Finite Group Databasebeta

← #13087047

Subgroups — #13087047

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×C32×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#67138C212yesmaximal, complemented
4#10623913C211yesmaximal, characteristic, complemented
5#10623771C212yesmaximal, complemented
6#91568—34nomaximal
7C23×C32×C5C2211yescharacteristic
8C22×C5×C3⋊D3—22no—
9C22×C5×C3⋊D3—24no—
10C22×C5×C3⋊D3C2212yes—
11C22×C32×D5C2211yescharacteristic, complemented
12C2×C3⋊Dic15C2212yescomplemented
13C32×C22⋊D5—22no—
14C2×C32×Dic5C2211yescharacteristic, complemented
15#67138—24no—
16#64146—51nomaximal, Hall
17C23×C5×D3—34no—
18C2×C3×C22⋊D5D314yescomplemented
19C2×#1201—38no—
20#6719—34no—
21(C2×D3)⋊Dic5—38no—
22C22×C32×C5—22no—
23C22×C32×C5D412yescomplemented
24C22×C32×C5C2311yescharacteristic
25C2×C5×C3⋊D3—28no—
26C2×C5×C3⋊D3—22no—
27C2×C5×C3⋊D3—22no—
28C2×C5×C3⋊D3D414yescomplemented
29C2×C32×D5—22no—
30C2×C32×D5—21no—
31C3⋊Dic15—22no—
32C32×Dic5—21no—
33#4099—91noHall
34C23×C3⋊D3D511yescharacteristic, complemented
35C2×C32×D4—51no—
36C2×#638—52no—
37#3757—51no—
38#3752—52no—
39C23×C3×C5C2×D314yes—
40C22×C5×D3—38no—
41C22×C5×D3—616no—
42C22×C5×D3—68no—
43C22×C3×D5C2×D314yescomplemented
44C2×Dic15—38no—
45C3×C22⋊D5—28no—
46C2×C3×Dic5C2×D314yescomplemented
47#1201—616no—
48#937—154no—
49C2×C32×C5—22no—
50C2×C32×C5C2×D412yes—
51C2×C32×C5C2×D411yescharacteristic
52C5×C3⋊D3—24no—
53C32×D5—41no—
54C24×C5—91no—
55C2×C22⋊D5—92no—
56C2×C22⋊D5C3⋊D311yescharacteristic, complemented
57C22⋊Dic5—91no—
58C22⋊Dic5—92no—
59C23×C32—51no—
60C23×C32C2×D511yescharacteristic
61C22×C3⋊D3—22no—
62C22×C3⋊D3—24no—
63C22×C3⋊D3C2×D512yes—
64C32×D4—102no—
65C2×C32×C4—51no—
66#638—104no—
67C2×C3⋊Dic3—52no—
68C22×C3×C5—28no—
69C22×C3×C5#6718yescomplemented
70C22×C3×C5C22×D314yes—
71C2×C5×D3—316no—
72C2×C5×D3—632no—
73C2×C5×D3—68no—
74C2×C5×D3—68no—
75C2×C3×D5—28no—
76C2×C3×D5—24no—
77Dic15—68no—
78C3×Dic5—24no—
79C23×D3—34no—
80C2×C3×D4—54no—
81C2×#67—158no—
82#217—154no—
83(C2×D3)⋊C4—158no—
84C32×C5#12011yescharacteristic, complemented, Hall
85C23×C5—92no—
86C23×C5—184no—
87C23×C5—182no—
88C23×C5C2×C3⋊D311yescharacteristic
89C22×D5C2×C3⋊D311yescharacteristic, complemented
90C22⋊D5—22no—
91C22⋊D5—184no—
92C2×Dic5—92no—
93C2×Dic5C2×C3⋊D311yescharacteristic, complemented
94C22×C32—22no—
95C22×C32—102no—
96C22×C32—101no—
97C22×C32C22⋊D512yescomplemented
98C22×C32C22×D511yescharacteristic
99C2×C3⋊D3—28no—
100C2×C3⋊D3—22no—
101C2×C3⋊D3—22no—
102C2×C3⋊D3C22⋊D514yescomplemented
103C32×C4—101no—
104C3⋊Dic3—102no—
