Finite Group Databasebeta

← #11751269

Subgroups — #11751269

Order 960.

260 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 71 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×C3×C5×SD16C211yesmaximal, characteristic, complemented
2#91836C211yesmaximal, characteristic, complemented
3C2×#6718C211yesmaximal, characteristic, complemented
4#91825C211yesmaximal, characteristic, complemented
5C2×#6715C211yesmaximal, characteristic
6C2×#6706C211yesmaximal, characteristic, complemented
7C8×Dic15C211yesmaximal, characteristic, complemented
8#65457—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×D4C2211yescharacteristic
11C2×D60C2211yescharacteristic
12C2×Dic30C2211yescharacteristic
13C3×C5×SD16—22no—
14C2×C3×C5×C8C2211yescharacteristic
15#6719—22no—
16#6718—22no—
17#6715—22no—
18#6714—22no—
19C4×Dic15C2211yescharacteristic
20C2×C3⋊#168C2211yescharacteristic
21#6706—22no—
22#5168—51nomaximal, Hall
23C2×C5×SD16D311yescharacteristic, complemented
24#4093—31no—
25C2×#689—31no—
26#4082—31no—
27C2×#686—31no—
28C2×#677—31no—
29C8×Dic5—31no—
30C23×C3×C5—21no—
31C22×D15—21no—
32C3×C5×Q8—21no—
33C3×C5×Q8—21no—
34C3×C5×D4—21no—
35C3×C5×D4—21no—
36C2×C3×C4×C5—21no—
37C2×C3×C4×C5C2311yescharacteristic
38C2×Dic15—21no—
39C2×Dic15D412yes—
40D60—21no—
41D60—21no—
42Dic30—21no—
43Dic30—21no—
44C3×C5×C8D412yes—
45C3⋊#168D412yes—
46C2×C3×SD16D511yescharacteristic, complemented
47#947—51no—
48C2×#216—51no—
49#936—51no—
50C2×#213—51no—
51C2×#204—51no—
52C8×Dic3—51no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×C5×D4C2×D311yescharacteristic
55C2×D20—31no—
56C2×Dic10—31no—
57C5×SD16—22no—
58C2×C5×C8C2×D311yescharacteristic
59C22⋊Dic5—62no—
60#689—62no—
61#686—62no—
62#685—62no—
63C4×Dic5—31no—
64C2×#168—31no—
65#677—62no—
66#495—151noSylow
67C22×C3×C5—41no—
68C22×C3×C5—42no—
69C22×C3×C5C2×D411yescharacteristic
70C2×D15—41no—
71C2×D15—42no—
72C3×C4×C5—41no—
73C3×C4×C5C2×D411yescharacteristic
74C3×C4×C5C2×D411yescharacteristic
75Dic15—22no—
76Dic15—41no—
77C2×C3×Q8C2×D511yescharacteristic
78C2×C3×D4C2×D511yescharacteristic
79C2×D12—51no—
80C2×Dic6—51no—
81C3×SD16—22no—
82C2×C3×C8C2×D511yescharacteristic
83#217—102no—
84#216—102no—
85#213—102no—
86(C2×D3)⋊C4—102no—
87C4×Dic3—51no—
88C2×C3⋊C8—51no—
89#204—102no—
90C23×C5—21no—
91C22×D5—61no—
92C5×Q8—21no—
93C5×Q8—21no—
94C5×D4—21no—
95C5×D4—21no—
96C2×C4×C5—21no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—32no—
99C2×Dic5—61no—
100D20—61no—
101D20—61no—
102Dic10—61no—
103Dic10—61no—
104C5×C8#6712yes—
105#168—32no—
106C2×Q16—151no—
107C2×SD16—151no—
108C2×SD16D1511yescharacteristic, complemented
109C2×D8—151no—
110#124—151no—
111#124—151no—
112C4×C8—151no—
113C2×C3×C5—81no—
114C2×C3×C5#12711yescharacteristic
115C2×C3×C5#13512yes—
116D15—81no—
117C23×C3—21no—
118C22×D3—101no—
119C3×Q8—21no—
120C3×Q8—21no—
121C3×D4—21no—
122C3×D4—21no—
123C2×C3×C4—21no—
124C2×C3×C4C22×D511yescharacteristic
125C2×Dic3—52no—
126C2×Dic3—101no—
127D12—101no—
128D12—101no—
129Dic6—101no—
130Dic6—101no—
131C3×C8C22⋊D512yes—
132C3⋊C8—52no—
133C22×C5—42no—
134C22×C5—41no—
135C22×C5D3×D411yescharacteristic
136C2×D5—122no—
137C2×D5—121no—
138C4×C5—41no—
139C4×C5D3×D411yescharacteristic
140C4×C5C2×#6711yescharacteristic
141Dic5—62no—
142Dic5—121no—
143C2×Q8—151no—
144C2×Q8C2×D1511yescharacteristic
145C2×D4—151no—
146C2×D4C2×D1511yescharacteristic
147Q16—302no—
148SD16—22no—
149SD16—302no—
150D8—302no—
151C2×C8—151no—
152C2×C8C2×D1511yescharacteristic
153C22⋊C4—302no—
154C22⋊C4—302no—
155C42—151no—
156C3×C5#49511yescharacteristic, complemented, Hall
157C22×C3—42no—
158C22×C3—41no—
159C22×C3D4×D511yescharacteristic
160C2×D3—202no—
161C2×D3—201no—
162C3×C4—41no—
163C3×C4D4×D511yescharacteristic
164C3×C4C2×C22⋊D511yescharacteristic
165Dic3—102no—
166Dic3—201no—
167C2×C5—81no—
168C2×C5#91612yes—
169C2×C5#94011yescharacteristic
170D5—241no—
171C23—21no—
172C23—301no—
173Q8—21no—
174Q8—21no—
175Q8—301no—
176Q8—301no—
177D4—21no—
178D4—21no—
179D4—301no—
180D4—301no—
181C2×C4—21no—
182C2×C4—152no—
183C2×C4—301no—
184C2×C4C22×D1511yescharacteristic
185C8—152no—
186C8#122012yes—
187C2×C3—81no—
188C2×C3#406212yes—
189C2×C3#408611yescharacteristic
190D3—401no—
191C5#516811yescharacteristic, complemented, Sylow
192C22—42no—
193C22—41no—
194C22—602no—
195C22—601no—
196C22D4×D1511yescharacteristic
197C4—41no—
198C4—302no—
199C4—601no—
200C4D4×D1511yescharacteristic
201C4C2×#122011yescharacteristic
202C3#6545711yescharacteristic, complemented, Sylow
203C2—81no—
204C2—1201no—
205C2#9180512yes—
206C2#9182911yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC2×C3×C5×SD16C2
socleC22×C3×C5C2×D4
prime radicalC2×#6715C2
hypercenterC2×SD16D15
hypocenterC3×C5#495
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×SD16C2semidirect
2. #91836C2semidirect
3. C2×#6718C2semidirect
4. #91825C2semidirect
6. C2×#6706C2semidirect
7. C8×Dic15C2semidirect
23. C2×C5×SD16D3semidirect
46. C2×C3×SD16D5semidirect
108. C2×SD16D15semidirect
156. C3×C5#495semidirect
191. C5#5168semidirect
202. C3#65457semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×SD162
#918362
C2×#67182
#918252
C2×#67152
C2×#67062
C8×Dic152
#654573
#51685