Finite Group Databasebeta

← #13086952

Subgroups — #13086952

Order 1440.

408 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 122 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×#67180C211yesmaximal, characteristic
2C2×#67141C211yesmaximal, characteristic
3C5×#3750C211yesmaximal, characteristic
4C32×#683C211yesmaximal, characteristic
5#10623775C211yesmaximal, characteristic
6#10623773C211yesmaximal, characteristic
7Dic5×C3⋊Dic3C211yesmaximal, characteristic
8#91328—34nomaximal
9C2×C32×C4×C5C2211yescharacteristic
10C2×C3⋊Dic15C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12#67180—22no—
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊Dic3C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67141—22no—
18#64097—51nomaximal, Hall
19C2×Dic30—34no—
20C2×#1204—34no—
21C5×Dic3⋊C4—34no—
22C3×#683D314yes—
23Dic3⋊Dic5—34no—
24#6668—34no—
25Dic3×Dic5—34no—
26C22×C32×C5C2311yescharacteristic
27C32×C4×C5—21no—
28C3⋊Dic15—21no—
29C3⋊Dic15D412yes—
30C5×C3⋊Dic3—21no—
31C5×C3⋊Dic3Q812yescomplemented
32C32×Dic5—21no—
33C32×Dic5Q812yescomplemented
34#4034—91noHall
35C2×#634—51no—
36C2×#634—51no—
37C32×C4⋊C4—51no—
38C4⋊(C3⋊Dic3)—51no—
39#3750—51no—
40#3750D511yescharacteristic
41C4×C3⋊Dic3—51no—
42C2×C3×C4×C5C2×D314yes—
43C2×Dic15—34no—
44C2×Dic15—34no—
45Dic30—68no—
46C2×C5×Dic3—34no—
47C2×C5×Dic3—34no—
48C2×C3×Dic5C2×D314yes—
49C2×C3×Dic5C2×D314yes—
50#1204—68no—
51#888—154no—
52C2×C32×C5C2×D411yescharacteristic
53C2×C32×C5C2×Q811yescharacteristic
54C2×C32×C5C2×Q811yescharacteristic
55C2×Dic10—91no—
56C2×Dic10—91no—
57C5×C4⋊C4—91no—
58C4⋊Dic5—91no—
59#683—91no—
60#683C3⋊D311yescharacteristic
61C4×Dic5—91no—
62C2×C32×C4—51no—
63C2×C32×C4—51no—
64C2×C32×C4C2×D511yescharacteristic
65C2×C3⋊Dic3—51no—
66C2×C3⋊Dic3—51no—
67C2×C3⋊Dic3C2×D511yescharacteristic
68C2×C3⋊Dic3C2×D511yescharacteristic
69#634—102no—
70#634—102no—
71C22×C3×C5C22×D314yes—
72C3×C4×C5—24no—
73Dic15—38no—
74Dic15—64no—
75C3×Dic5—24no—
76C3×Dic5Dic618yescomplemented
77C5×Dic3—38no—
78C5×Dic3—64no—
79C2×Dic6—154no—
80C2×Dic6—154no—
81C3×C4⋊C4—54no—
82C4⋊Dic3—154no—
83Dic3⋊C4—34no—
84Dic3⋊C4—154no—
85C4×Dic3—154no—
86C32×C5C4⋊Q811yescharacteristic, complemented, Hall
87C2×C4×C5—91no—
88C2×C4×C5—91no—
89C2×C4×C5C2×C3⋊D311yescharacteristic
90C2×Dic5—91no—
91C2×Dic5—91no—
92C2×Dic5C2×C3⋊D311yescharacteristic
93C2×Dic5C2×C3⋊D311yescharacteristic
94Dic10—182no—
95Dic10—182no—
96C22×C32C22×D511yescharacteristic
97C32×C4—21no—
98C32×C4—52no—
99C32×C4—101no—
100C3⋊Dic3—21no—
101C3⋊Dic3—52no—
102C3⋊Dic3—101no—
103C3⋊Dic3Dic1012yescomplemented
104C4⋊Q8—451noSylow
105C2×C3×C5C2×Dic614yes—
106C2×C3×C5D3×D414yes—
107C2×C3×C5D3×Q814yes—
108C2×C3×C4—54no—
109C2×C3×C4—54no—
110C2×C3×C4D3×D514yes—
111C2×Dic3—34no—
112C2×Dic3—34no—
113C2×Dic3—154no—
114C2×Dic3—154no—
115Dic6—308no—
116Dic6—308no—
117C22×C5C22×C3⋊D311yescharacteristic
118C4×C5—21no—
119C4×C5—92no—
120C4×C5—181no—
121Dic5—21no—
122Dic5—92no—
123Dic5—181no—
124Dic5#63412yescomplemented
125C2×C32C2×Dic1011yescharacteristic
126C2×C32D4×D511yescharacteristic
127C2×C32Q8×D511yescharacteristic
128C2×Q8—451no—
129C2×Q8—451no—
130C4⋊C4—51no—
131C4⋊C4—91no—
132C4⋊C4—451no—
133C4⋊C4—451no—
134C42—451no—
135C3×C5#88814yescomplemented
136C22×C3C2×D3×D514yes—
137C3×C4—24no—
138C3×C4—58no—
139C3×C4—104no—
140Dic3—38no—
141Dic3—64no—
142Dic3—158no—
143Dic3—304no—
144C2×C5C2×#63411yescharacteristic
145C2×C5D4×C3⋊D311yescharacteristic
146C2×C5Q8×C3⋊D311yescharacteristic
147C32#403411yescharacteristic, complemented, Sylow
148Q8—902no—
149Q8—902no—
150C2×C4—51no—
151C2×C4—51no—
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—451no—
155C2×C4—451no—
156C2×C4D5×C3⋊D311yescharacteristic
157C2×C3D5×Dic614yes—
158C2×C3D3×Dic1014yes—
159C2×C3#679014yes—
160C5#6409711yescharacteristic, complemented, Sylow
161C22C2×D5×C3⋊D311yescharacteristic
162C4—21no—
163C4—52no—
164C4—92no—
165C4—101no—
166C4—181no—
167C4—452no—
168C4—901no—
169C3#9132814yescomplemented
170C2D5×#63411yescharacteristic
171C2C3⋊D3×Dic1011yescharacteristic
172C2#1062417311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutator, socle, prime radical, cosocleC22×C32×C5C23
FittingC2×C32×C4×C5C22
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5C4⋊Q8
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
31. C5×C3⋊Dic3Q8semidirect
33. C32×Dic5Q8semidirect
76. C3×Dic5Dic6semidirect
86. C32×C5C4⋊Q8semidirect
103. C3⋊Dic3Dic10semidirect
124. Dic5#634semidirect
135. C3×C5#888semidirect
147. C32#4034semidirect
160. C5#64097semidirect
169. C3#91328semidirect

Maximal subgroups

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

subgroupindex
C2×#671802
C2×#671412
C5×#37502
C32×#6832
#106237752
#106237732
Dic5×C3⋊Dic32
#913283
#640975