105#120—451noSylow
106C2×C3×C5—28no—
107C2×C3×C5D3×D418yes—
108C2×C3×C5C2×#6714yes—
109C3×D5—44no—
110C5×D3—616no—
111C23×C3—54no—
112C23×C3D3×D514yes—
113C22×D3—38no—
114C22×D3—616no—
115C22×D3—68no—
116C3×D4—108no—
117C2×C3×C4—54no—
118#67—3016no—
119C2×Dic3—158no—
120C22×C5—22no—
121C22×C5—94no—
122C22×C5—188no—
123C22×C5—182no—
124C22×C5—182no—
125C22×C5#63812yescomplemented
126C22×C5C22×C3⋊D311yescharacteristic
127C2×D5—22no—
128C2×D5—21no—
129Dic5—21no—
130Dic5—182no—
131C2×C32—22no—
132C2×C32—201no—
133C2×C32C2×C22⋊D511yescharacteristic
134C2×C32C2×C22⋊D512yes—
135C3⋊D3—24no—
136C24—91no—
137C2×D4—51no—
138C2×D4—452no—
139C22⋊C4—452no—
140C22⋊C4—451no—
141C3×C5#93714yescomplemented
142C22×C3—28no—
143C22×C3—104no—
144C22×C3—108no—
145C22×C3#120118yescomplemented
146C22×C3C2×D3×D514yes—
147C2×D3—316no—
148C2×D3—632no—
149C2×D3—68no—
150C2×D3—68no—
151C3×C4—104no—
152Dic3—308no—
153C2×C5—22no—
154C2×C5—184no—
155C2×C5D4×C3⋊D312yes—
156C2×C5C2×#63811yescharacteristic
157D5—41no—
158C32#409911yescharacteristic, complemented, Sylow
159C23—51no—
160C23—92no—
161C23—184no—
162C23—182no—
163C23D5×C3⋊D311yescharacteristic
164D4—102no—
165D4—904no—
166C2×C4—51no—
167C2×C4—452no—
168C2×C3—28no—
169C2×C3—204no—
170C2×C3C2×#120114yes—
171C2×C3D3×C22⋊D518yes—
172D3—616no—
173C5#6414611yescharacteristic, complemented, Sylow
174C22—22no—
175C22—94no—
176C22—101no—
177C22—102no—
178C22—188no—
179C22—182no—
180C22—182no—
181C22#6713812yescomplemented
182C22C2×D5×C3⋊D311yescharacteristic
183C4—101no—
184C4—902no—
185C3#9156814yescomplemented
186C2—22no—
187C2—184no—
188C2—201no—
189C2C2×#6713811yescharacteristic
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×C32×C22⋊D5C2semidirect
3. C2×#67138C2semidirect
4. #10623913C2semidirect
5. #10623771C2semidirect
11. C22×C32×D5C22semidirect
12. C2×C3⋊Dic15C22semidirect
14. C2×C32×Dic5C22semidirect
18. C2×C3×C22⋊D5D3semidirect
23. C22×C32×C5D4semidirect
28. C2×C5×C3⋊D3D4semidirect
34. C23×C3⋊D3D5semidirect
43. C22×C3×D5C2×D3semidirect
46. C2×C3×Dic5C2×D3semidirect
56. C2×C22⋊D5C3⋊D3semidirect
69. C22×C3×C5#67semidirect
84. C32×C5#120semidirect
89. C22×D5C2×C3⋊D3semidirect
93. C2×Dic5C2×C3⋊D3semidirect
97. C22×C32C22⋊D5semidirect
102. C2×C3⋊D3C22⋊D5semidirect
125. C22×C5#638semidirect
141. C3×C5#937semidirect
145. C22×C3#1201semidirect
158. C32#4099semidirect
173. C5#64146semidirect
181. C22#67138semidirect
185. C3#91568semidirect

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×C32×C22⋊D52
C2×#671382
#106239132
#106237712
#915683
#641465