Finite Group Databasebeta

← #11748845

Subgroups — #11748845

Order 960.

364 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 112 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×C5×Dic6C211yesmaximal, characteristic
2C2×C3×#683C211yesmaximal, characteristic
3C2×#6669C212yesmaximal
4#91115C211yesmaximal, characteristic
5#90994C212yesmaximal
6#65518—31nomaximal, Hall
7C22×C3×C4×C5C2211yescharacteristic
8C22×Dic15C2212yes—
9C22×C5×Dic3C2212yes—
10C2×C5×Dic6—22no—
11C2×C5×Dic6—24no—
12C22×C3×Dic5C2211yescharacteristic
13C22×C3×Dic5C2211yescharacteristic
14C3×#683—22no—
15#6669—24no—
16#4979—51nomaximal, Hall
17C22×C5×Q8—31no—
18C2×#683—32no—
19C2×#683D311yescharacteristic
20#3963—31no—
21#3963—32no—
22C23×C3×C5C2311yescharacteristic
23C2×C3×C4×C5—22no—
24C2×C3×C4×C5D412yes—
25C2×Dic15—22no—
26C2×Dic15—22no—
27C2×Dic15Q814yescomplemented
28C2×C5×Dic3—22no—
29C2×C5×Dic3—22no—
30C2×C5×Dic3D414yes—
31C5×Dic6—28no—
32C2×C3×Dic5—21no—
33C2×C3×Dic5—21no—
34C2×C3×Dic5—22no—
35C2×C3×Dic5—21no—
36C2×C3×Dic5Q812yescomplemented
37C22×Dic6D511yescharacteristic
38C2×C3×C4⋊C4—51no—
39C2×Dic3⋊C4—52no—
40C3⋊#95—51no—
41C3⋊#95—52no—
42C2×C5×Q8—64no—
43C2×C5×Q8—62no—
44C22×C4×C5—32no—
45C22×C4×C5C2×D311yescharacteristic
46C22×Dic5—32no—
47C22×Dic5C2×D311yescharacteristic
48C22×Dic5C2×D311yescharacteristic
49#683—22no—
50#683—64no—
51#395—151noSylow
52C22×C3×C5C2×D412yes—
53C22×C3×C5C2×D411yescharacteristic
54C22×C3×C5C2×Q811yescharacteristic
55C22×C3×C5C2×Q812yes—
56C22×C3×C5#4111yescharacteristic
57C3×C4×C5—22no—
58Dic15—24no—
59C3×Dic5—22no—
60C3×Dic5—41no—
61C5×Dic3—24no—
62C22×C3×C4—51no—
63C22×C3×C4—51no—
64C22×C3×C4C2×D511yescharacteristic
65C22×Dic3—52no—
66C22×Dic3C2×D512yes—
67C2×Dic6—22no—
68C2×Dic6—24no—
69C3×C4⋊C4—102no—
70Dic3⋊C4—104no—
71C23×C5C22×D311yescharacteristic
72C5×Q8—68no—
73C2×C4×C5—22no—
74C2×C4×C5—34no—
75C2×C4×C5—62no—
76C2×C4×C5—62no—
77C2×C4×C5#6712yes—
78C2×Dic5—21no—
79C2×Dic5—21no—
80C2×Dic5—22no—
81C2×Dic5—21no—
82C2×Dic5—34no—
83C2×Dic5—62no—
84C2×Dic5—62no—
85C2×Dic5Dic612yescomplemented
86C22×Q8—31no—
87C2×C4⋊C4—51no—
88C2×C4⋊C4—152no—
89#95—152no—
90#95—151no—
91C2×C3×C5#12011yescharacteristic
92C2×C3×C5C22⋊Q812yes—
93C2×C3×C5C22⋊Q811yescharacteristic
94C2×C3×C5C4⋊Q812yes—
95C2×C3×C5C4⋊Q811yescharacteristic
96C23×C3C22×D511yescharacteristic
97C2×C3×C4—22no—
98C2×C3×C4—52no—
99C2×C3×C4—101no—
100C2×C3×C4—101no—
101C2×C3×C4—102no—
102C2×C3×C4—101no—
103C2×C3×C4C22⋊D512yes—
104C2×Dic3—22no—
105C2×Dic3—22no—
106C2×Dic3—54no—
107C2×Dic3—102no—
108C2×Dic3—102no—
109C2×Dic3C22⋊D514yes—
110Dic6—28no—
111C22×C5C2×Dic611yescharacteristic
112C22×C5#23511yescharacteristic
113C22×C5D3×D412yes—
114C22×C5D3×Q812yes—
115C22×C5C2×#6711yescharacteristic
116C4×C5—22no—
117C4×C5—64no—
118Dic5—22no—
119Dic5—41no—
120Dic5—64no—
121C2×Q8—64no—
122C2×Q8—62no—
123C22×C4—32no—
124C22×C4—51no—
125C22×C4—51no—
126C22×C4—152no—
127C22×C4D3×D511yescharacteristic
128C4⋊C4—102no—
129C4⋊C4—304no—
130C3×C5#39511yescharacteristic, complemented, Hall
131C22×C3Q8×D511yescharacteristic
132C22×C3Q8×D512yes—
133C22×C3#71311yescharacteristic
134C22×C3C2×C22⋊D511yescharacteristic
135C22×C3C2×C22⋊D512yes—
136C3×C4—22no—
137C3×C4—102no—
138C3×C4—201no—
139Dic3—24no—
140Dic3—104no—
141C2×C5#88812yes—
142C2×C5#89612yes—
143C2×C5#92411yescharacteristic
144C2×C5#93711yescharacteristic
145C2×C5#94411yescharacteristic
146C23C2×D3×D511yescharacteristic
147Q8—68no—
148C2×C4—22no—
149C2×C4—34no—
150C2×C4—52no—
151C2×C4—62no—
152C2×C4—62no—
153C2×C4—101no—
154C2×C4—101no—
155C2×C4—101no—
156C2×C4—102no—
157C2×C4—154no—
158C2×C4—302no—
159C2×C4—302no—
160C2×C4#120112yes—
161C2×C3#409012yes—
162C2×C3#409011yescharacteristic
163C2×C3#409212yes—
164C2×C3#409211yescharacteristic
165C2×C3#409911yescharacteristic
166C5#497911yescharacteristic, complemented, Sylow
167C22D5×Dic611yescharacteristic
168C22D15⋊Q812yes—
169C22#677311yescharacteristic
170C22C2×#120111yescharacteristic
171C22D3×C22⋊D512yes—
172C4—22no—
173C4—64no—
174C4—102no—
175C4—201no—
176C4—304no—
177C3#6551811yescharacteristic, complemented, Sylow
178C2#9132912yes—
179C2#9135911yescharacteristic
180C2#9138511yescharacteristic
181C2#9142412yes—
182C2#9156811yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×D5
commutator, socle, prime radical, cosocleC23×C3×C5C23
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#395
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
27. C2×Dic15Q8semidirect
36. C2×C3×Dic5Q8semidirect
85. C2×Dic5Dic6semidirect
130. C3×C5#395semidirect
166. C5#4979semidirect
177. C3#65518semidirect

Maximal subgroups

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

subgroupindex
C22×C5×Dic62
C2×C3×#6832
C2×#66692
#911152
#909942
#655183
#49795