Finite Group Databasebeta

← #11751291

Subgroups — #11751291

Order 960.

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

normal subgroups only

This group has 248 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×Q16C211yesmaximal, characteristic, complemented
2#91836C211yesmaximal, characteristic
3#91833C211yesmaximal, characteristic, complemented
4C2×#6718C211yesmaximal, characteristic, complemented
5C2×#6717C211yesmaximal, characteristic
6C2×#6706C211yesmaximal, characteristic
7#91099C211yesmaximal, characteristic, complemented
8#65479—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C3×C5×Q8C2211yescharacteristic
11C2×D60C2211yescharacteristic
12C2×Dic30C2211yescharacteristic
13C3×C5×Q16—22no—
14C2×C3×C5×C8C2211yescharacteristic
15#6718—22no—
16#6717—22no—
17#6714—22no—
18#6712—22no—
19C4×Dic15C2211yescharacteristic
20C2×C3⋊#168C2211yescharacteristic
21#6706—22no—
22#5190—51nomaximal, Hall
23C2×C5×Q16D311yescharacteristic, complemented
24#4093—31no—
25#4090—31no—
26C2×#689—31no—
27C2×#688—31no—
28C2×#677—31no—
29#3947—31no—
30C22×D15—21no—
31C3×C5×Q8—21no—
32C3×C5×Q8—21no—
33C3×C5×Q8—21no—
34C3×C5×Q8—21no—
35C2×C3×C4×C5—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×Q16D511yescharacteristic, complemented
47#947—51no—
48#944—51no—
49C2×#216—51no—
50C2×#215—51no—
51C2×#204—51no—
52#815—51no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×C5×Q8C2×D311yescharacteristic
55C2×D20—31no—
56C2×Dic10—31no—
57C5×Q16—22no—
58C2×C5×C8C2×D311yescharacteristic
59#689—62no—
60#688—62no—
61#685—62no—
62#683—62no—
63C4×Dic5—31no—
64C2×#168—31no—
65#677—62no—
66#497—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×D15—41no—
69C2×D15—42no—
70C3×C4×C5—41no—
71C3×C4×C5—41no—
72C3×C4×C5C2×D411yescharacteristic
73C3×C4×C5C2×D411yescharacteristic
74Dic15—22no—
75Dic15—41no—
76C2×C3×Q8C2×D511yescharacteristic
77C2×C3×Q8C2×D511yescharacteristic
78C2×D12—51no—
79C2×Dic6—51no—
80C3×Q16—22no—
81C2×C3×C8C2×D511yescharacteristic
82#216—102no—
83#215—102no—
84(C2×D3)⋊C4—102no—
85Dic3⋊C4—102no—
86C4×Dic3—51no—
87C2×C3⋊C8—51no—
88#204—102no—
89C22×D5—61no—
90C5×Q8—21no—
91C5×Q8—21no—
92C5×Q8—21no—
93C5×Q8—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5C22×D311yescharacteristic
97C2×Dic5—32no—
98C2×Dic5—61no—
99D20—61no—
100D20—61no—
101Dic10—61no—
102Dic10—61no—
103C5×C8#6712yes—
104#168—32no—
105C2×Q16—151no—
106C2×Q16D1511yescharacteristic, complemented
107C2×SD16—151no—
108C2×SD16—151no—
109C4⋊Q8—151no—
110#124—151no—
111#97—151no—
112C2×C3×C5#12711yescharacteristic
113C2×C3×C5#13712yes—
114D15—81no—
115C22×D3—101no—
116C3×Q8—21no—
117C3×Q8—21no—
118C3×Q8—21no—
119C3×Q8—21no—
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4C22×D511yescharacteristic
123C2×Dic3—52no—
124C2×Dic3—101no—
125D12—101no—
126D12—101no—
127Dic6—101no—
128Dic6—101no—
129C3×C8C22⋊D512yes—
130C3⋊C8—52no—
131C22×C5D3×D411yescharacteristic
132C2×D5—122no—
133C2×D5—121no—
134C4×C5—41no—
135C4×C5—41no—
136C4×C5D3×D411yescharacteristic
137C4×C5C2×#6711yescharacteristic
138Dic5—62no—
139Dic5—121no—
140C2×Q8—151no—
141C2×Q8C2×D1511yescharacteristic
142C2×Q8C2×D1511yescharacteristic
143C2×D4—151no—
144Q16—22no—
145Q16—302no—
146SD16—302no—
147SD16—302no—
148C2×C8—151no—
149C2×C8C2×D1511yescharacteristic
150C4⋊C4—302no—
151C22⋊C4—302no—
152C42—151no—
153C3×C5#49711yescharacteristic, complemented, Hall
154C22×C3D4×D511yescharacteristic
155C2×D3—202no—
156C2×D3—201no—
157C3×C4—41no—
158C3×C4—41no—
159C3×C4D4×D511yescharacteristic
160C3×C4C2×C22⋊D511yescharacteristic
161Dic3—102no—
162Dic3—201no—
163C2×C5#91812yes—
164C2×C5#94011yescharacteristic
165D5—241no—
166C23—301no—
167Q8—21no—
168Q8—21no—
169Q8—21no—
170Q8—21no—
171Q8—301no—
172Q8—301no—
173D4—301no—
174D4—301no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—152no—
178C2×C4—301no—
179C2×C4C22×D1511yescharacteristic
180C8—152no—
181C8#122012yes—
182C2×C3#406412yes—
183C2×C3#408611yescharacteristic
184D3—401no—
185C5#519011yescharacteristic, complemented, Sylow
186C22—602no—
187C22—601no—
188C22D4×D1511yescharacteristic
189C4—41no—
190C4—41no—
191C4—302no—
192C4—601no—
193C4D4×D1511yescharacteristic
194C4C2×#122011yescharacteristic
195C3#6547911yescharacteristic, complemented, Sylow
196C2—1201no—
197C2#9180712yes—
198C2#9182911yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC2×C3×C5×Q16C2
socleC22×C3×C5C2×D4
prime radicalC2×D60C22
hypercenterC2×Q16D15
hypocenterC3×C5#497
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×Q16C2semidirect
3. #91833C2semidirect
4. C2×#6718C2semidirect
7. #91099C2semidirect
23. C2×C5×Q16D3semidirect
46. C2×C3×Q16D5semidirect
106. C2×Q16D15semidirect
153. C3×C5#497semidirect
185. C5#5190semidirect
195. C3#65479semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×Q162
#918362
#918332
C2×#67182
C2×#67172
C2×#67062
#910992
#654793
#51905