Finite Group Databasebeta

← #13088198

Subgroups — #13088198

Order 1440.

468 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×C32×C4×C5C211yesmaximal, characteristic, complemented
2C2×#67184C211yesmaximal, characteristic
3#10623913C211yesmaximal, characteristic, complemented
4#10623908C212yesmaximal, complemented
5#10623906C212yesmaximal, complemented
6#91818—34nomaximal
7C23×C32×C5C2211yescharacteristic
8C22×C3⋊D15C2211yescharacteristic
9C2×C32×C4×C5—22no—
10C2×C32×C4×C5C2212yes—
11#67184—22no—
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3⋊Dic15C2212yes—
14#64138—51nomaximal, Hall
15C22×C3×C4×C5D314yescomplemented
16C2×#1220—34no—
17#6719—34no—
18#6714—38no—
19#6712—38no—
20C22×C32×C5—22no—
21C22×C32×C5D412yes—
22C22×C32×C5C2311yescharacteristic
23C2×C3⋊D15—21no—
24C2×C3⋊D15—22no—
25C32×C4×C5—22no—
26C3⋊Dic15—21no—
27C3⋊Dic15—22no—
28#4075—91noHall
29C22×C32×C4D511yescharacteristic, complemented
30C2×#638—51no—
31#3757—51no—
32#3752—52no—
33#3750—52no—
34C23×C3×C5C2×D314yes—
35C22×D15—34no—
36C2×C3×C4×C5—28no—
37C2×C3×C4×C5C2×D318yes—
38#1220—68no—
39C2×Dic15—34no—
40C2×Dic15—38no—
41#929—154no—
42C2×C32×C5—22no—
43C2×C32×C5C2×D411yescharacteristic
44C2×C32×C5#4112yes—
45C3⋊D15—41no—
46C22×C4×C5C3⋊D311yescharacteristic, complemented
47C2×C22⋊D5—91no—
48C22⋊Dic5—91no—
49#685—92no—
50#683—92no—
51C23×C32C2×D511yescharacteristic
52C22×C3⋊D3—51no—
53C2×C32×C4—22no—
54C2×C32×C4C2×D512yes—
55#638—102no—
56C2×C3⋊Dic3—51no—
57C2×C3⋊Dic3—52no—
58C22×C3×C5—28no—
59C22×C3×C5#6718yes—
60C22×C3×C5C22×D314yes—
61C2×D15—68no—
62C2×D15—64no—
63C3×C4×C5—28no—
64Dic15—68no—
65Dic15—64no—
66C22×C3×C4D1514yescomplemented
67C2×#67—154no—
68#217—154no—
69(C2×D3)⋊C4—158no—
70Dic3⋊C4—158no—
71C32×C5#12311yescharacteristic, complemented, Hall
72C23×C5C2×C3⋊D311yescharacteristic
73C22×D5—91no—
74C2×C4×C5—22no—
75C2×C4×C5C2×C3⋊D312yes—
76C22⋊D5—182no—
77C2×Dic5—91no—
78C2×Dic5—92no—
79C22×C32—22no—
80C22×C32C22⋊D512yes—
81C22×C32C22×D511yescharacteristic
82C2×C3⋊D3—102no—
83C2×C3⋊D3—101no—
84C32×C4—22no—
85C3⋊Dic3—102no—
86C3⋊Dic3—101no—
87#123—451noSylow
88C2×C3×C5—28no—
89C2×C3×C5#23518yes—
90C2×C3×C5C2×#6714yes—
91D15—124no—
92C23×C3C2×D1514yes—
93C22×D3—154no—
94C2×C3×C4—28no—
95C2×C3×C4C2×D1518yes—
96#67—308no—
97C2×Dic3—154no—
98C2×Dic3—158no—
99C22×C5—22no—
100C22×C5#63812yes—
101C22×C5C22×C3⋊D311yescharacteristic
102C2×D5—182no—
103C2×D5—181no—
104C4×C5—22no—
105Dic5—182no—
106Dic5—181no—
107C2×C32—22no—
108C2×C32#70912yes—
109C2×C32C2×C22⋊D511yescharacteristic
110C3⋊D3—201no—
111C2×D4—451no—
112C22×C4C3⋊D1511yescharacteristic, complemented
113C4⋊C4—452no—
114C22⋊C4—451no—
115C22⋊C4—452no—
116C3×C5#92914yescomplemented
117C22×C3—28no—
118C22×C3#122018yes—
119C22×C3C22×D1514yes—
120C2×D3—308no—
121C2×D3—304no—
122C3×C4—28no—
123Dic3—308no—
124Dic3—304no—
125C2×C5—22no—
126C2×C5#382812yes—
127C2×C5C2×#63811yescharacteristic
128D5—361no—
129C32#407511yescharacteristic, complemented, Sylow
130C23—451no—
131C23C2×C3⋊D1511yescharacteristic
132D4—902no—
133C2×C4—22no—
134C2×C4—452no—
135C2×C4—451no—
136C2×C4C2×C3⋊D1512yes—
137C2×C3—28no—
138C2×C3#681718yes—
139C2×C3C2×#122014yes—
140D3—604no—
141C5#6413811yescharacteristic, complemented, Sylow
142C22—22no—
143C22—902no—
144C22—901no—
145C22#6718412yes—
146C22C22×C3⋊D1511yescharacteristic
147C4—22no—
148C4—902no—
149C4—901no—
150C3#9181814yescomplemented
151C2—22no—
152C2—1801no—
153C2#1062428312yes—
154C2C2×#6718411yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊D15
commutator, socle, cosocleC22×C32×C5C23
FittingC22×C32×C4×C5C2
prime radicalC2×#67184C2
hypercenterC22×C4C3⋊D15
hypocenterC32×C5#123
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4×C5C2semidirect
3. #10623913C2semidirect
4. #10623908C2semidirect
5. #10623906C2semidirect
15. C22×C3×C4×C5D3semidirect
29. C22×C32×C4D5semidirect
46. C22×C4×C5C3⋊D3semidirect
66. C22×C3×C4D15semidirect
71. C32×C5#123semidirect
112. C22×C4C3⋊D15semidirect
116. C3×C5#929semidirect
129. C32#4075semidirect
141. C5#64138semidirect
150. C3#91818semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×C52
C2×#671842
#106239132
#106239082
#106239062
#918183
#641385