Finite Group Databasebeta

← #11749321

Subgroups — #11749321

Order 960.

260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 66 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
1#91836C211yesmaximal, characteristic, complemented
2C2×C5×#215C211yesmaximal, characteristic, complemented
3C2×C3×#689C211yesmaximal, characteristic, complemented
4#91370C211yesmaximal, characteristic, complemented
5C2×#6658C211yesmaximal, characteristic, complemented
6C2×#6654C211yesmaximal, characteristic
7#90951C211yesmaximal, characteristic, complemented
8#65457—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×D60C2211yescharacteristic
11C2×C5×D12C2211yescharacteristic
12C2×C3×Dic10C2211yescharacteristic
13#6714—22no—
14C4×Dic15C2211yescharacteristic
15C5×#215—22no—
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#689—22no—
18C2×C3×#168C2211yescharacteristic
19(C2×D3)⋊Dic5—22no—
20#6658—22no—
21#6654—22no—
22#5191—51nomaximal, Hall
23C2×C5×SD16—31no—
24#4093—31no—
25C2×#689D311yescharacteristic, complemented
26#4082—31no—
27C2×#686—31no—
28C2×#677—31no—
29C8×Dic5—31no—
30C22×D15—21no—
31C22×C5×D3—21no—
32C3×C5×Q8—21no—
33C3×C5×Q8—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36C2×Dic15D412yes—
37D60—21no—
38D60—21no—
39C5×D12—21no—
40C5×D12—21no—
41C2×C3×Dic5—21no—
42C3×Dic10—21no—
43C3×Dic10—21no—
44C3×#168D412yes—
45C5×C3⋊C8D412yes—
46C2×C3×Q16—51no—
47#947—51no—
48#947—51no—
49C2×#215—51no—
50C2×#215D511yescharacteristic, complemented
51C2×D24—51no—
52C8×Dic3—51no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×C5×D4—31no—
55C2×D20—31no—
56C2×Dic10C2×D311yescharacteristic
57C5×SD16—62no—
58C2×C5×C8—31no—
59C22⋊Dic5—62no—
60#689—22no—
61#686—62no—
62#685—62no—
63C4×Dic5—31no—
64C2×#168C2×D311yescharacteristic
65#677—62no—
66#495—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×D15—41no—
69C2×D15—42no—
70C2×C5×D3—41no—
71C2×C5×D3—42no—
72C3×C4×C5—41no—
73C3×C4×C5C2×D411yescharacteristic
74C3×C4×C5C2×D411yescharacteristic
75Dic15—22no—
76C3×Dic5—41no—
77C2×C3×Q8—51no—
78C2×C3×Q8C2×D511yescharacteristic
79C2×D12—51no—
80C2×D12C2×D511yescharacteristic
81C3×Q16—102no—
82C2×C3×C8—51no—
83#215—22no—
84#215—102no—
85(C2×D3)⋊C4—102no—
86(C2×D3)⋊C4—102no—
87C4×Dic3—51no—
88C2×C3⋊C8C2×D511yescharacteristic
89D24—102no—
90C23×C5—61no—
91C22×D5—61no—
92C5×Q8—21no—
93C5×Q8—21no—
94C5×D4—61no—
95C5×D4—61no—
96C2×C4×C5—21no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—21no—
99C2×Dic5—32no—
100D20—61no—
101D20—61no—
102Dic10—21no—
103Dic10—21no—
104C5×C8—32no—
105#168#6712yes—
106C2×Q16—51no—
107C2×SD16—31no—
108C2×SD16—151no—
109C2×D8—151no—
110#124—151no—
111#124—151no—
112C4×C8—151no—
113C2×C3×C5#12711yescharacteristic
114C2×C3×C5#13512yes—
115D15—81no—
116C5×D3—81no—
117C22×D3—21no—
118C22×D3—101no—
119C3×Q8—21no—
120C3×Q8—21no—
121C3×Q8—101no—
122C3×Q8—101no—
123C2×C3×C4—21no—
124C2×C3×C4—101no—
125C2×C3×C4C22×D511yescharacteristic
126C2×Dic3—52no—
127D12—21no—
128D12—21no—
129D12—101no—
130D12—101no—
131C3×C8—52no—
132C3⋊C8C22⋊D512yes—
133C22×C5—122no—
134C22×C5—121no—
135C22×C5D3×D411yescharacteristic
136C2×D5—122no—
137C2×D5—121no—
138C4×C5—41no—
139C4×C5D3×D411yescharacteristic
140C4×C5C2×#6711yescharacteristic
141Dic5—41no—
142Dic5—62no—
143C2×Q8—51no—
144C2×Q8D3×D511yescharacteristic
145C2×D4—31no—
146C2×D4—151no—
147Q16—102no—
148SD16—62no—
149SD16—302no—
150D8—302no—
151C2×C8—31no—
152C2×C8—51no—
153C22⋊C4—302no—
154C22⋊C4—302no—
155C42—151no—
156C3×C5#49511yescharacteristic, complemented, Hall
157C22×C3D4×D511yescharacteristic
158C2×D3—42no—
159C2×D3—41no—
160C2×D3—202no—
161C2×D3—201no—
162C3×C4—41no—
163C3×C4—201no—
164C3×C4D4×D511yescharacteristic
165C3×C4C2×C22⋊D511yescharacteristic
166Dic3—102no—
167C2×C5—241no—
168C2×C5#91912yes—
169C2×C5#94011yescharacteristic
170D5—241no—
171C23—61no—
172C23—301no—
173Q8—21no—
174Q8—21no—
175Q8—101no—
176Q8—101no—
177D4—61no—
178D4—61no—
179D4—301no—
180D4—301no—
181C2×C4—21no—
182C2×C4—101no—
183C2×C4—152no—
184C2×C4C2×D3×D511yescharacteristic
185C8—32no—
186C8—52no—
187C2×C3#406212yes—
188C2×C3#408611yescharacteristic
189D3—81no—
190D3—401no—
191C5#519111yescharacteristic, complemented, Sylow
192C22—122no—
193C22—121no—
194C22—602no—
195C22—601no—
196C22#679011yescharacteristic
197C4—41no—
198C4—201no—
199C4—302no—
200C4D5×#6711yescharacteristic
201C4D3×C22⋊D511yescharacteristic
202C3#6545711yescharacteristic, complemented, Sylow
203C2—241no—
204C2—1201no—
205C2#9152312yes—
206C2#9156711yescharacteristic
subgroupG/H
centerC22#6790
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC2×#6654C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#495
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #91836C2semidirect
2. C2×C5×#215C2semidirect
3. C2×C3×#689C2semidirect
4. #91370C2semidirect
5. C2×#6658C2semidirect
7. #90951C2semidirect
25. C2×#689D3semidirect
50. C2×#215D5semidirect
156. C3×C5#495semidirect
191. C5#5191semidirect
202. C3#65457semidirect

Maximal subgroups

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

subgroupindex
#918362
C2×C5×#2152
C2×C3×#6892
#913702
C2×#66582
C2×#66542
#909512
#654573
#51915