32#408311yescharacteristic, complemented, Sylow
159C23—52no—
160C23—91no—
161C23—104no—
162C23—102no—
163C23D5×C3⋊D311yescharacteristic
164D4—182no—
165D4—904no—
166C2×C4—91no—
167C2×C4—452no—
168C2×C3—28no—
169C2×C3—1016no—
170C2×C3C2×#120114yes—
171C2×C3D5×#6718yes—
172D3—124no—
173C5#6416211yescharacteristic, complemented, Sylow
174C22—22no—
175C22—54no—
176C22—108no—
177C22—102no—
178C22—102no—
179C22—181no—
180C22—182no—
181C22#6713812yescomplemented
182C22C2×D5×C3⋊D311yescharacteristic
183C4—181no—
184C4—902no—
185C3#9156314yescomplemented
186C2—22no—
187C2—104no—
188C2—361no—
189C2C2×#6713811yescharacteristic
190C2D5×#63812yes—
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×C32×D5C2semidirect
2. C2×C5×#638C2semidirect
3. C2×#67138C2semidirect
4. #10623913C2semidirect
5. #10623770C2semidirect
8. C22×C5×C3⋊D3C22semidirect
12. C2×C3⋊Dic15C22semidirect
14. C2×C5×C3⋊Dic3C22semidirect
17. C23×C3×D5D3semidirect
23. C22×C32×C5D4semidirect
30. C2×C32×D5D4semidirect
36. C2×#638D5semidirect
54. C23×D5C3⋊D3semidirect
63. C22×C3⋊D3C2×D5semidirect
67. C2×C3⋊Dic3C2×D5semidirect
69. C22×C3×C5#67semidirect
76. C2×C3×D5#67semidirect
84. C32×C5#120semidirect
99. C22×C32C22⋊D5semidirect
123. C22×C5#638semidirect
128. C2×D5#638semidirect
141. C3×C5#953semidirect
147. C22×C3#1201semidirect
158. C32#4083semidirect
173. C5#64162semidirect
181. C22#67138semidirect
185. C3#91563semidirect

Maximal subgroups

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

subgroupindex
C23×C32×D52
C2×C5×#6382
C2×#671382
#106239132
#106237702
#915633
#641625