Finite Group Databasebeta

← #11749072

Subgroups — #11749072

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#91825C211yesmaximal, characteristic, complemented
2C2×C5×#214C211yesmaximal, characteristic, complemented
3C2×C3×#686C211yesmaximal, characteristic
4#91368C211yesmaximal, characteristic, complemented
5C2×#6663C211yesmaximal, characteristic, complemented
6C2×#6657C211yesmaximal, characteristic, complemented
7#90951C211yesmaximal, characteristic, complemented
8#65457—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10C2×Dic30C2211yescharacteristic
11C2×C5×Dic6C2211yescharacteristic
12C2×C3×D20C2211yescharacteristic
13#6719—22no—
14C4×Dic15C2211yescharacteristic
15C5×#214—22no—
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#686—22no—
18C2×C3×#168C2211yescharacteristic
19#6665—22no—
20#6663—22no—
21#6657—22no—
22#5155—51nomaximal, Hall
23C2×C5×SD16—31no—
24#4093—31no—
25C2×#689—31no—
26#4082—31no—
27C2×#686D311yescharacteristic
28C2×#677—31no—
29C8×Dic5—31no—
30C23×C3×C5—21no—
31C22×C3×D5—21no—
32C3×C5×D4—21no—
33C3×C5×D4—21no—
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15—21no—
36C2×Dic15D412yes—
37Dic30—21no—
38Dic30—21no—
39C2×C5×Dic3—21no—
40C5×Dic6—21no—
41C5×Dic6—21no—
42C3×D20—21no—
43C3×D20—21no—
44C3×#168D412yes—
45C5×C3⋊C8D412yes—
46C2×C3×D8—51no—
47#936—51no—
48#936—51no—
49C2×#214—51no—
50C2×#214D511yescharacteristic, complemented
51C2×Dic12—51no—
52C8×Dic3—51no—
53C2×C5×Q8—31no—
54C2×C5×D4C2×D311yescharacteristic
55C2×D20C2×D311yescharacteristic
56C2×Dic10—31no—
57C5×SD16—62no—
58C2×C5×C8—31no—
59C22⋊Dic5—62no—
60#689—62no—
61#686—22no—
62#685—62no—
63C4×Dic5—31no—
64C2×#168C2×D311yescharacteristic
65#677—62no—
66#495—151noSylow
67C22×C3×C5—41no—
68C22×C3×C5—42no—
69C22×C3×C5C2×D411yescharacteristic
70C2×C3×D5—41no—
71C2×C3×D5—42no—
72C3×C4×C5C2×D411yescharacteristic
73C3×C4×C5C2×D411yescharacteristic
74Dic15—22no—
75Dic15—41no—
76C5×Dic3—41no—
77C2×C3×D4—51no—
78C2×C3×D4C2×D511yescharacteristic
79C2×Dic6—51no—
80C2×Dic6C2×D511yescharacteristic
81C3×D8—102no—
82C2×C3×C8—51no—
83#217—102no—
84#217—102no—
85#214—22no—
86#214—102no—
87C4×Dic3—51no—
88C2×C3⋊C8C2×D511yescharacteristic
89Dic12—102no—
90C23×C5—21no—
91C22×D5—21no—
92C5×Q8—61no—
93C5×Q8—61no—
94C5×D4—21no—
95C5×D4—21no—
96C2×C4×C5—61no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—32no—
99C2×Dic5—61no—
100D20—21no—
101D20—21no—
102Dic10—61no—
103Dic10—61no—
104C5×C8—32no—
105#168#6712yes—
106C2×Q16—151no—
107C2×SD16—31no—
108C2×SD16—151no—
109C2×D8—51no—
110#124—151no—
111#124—151no—
112C4×C8—151no—
113C2×C3×C5—81no—
114C2×C3×C5#12711yescharacteristic
115C2×C3×C5#13512yes—
116C3×D5—81no—
117C23×C3—21no—
118C23×C3—101no—
119C3×D4—21no—
120C3×D4—21no—
121C3×D4—101no—
122C3×D4—101no—
123C2×C3×C4C22×D511yescharacteristic
124C2×Dic3—21no—
125C2×Dic3—52no—
126C2×Dic3—101no—
127Dic6—21no—
128Dic6—21no—
129Dic6—101no—
130Dic6—101no—
131C3×C8—52no—
132C3⋊C8C22⋊D512yes—
133C22×C5—42no—
134C22×C5—41no—
135C22×C5D3×D411yescharacteristic
136C2×D5—42no—
137C2×D5—41no—
138C4×C5—121no—
139C4×C5D3×D411yescharacteristic
140C4×C5C2×#6711yescharacteristic
141Dic5—62no—
142Dic5—121no—
143C2×Q8—31no—
144C2×Q8—151no—
145C2×D4—51no—
146C2×D4D3×D511yescharacteristic
147Q16—302no—
148SD16—62no—
149SD16—302no—
150D8—102no—
151C2×C8—31no—
152C2×C8—51no—
153C22⋊C4—302no—
154C22⋊C4—302no—
155C42—151no—
156C3×C5#49511yescharacteristic, complemented, Hall
157C22×C3—42no—
158C22×C3—41no—
159C22×C3—202no—
160C22×C3—201no—
161C22×C3D4×D511yescharacteristic
162C3×C4D4×D511yescharacteristic
163C3×C4C2×C22⋊D511yescharacteristic
164Dic3—41no—
165Dic3—102no—
166Dic3—201no—
167C2×C5—81no—
168C2×C5#91212yes—
169C2×C5#94011yescharacteristic
170D5—81no—
171C23—21no—
172C23—101no—
173Q8—61no—
174Q8—61no—
175Q8—301no—
176Q8—301no—
177D4—21no—
178D4—21no—
179D4—101no—
180D4—101no—
181C2×C4—61no—
182C2×C4—152no—
183C2×C4—301no—
184C2×C4C2×D3×D511yescharacteristic
185C8—32no—
186C8—52no—
187C2×C3—81no—
188C2×C3—401no—
189C2×C3#406212yes—
190C2×C3#408611yescharacteristic
191C5#515511yescharacteristic, complemented, Sylow
192C22—42no—
193C22—41no—
194C22—202no—
195C22—201no—
196C22#679011yescharacteristic
197C4—121no—
198C4—302no—
199C4—601no—
200C4D5×#6711yescharacteristic
201C4D3×C22⋊D511yescharacteristic
202C3#6545711yescharacteristic, complemented, Sylow
203C2—81no—
204C2—401no—
205C2#9149712yes—
206C2#9156711yescharacteristic
subgroupG/H
centerC22#6790
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×D4C22
socleC22×C3×C5C2×D4
prime radicalC2×C3×#686C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#495
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #91825C2semidirect
2. C2×C5×#214C2semidirect
4. #91368C2semidirect
5. C2×#6663C2semidirect
6. C2×#6657C2semidirect
7. #90951C2semidirect
50. C2×#214D5semidirect
156. C3×C5#495semidirect
191. C5#5155semidirect
202. C3#65457semidirect

Maximal subgroups

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

subgroupindex
#918252
C2×C5×#2142
C2×C3×#6862
#913682
C2×#66632
C2×#66572
#909512
#654573
#51555