Finite Group Databasebeta

← #13086942

Subgroups — #13086942

Order 1440.

420 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 138 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×#67141C211yesmaximal, characteristic
2#10623906C211yesmaximal, characteristic
3C5×#3750C211yesmaximal, characteristic
4C32×C4×Dic5C211yesmaximal, characteristic
5#10623773C211yesmaximal, characteristic
6Dic5×C3⋊Dic3C211yesmaximal, characteristic
7Dic5×C3⋊Dic3C211yesmaximal, characteristic
8#91323—34nomaximal
9C2×C32×C4×C5C2211yescharacteristic
10C2×C3⋊Dic15C2211yescharacteristic
11C2×C3⋊Dic15C2211yescharacteristic
12C2×C5×C3⋊Dic3C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C32×Dic5C2211yescharacteristic
15C2×C32×Dic5C2211yescharacteristic
16#67141C414yescomplemented
17C4×#634—51nomaximal, Hall
18C2×#1204—34no—
19#6712—34no—
20C5×Dic3⋊C4—34no—
21C3×C4×Dic5D314yes—
22#6668—34no—
23Dic3×Dic5—34no—
24Dic3×Dic5—34no—
25C22×C32×C5C2311yescharacteristic
26C32×C4×C5—21no—
27C3⋊Dic15—21no—
28C3⋊Dic15C2×C412yes—
29C5×C3⋊Dic3—21no—
30C5×C3⋊Dic3C2×C412yes—
31C32×Dic5C2×C412yes—
32C32×Dic5Q812yescomplemented
33#4033—91noHall
34C2×#634—51no—
35C32×C42—51no—
36C4⋊(C3⋊Dic3)—51no—
37#3750—51no—
38#3750D511yescharacteristic
39C4×C3⋊Dic3—51no—
40C4×C3⋊Dic3—51no—
41C2×C3×C4×C5C2×D314yes—
42C2×Dic15—34no—
43C2×Dic15—34no—
44C2×C5×Dic3—34no—
45C2×C5×Dic3—34no—
46C2×C3×Dic5C2×D314yes—
47C2×C3×Dic5C2×D314yes—
48#1204—316no—
49C4×Dic6—154no—
50C2×C32×C5C22×C411yescharacteristic
51C2×C32×C5C2×Q811yescharacteristic
52C2×C32×C5#4111yescharacteristic
53C2×Dic10—91no—
54C5×C4⋊C4—91no—
55#683—91no—
56#683—91no—
57C4×Dic5—91no—
58C4×Dic5—91no—
59C4×Dic5C3⋊D311yescharacteristic
60C2×C32×C4—51no—
61C2×C32×C4—51no—
62C2×C32×C4C2×D511yescharacteristic
63C2×C3⋊Dic3—51no—
64C2×C3⋊Dic3—51no—
65C2×C3⋊Dic3C2×D511yescharacteristic
66C2×C3⋊Dic3C2×D511yescharacteristic
67#634—54no—
68C22×C3×C5C22×D314yes—
69C3×C4×C5—24no—
70Dic15—38no—
71Dic15—64no—
72C3×Dic5Dic618yescomplemented
73C3×Dic5C4×D318yes—
74C5×Dic3—38no—
75C5×Dic3—64no—
76C2×Dic6—154no—
77C3×C42—54no—
78C4⋊Dic3—154no—
79Dic3⋊C4—34no—
80Dic3⋊C4—154no—
81C4×Dic3—154no—
82C4×Dic3—154no—
83C32×C5C4×Q811yescharacteristic, complemented, Hall
84C2×C4×C5—91no—
85C2×C4×C5—91no—
86C2×C4×C5C2×C3⋊D311yescharacteristic
87C2×Dic5—91no—
88C2×Dic5—91no—
89C2×Dic5C2×C3⋊D311yescharacteristic
90C2×Dic5C2×C3⋊D311yescharacteristic
91Dic10—94no—
92C22×C32C22×D511yescharacteristic
93C32×C4—21no—
94C32×C4—52no—
95C32×C4—52no—
96C3⋊Dic3—21no—
97C3⋊Dic3—52no—
98C3⋊Dic3—101no—
99C3⋊Dic3C4×D512yes—
100C4×Q8—451noSylow
101C2×C3×C5C2×Dic614yes—
102C2×C3×C5C2×C4×D314yes—
103C2×C3×C5#23514yes—
104C2×C3×C4—54no—
105C2×C3×C4—54no—
106C2×C3×C4D3×D514yes—
107C2×Dic3—34no—
108C2×Dic3—34no—
109C2×Dic3—154no—
110C2×Dic3—154no—
111Dic6—1516no—
112C22×C5C22×C3⋊D311yescharacteristic
113C4×C5—21no—
114C4×C5—92no—
115C4×C5—181no—
116Dic5—92no—
117Dic5—181no—
118Dic5#63412yescomplemented
119Dic5C4×C3⋊D312yes—
120C2×C32C2×C4×D511yescharacteristic
121C2×C32#71111yescharacteristic
122C2×C32Q8×D511yescharacteristic
123C2×Q8—451no—
124C4⋊C4—91no—
125C4⋊C4—451no—
126C4⋊C4—451no—
127C42—51no—
128C42—451no—
129C42—451no—
130C3×C5C4×Dic614yescomplemented
131C22×C3C2×D3×D514yes—
132C3×C4—24no—
133C3×C4—58no—
134C3×C4—58no—
135Dic3—38no—
136Dic3—64no—
137Dic3—158no—
138Dic3—304no—
139C2×C5C2×#63411yescharacteristic
140C2×C5C2×C4×C3⋊D311yescharacteristic
141C2×C5#382811yescharacteristic
142C32#403311yescharacteristic, complemented, Sylow
143Q8—454no—
144C2×C4—51no—
145C2×C4—51no—
146C2×C4—91no—
147C2×C4—91no—
148C2×C4—451no—
149C2×C4—451no—
150C2×C4D5×C3⋊D311yescharacteristic
151C2×C3D5×Dic614yes—
152C2×C3C4×D3×D514yes—
153C2×C3#678214yes—
154C5C4×#63411yescharacteristic, complemented, Sylow
155C22C2×D5×C3⋊D311yescharacteristic
156C4—21no—
157C4—52no—
158C4—52no—
159C4—92no—
160C4—181no—
161C4—452no—
162C4—901no—
163C3#9132314yescomplemented
164C2D5×#63411yescharacteristic
165C2C4×D5×C3⋊D311yescharacteristic
166C2#1062416511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D5×C3⋊D3
commutatorC2×C32×C5C22×C4
FittingC2×C32×C4×C5C22
socle, prime radical, cosocleC22×C32×C5C23
hypercenterC2×C4D5×C3⋊D3
hypocenterC32×C5C4×Q8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
16. #67141C4semidirect
32. C32×Dic5Q8semidirect
72. C3×Dic5Dic6semidirect
83. C32×C5C4×Q8semidirect
118. Dic5#634semidirect
130. C3×C5C4×Dic6semidirect
142. C32#4033semidirect
154. C5C4×#634semidirect
163. C3#91323semidirect

Maximal subgroups

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

subgroupindex
C2×#671412
#106239062
C5×#37502
C32×C4×Dic52
#106237732
Dic5×C3⋊Dic32
#913233
C4×#6345