Finite Group Databasebeta

← #13086201

Subgroups — #13086201

Order 1440.

310 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 82 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×C5×#627C211yesmaximal, characteristic
2C2×#67141C211yesmaximal, characteristic
3#10623828C211yesmaximal, characteristic
4#10623814C212yesmaximal
5C3×#6669C212yesmaximal
6#91329—32nomaximal
7C2×C3⋊Dic15C2211yescharacteristic
8C2×C5×C3⋊Dic3C2211yescharacteristic
9C2×C3×Dic15C2212yes—
10C2×C3×C5×Dic3C2212yes—
11C2×C32×Dic5C2211yescharacteristic
12C5×#627—22no—
13#67141—22no—
14#63840—51nomaximal, Hall
15C2×C5×Dic6—32no—
16C2×#1204—32no—
17C2×#1204—61no—
18#6712—32no—
19C3×#683—32no—
20#6669D312yes—
21#6668—32no—
22Dic3×Dic5—32no—
23C22×C32×C5C2311yescharacteristic
24C3⋊Dic15—21no—
25C5×C3⋊Dic3D412yes—
26C3×Dic15Q814yescomplemented
27C3×C5×Dic3—22no—
28C32×Dic5—21no—
29#4090—91noHall
30C2×#634—51no—
31C2×#627D511yescharacteristic
32C3×Dic3⋊C4—52no—
33Dic3⋊Dic3—52no—
34Dic32—51no—
35C2×C3×C4×C5—32no—
36C2×Dic15—32no—
37C2×Dic15—61no—
38C2×Dic15C2×D312yes—
39C2×C5×Dic3—32no—
40C2×C5×Dic3—61no—
41C2×C5×Dic3C2×D312yes—
42C5×Dic6—64no—
43C2×C3×Dic5—21no—
44C2×C3×Dic5—32no—
45C2×C3×Dic5C2×D312yes—
46#1204—64no—
47#1204—64no—
48#888—152no—
49C2×C32×C5C2×D411yescharacteristic
50C2×C32×C5C2×Q812yes—
51C2×C5×Q8—91no—
52C2×Dic10—91no—
53#683—32no—
54#683—92no—
55C4×Dic5—91no—
56C2×C32×C4—51no—
57C2×C3⋊Dic3—51no—
58C2×C3⋊Dic3C2×D511yescharacteristic
59#634—102no—
60C2×C3×Dic3—52no—
61C2×C3×Dic3C2×D512yes—
62#627—22no—
63C22×C3×C5—21no—
64C22×C3×C5C22×D312yes—
65C3×C4×C5—62no—
66Dic15—62no—
67Dic15—62no—
68Dic15Dic614yescomplemented
69C3×Dic5—22no—
70C3×Dic5—22no—
71C3×Dic5—34no—
72C5×Dic3—22no—
73C5×Dic3—34no—
74C5×Dic3—62no—
75C2×Dic6—32no—
76C2×Dic6—152no—
77C2×Dic6—301no—
78C3×C4⋊C4—152no—
79C4⋊Dic3—152no—
80Dic3⋊C4—52no—
81Dic3⋊C4—152no—
82C4×Dic3—152no—
83C32×C5C4⋊Q811yescharacteristic, complemented, Hall
84C5×Q8—182no—
85C2×C4×C5—32no—
86C2×C4×C5—91no—
87C2×Dic5—32no—
88C2×Dic5—91no—
89C2×Dic5D3211yescharacteristic
90Dic10—182no—
91C22×C32C22×D511yescharacteristic
92C32×C4—101no—
93C3⋊Dic3—101no—
94C3⋊Dic3C22⋊D512yes—
95C3×Dic3—22no—
96C3×Dic3—54no—
97C4⋊Q8—451noSylow
98C2×C3×C5—22no—
99C2×C3×C5—21no—
100C2×C3×C5C2×Dic612yes—
101C2×C3×C5D3×D412yes—
102C2×C3×C5D3×Q812yes—
103C2×C3×C4—32no—
104C2×C3×C4—52no—
105C2×C3×C4—101no—
106C2×C3×C4—152no—
107C2×Dic3—32no—
108C2×Dic3—52no—
109C2×Dic3—61no—
110C2×Dic3—152no—
111C2×Dic3—301no—
112C2×Dic3D3×D512yes—
113Dic6—64no—
114Dic6—304no—
115Dic6—304no—
116C22×C5C2×D3211yescharacteristic
117C4×C5—62no—
118C4×C5—92no—
119Dic5—21no—
120Dic5—34no—
121Dic5—181no—
122C2×C32Q8×D512yes—
123C2×C32C2×C22⋊D511yescharacteristic
124C2×Q8—91no—
125C2×Q8—451no—
126C4⋊C4—152no—
127C4⋊C4—452no—
128C42—451no—
129C3×C5—21no—
130C3×C5#88812yescomplemented
131C22×C3—21no—
132C22×C3C2×D3×D512yes—
133C3×C4—62no—
134C3×C4—102no—
135C3×C4—102no—
136C3×C4—154no—
137Dic3—22no—
138Dic3—34no—
139Dic3—54no—
140Dic3—62no—
141Dic3—302no—
142Dic3—302no—
143C2×C5D3×Dic612yes—
144C2×C5#381111yescharacteristic
145C32#409011yescharacteristic, complemented, Sylow
146Q8—182no—
147Q8—902no—
148C2×C4—32no—
149C2×C4—51no—
150C2×C4—91no—
151C2×C4—152no—
152C2×C4—451no—
153C2×C3—21no—
154C2×C3—22no—
155C2×C3D5×Dic612yes—
156C2×C3D15⋊Q812yes—
157C2×C3D3×C22⋊D512yes—
158C5#6384011yescharacteristic, complemented, Sylow
159C22D32×D511yescharacteristic
160C4—62no—
161C4—92no—
162C4—101no—
163C4—154no—
164C4—901no—
165C3—21no—
166C3#9132912yescomplemented
167C2#1062402911yescharacteristic
168C2#1062403812yes—
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, prime radical, cosocleC22×C32×C5C23
hypocenterC32×C5C4⋊Q8
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
26. C3×Dic15Q8semidirect
68. Dic15Dic6semidirect
83. C32×C5C4⋊Q8semidirect
130. C3×C5#888semidirect
145. C32#4090semidirect
158. C5#63840semidirect
166. C3#91329semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6272
C2×#671412
#106238282
#106238142
C3×#66692
#913293
#638405