Finite Group Databasebeta

← #13086826

Subgroups — #13086826

Order 1440.

408 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×C4×C3⋊D15C211yesmaximal, characteristic
2C5×#3748C211yesmaximal, characteristic, complemented
3C32×#681C211yesmaximal, characteristic, complemented
4#10623756C212yesmaximal, complemented
5#10623753C212yesmaximal, complemented
6#91292—34nomaximal
7C22×C3⋊D15C411yescharacteristic
8C2×C32×C4×C5C2211yescharacteristic
9C2×C3⋊Dic15C411yescharacteristic
10C4×C3⋊D15C411yescharacteristic
11C4×C3⋊D15C411yescharacteristic
12C4×C3⋊D15C2211yescharacteristic
13C4×C3⋊D15C2211yescharacteristic
14C5×C3⋊(C3⋊C8)C2212yescomplemented
15C32×#168C2212yescomplemented
16M16×C3⋊D3—51nomaximal, Hall
17C2×C4×D15—34no—
18C5×#208—34no—
19C3×#681D314yescomplemented
20#6651—38no—
21#6648—38no—
22C22×C32×C5C2×C411yescharacteristic
23C2×C3⋊D15—22no—
24C2×C3⋊D15C2×C411yescharacteristic
25C2×C3⋊D15C2×C411yescharacteristic
26C32×C4×C5C2×C411yescharacteristic
27C32×C4×C5C2311yescharacteristic
28C3⋊Dic15C2×C411yescharacteristic
29C3⋊Dic15C2×C411yescharacteristic
30D5×M16—91noHall
31C2×C4×C3⋊D3—51no—
32C32×M16—51no—
33#3748D511yescharacteristic, complemented
34#3743—52no—
35C8×C3⋊D3—52no—
36C22×D15—34no—
37C2×C3×C4×C5C2×D314yes—
38C2×Dic15—34no—
39C4×D15—34no—
40C4×D15—34no—
41C4×D15—34no—
42C4×D15—34no—
43C3×#168C2×D318yescomplemented
44C5×C3⋊C8—38no—
45D3×M16—154no—
46C2×C32×C5—21no—
47C2×C32×C5C22×C411yescharacteristic
48C3⋊D15—21no—
49C3⋊D15M1612yescomplemented
50C2×C4×D5—91no—
51C5×M16—91no—
52#681C3⋊D311yescharacteristic, complemented
53#676—92no—
54C8×D5—92no—
55C22×C3⋊D3—51no—
56C2×C32×C4C2×D511yescharacteristic
57C2×C3⋊Dic3—51no—
58C4×C3⋊D3—51no—
59C4×C3⋊D3—51no—
60C4×C3⋊D3—51no—
61C4×C3⋊D3—51no—
62C32×C8—52no—
63C3⋊(C3⋊C8)C2×D512yescomplemented
64C22×C3×C5C4×D314yes—
65C2×D15—34no—
66C2×D15—34no—
67C2×D15—68no—
68C3×C4×C5C4×D314yes—
69C3×C4×C5C22×D314yes—
70Dic15—34no—
71Dic15—34no—
72C2×C4×D3—154no—
73C3×M16—54no—
74#208—34no—
75ΓL(1,𝔽25)—158no—
76D3×C8—158no—
77C32×C5C2×M1611yescharacteristic, complemented, Hall
78C22×D5—91no—
79C2×C4×C5C2×C3⋊D311yescharacteristic
80C2×Dic5—91no—
81C4×D5—91no—
82C4×D5—91no—
83C4×D5—91no—
84C4×D5—91no—
85C5×C8—92no—
86#168C2×C3⋊D312yescomplemented
87C22×C32C4×D511yescharacteristic
88C2×C3⋊D3—51no—
89C2×C3⋊D3—51no—
90C2×C3⋊D3—102no—
91C32×C4C4×D511yescharacteristic
92C32×C4C22×D511yescharacteristic
93C3⋊Dic3—51no—
94C3⋊Dic3—51no—
95C2×M16—451noSylow
96C2×C3×C5—24no—
97C2×C3×C5C2×C4×D314yes—
98D15—38no—
99D15—64no—
100C22×D3—154no—
101C2×C3×C4D3×D514yes—
102C2×Dic3—154no—
103C4×D3—154no—
104C4×D3—154no—
105C4×D3—154no—
106C4×D3—154no—
107C3×C8—58no—
108C3⋊C8—38no—
109C22×C5C4×C3⋊D311yescharacteristic
110C2×D5—91no—
111C2×D5—91no—
112C2×D5—182no—
113C4×C5C4×C3⋊D311yescharacteristic
114C4×C5C22×C3⋊D311yescharacteristic
115Dic5—91no—
116Dic5—91no—
117C2×C32—21no—
118C2×C32C2×C4×D511yescharacteristic
119C3⋊D3—52no—
120C3⋊D3—101no—
121C22×C4—451no—
122M16—51no—
123M16—91no—
124M16—452no—
125C2×C8—452no—
126C3×C5D3×M1614yescomplemented
127C22×C3#120014yes—
128C2×D3—154no—
129C2×D3—154no—
130C2×D3—308no—
131C3×C4#120014yes—
132C3×C4C2×D3×D514yes—
133Dic3—154no—
134Dic3—154no—
135C2×C5—21no—
136C2×C5C2×C4×C3⋊D311yescharacteristic
137D5—92no—
138D5—181no—
139C32D5×M1611yescharacteristic, complemented, Sylow
140C23—451no—
141C2×C4—451no—
142C2×C4—451no—
143C2×C4—451no—
144C2×C4—451no—
145C2×C4—451no—
146C2×C4D5×C3⋊D311yescharacteristic
147C8—52no—
148C8—92no—
149C2×C3—24no—
150C2×C3C2×#120014yes—
151D3—158no—
152D3—304no—
153C5M16×C3⋊D311yescharacteristic, complemented, Sylow
154C22—451no—
155C22—451no—
156C22—902no—
157C22#6713711yescharacteristic
158C4—451no—
159C4—451no—
160C4#6713711yescharacteristic
161C4C2×D5×C3⋊D311yescharacteristic
162C3#9129214yescomplemented
163C2—21no—
164C2—452no—
165C2—901no—
166C2C2×#6713711yescharacteristic
subgroupG/H
center, FrattiniC4C2×D5×C3⋊D3
commutator, socleC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
prime radicalC22×C3⋊D15C4
cosocleC32×C4×C5C23
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5C2×M16
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C5×#3748C2semidirect
3. C32×#681C2semidirect
4. #10623756C2semidirect
5. #10623753C2semidirect
14. C5×C3⋊(C3⋊C8)C22semidirect
15. C32×#168C22semidirect
19. C3×#681D3semidirect
33. #3748D5semidirect
43. C3×#168C2×D3semidirect
49. C3⋊D15M16semidirect
52. #681C3⋊D3semidirect
63. C3⋊(C3⋊C8)C2×D5semidirect
77. C32×C5C2×M16semidirect
86. #168C2×C3⋊D3semidirect
126. C3×C5D3×M16semidirect
139. C32D5×M16semidirect
153. C5M16×C3⋊D3semidirect
162. C3#91292semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊D152
C5×#37482
C32×#6812
#106237562
#106237532
#912923
M16×C3⋊D35