Finite Group Databasebeta

← #11749356

Subgroups — #11749356

Order 960.

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

normal subgroups only

This group has 248 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
2C2×C5×#216C211yesmaximal, characteristic, complemented
3C2×C3×#689C211yesmaximal, characteristic, complemented
4#91385C211yesmaximal, characteristic, complemented
5C2×#6660C211yesmaximal, characteristic
6C2×#6658C211yesmaximal, characteristic
7#90954C211yesmaximal, characteristic, complemented
8#65479—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×D60C2211yescharacteristic
11C2×C5×Dic6C2211yescharacteristic
12C2×C3×Dic10C2211yescharacteristic
13#6714—22no—
14C4×Dic15C2211yescharacteristic
15C5×#216—22no—
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#689—22no—
18C2×C3×#168C2211yescharacteristic
19#6669—22no—
20#6660—22no—
21#6658—22no—
22#5190—51nomaximal, Hall
23C2×C5×Q16—31no—
24#4093—31no—
25#4090—31no—
26C2×#689D311yescharacteristic, complemented
27C2×#688—31no—
28C2×#677—31no—
29#3947—31no—
30C22×D15—21no—
31C3×C5×Q8—21no—
32C3×C5×Q8—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15D412yes—
36D60—21no—
37D60—21no—
38C2×C5×Dic3—21no—
39C5×Dic6—21no—
40C5×Dic6—21no—
41C2×C3×Dic5—21no—
42C3×Dic10—21no—
43C3×Dic10—21no—
44C3×#168D412yes—
45C5×C3⋊C8D412yes—
46C2×C3×Q16—51no—
47#947—51no—
48#944—51no—
49C2×#216D511yescharacteristic, complemented
50C2×#215—51no—
51C2×#204—51no—
52#815—51no—
53C2×C5×Q8—31no—
54C2×C5×Q8C2×D311yescharacteristic
55C2×D20—31no—
56C2×Dic10C2×D311yescharacteristic
57C5×Q16—62no—
58C2×C5×C8—31no—
59#689—22no—
60#688—62no—
61#685—62no—
62#683—62no—
63C4×Dic5—31no—
64C2×#168C2×D311yescharacteristic
65#677—62no—
66#497—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×D15—41no—
69C2×D15—42no—
70C3×C4×C5—41no—
71C3×C4×C5C2×D411yescharacteristic
72C3×C4×C5C2×D411yescharacteristic
73Dic15—22no—
74C3×Dic5—41no—
75C5×Dic3—41no—
76C2×C3×Q8—51no—
77C2×C3×Q8C2×D511yescharacteristic
78C2×D12—51no—
79C2×Dic6C2×D511yescharacteristic
80C3×Q16—102no—
81C2×C3×C8—51no—
82#216—22no—
83#215—102no—
84(C2×D3)⋊C4—102no—
85Dic3⋊C4—102no—
86C4×Dic3—51no—
87C2×C3⋊C8C2×D511yescharacteristic
88#204—102no—
89C22×D5—61no—
90C5×Q8—21no—
91C5×Q8—21no—
92C5×Q8—61no—
93C5×Q8—61no—
94C2×C4×C5—21no—
95C2×C4×C5—61no—
96C2×C4×C5C22×D311yescharacteristic
97C2×Dic5—21no—
98C2×Dic5—32no—
99D20—61no—
100D20—61no—
101Dic10—21no—
102Dic10—21no—
103C5×C8—32no—
104#168#6712yes—
105C2×Q16—31no—
106C2×Q16—51no—
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—101no—
119C3×Q8—101no—
120C2×C3×C4—21no—
121C2×C3×C4—101no—
122C2×C3×C4C22×D511yescharacteristic
123C2×Dic3—21no—
124C2×Dic3—52no—
125D12—101no—
126D12—101no—
127Dic6—21no—
128Dic6—21no—
129C3×C8—52no—
130C3⋊C8C22⋊D512yes—
131C22×C5D3×D411yescharacteristic
132C2×D5—122no—
133C2×D5—121no—
134C4×C5—41no—
135C4×C5—121no—
136C4×C5D3×D411yescharacteristic
137C4×C5C2×#6711yescharacteristic
138Dic5—41no—
139Dic5—62no—
140C2×Q8—31no—
141C2×Q8—51no—
142C2×Q8D3×D511yescharacteristic
143C2×D4—151no—
144Q16—62no—
145Q16—102no—
146SD16—302no—
147SD16—302no—
148C2×C8—31no—
149C2×C8—51no—
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—201no—
159C3×C4D4×D511yescharacteristic
160C3×C4C2×C22⋊D511yescharacteristic
161Dic3—41no—
162Dic3—102no—
163C2×C5#91812yes—
164C2×C5#94011yescharacteristic
165D5—241no—
166C23—301no—
167Q8—21no—
168Q8—21no—
169Q8—61no—
170Q8—61no—
171Q8—101no—
172Q8—101no—
173D4—301no—
174D4—301no—
175C2×C4—21no—
176C2×C4—61no—
177C2×C4—101no—
178C2×C4—152no—
179C2×C4C2×D3×D511yescharacteristic
180C8—32no—
181C8—52no—
182C2×C3#406412yes—
183C2×C3#408611yescharacteristic
184D3—401no—
185C5#519011yescharacteristic, complemented, Sylow
186C22—602no—
187C22—601no—
188C22#679011yescharacteristic
189C4—41no—
190C4—121no—
191C4—201no—
192C4—302no—
193C4D5×#6711yescharacteristic
194C4D3×C22⋊D511yescharacteristic
195C3#6547911yescharacteristic, complemented, Sylow
196C2—1201no—
197C2#9151212yes—
198C2#9156711yescharacteristic
subgroupG/H
centerC22#6790
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC2×D60C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#497
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
2. C2×C5×#216C2semidirect
3. C2×C3×#689C2semidirect
4. #91385C2semidirect
7. #90954C2semidirect
26. C2×#689D3semidirect
49. C2×#216D5semidirect
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
#918362
C2×C5×#2162
C2×C3×#6892
#913852
C2×#66602
C2×#66582
#909542
#654793
#51905