Finite Group Databasebeta

← #11749210

Subgroups — #11749210

Order 960.

192 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C3×#4092C211yesmaximal, characteristic
2#91358C211yesmaximal, characteristic
3#91119C211yesmaximal, characteristic, complemented
4C5×#835C211yesmaximal, characteristic, complemented
5#90989C211yesmaximal, characteristic, complemented
6#90987C211yesmaximal, characteristic, complemented
7#90955C211yesmaximal, characteristic
8#65104—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C3×C4×D5C2211yescharacteristic
11C4⋊Dic15C2211yescharacteristic
12C2×C3⋊#168C2211yescharacteristic
13C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×C3⋊C8C2211yescharacteristic
15C3×#685—21no—
16C3×C4⋊Dic5C2211yescharacteristic
17C3×#683—21no—
18#6665—21no—
19Dic3×Dic5—21no—
20#5045—51nomaximal, Hall
21#4092D311yescharacteristic
22#4038—31no—
23C5×#103—31no—
24#3967—31no—
25#3952—31no—
26#3949—31no—
27#3939—31no—
28C22×C3×D5D411yescharacteristic
29C3×C5×Q8—21no—
30C3×C5×Q8—21no—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15—21no—
34C2×C5×Dic3—21no—
35C2×C3×Dic5—21no—
36C2×C3×Dic5D411yescharacteristic
37C3×C4×D5—21no—
38C3×C4×D5—21no—
39C3⋊#168—21no—
40C5×C3⋊C8—21no—
41C3×C22⋊Q8—51no—
42#926—51no—
43#835—51no—
44#835D511yescharacteristic, complemented
45#830—51no—
46#808—51no—
47#807—51no—
48C2×C5×Q8C2×D311yescharacteristic
49C2×C4×D5C2×D311yescharacteristic
50C2×C5×C8—31no—
51C5×C4⋊C4—31no—
52#685—21no—
53#685—61no—
54C4⋊Dic5—31no—
55C4⋊Dic5C2×D311yescharacteristic
56#683—21no—
57C4×Dic5—61no—
58C2×#168—31no—
59#485—151noSylow
60C22×C3×C5C2×D411yescharacteristic
61C2×C3×D5—21no—
62C2×C3×D5—21no—
63C2×C3×D5—21no—
64C3×C4×C5—41no—
65C3×C4×C5#4111yescharacteristic
66C3×C4×C5#4111yescharacteristic
67Dic15—41no—
68C3×Dic5—21no—
69C3×Dic5—41no—
70C5×Dic3—41no—
71C2×C3×Q8C2×D511yescharacteristic
72C22×C3×C4—51no—
73C3×C4⋊C4—51no—
74C3×C4⋊C4—101no—
75C3×C22⋊C4—101no—
76#217—101no—
77C4⋊Dic3—51no—
78C4⋊Dic3C2×D511yescharacteristic
79C4×Dic3—101no—
80C2×C3⋊C8—51no—
81C2×C3⋊C8C2×D511yescharacteristic
82C22×D5#6711yescharacteristic
83C5×Q8—21no—
84C5×Q8—21no—
85C2×C4×C5—21no—
86C2×C4×C5—61no—
87C2×C4×C5C22×D311yescharacteristic
88C2×Dic5—21no—
89C2×Dic5—61no—
90C2×Dic5#6711yescharacteristic
91C4×D5—21no—
92C4×D5—21no—
93C5×C8—61no—
94#168—61no—
95C22⋊Q8—51no—
96#117—151no—
97#107—151no—
98#106—151no—
99#103—31no—
100#103—151no—
101C22⋊C8—151no—
102C2×C3×C5#12311yescharacteristic
103C2×C3×C5#13511yescharacteristic
104C2×C3×C5#13711yescharacteristic
105C3×D5—41no—
106C23×C3—51no—
107C3×Q8—21no—
108C3×Q8—21no—
109C2×C3×C4—21no—
110C2×C3×C4—51no—
111C2×C3×C4—101no—
112C2×C3×C4—101no—
113C2×C3×C4—101no—
114C2×C3×C4C22×D511yescharacteristic
115C2×Dic3—21no—
116C2×Dic3—101no—
117C3⋊C8—21no—
118C3⋊C8—101no—
119C22×C5C2×#6711yescharacteristic
120C2×D5—21no—
121C2×D5—21no—
122C2×D5—21no—
123C4×C5—41no—
124C4×C5—121no—
125C4×C5#23711yescharacteristic
126C4×C5#23711yescharacteristic
127Dic5—21no—
128Dic5—41no—
129Dic5—121no—
130C2×Q8D3×D511yescharacteristic
131C22×C4—51no—
132C2×C8—31no—
133C2×C8—151no—
134C4⋊C4—31no—
135C4⋊C4—51no—
136C4⋊C4—101no—
137C4⋊C4—151no—
138C22⋊C4—101no—
139C22⋊C4—301no—
140C42—301no—
141C3×C5#48511yescharacteristic, complemented, Hall
142C22×C3—101no—
143C22×C3—101no—
144C22×C3—101no—
145C22×C3D4×D511yescharacteristic
146C3×C4—41no—
147C3×C4—101no—
148C3×C4—201no—
149C3×C4#70911yescharacteristic
150C3×C4#71111yescharacteristic
151Dic3—41no—
152Dic3—201no—
153C2×C5#93511yescharacteristic
154C2×C5#94211yescharacteristic
155C2×C5#95011yescharacteristic
156D5—41no—
157C23—51no—
158Q8—21no—
159Q8—21no—
160C2×C4—21no—
161C2×C4—51no—
162C2×C4—61no—
163C2×C4—101no—
164C2×C4—101no—
165C2×C4—101no—
166C2×C4—301no—
167C2×C4C2×D3×D511yescharacteristic
168C8—61no—
169C8—301no—
170C2×C3—201no—
171C2×C3#402911yescharacteristic
172C2×C3#406211yescharacteristic
173C2×C3#406411yescharacteristic
174C5#504511yescharacteristic, complemented, Sylow
175C22—101no—
176C22—101no—
177C22—101no—
178C22D5×#6711yescharacteristic
179C4—41no—
180C4—101no—
181C4—121no—
182C4—201no—
183C4—601no—
184C4#677911yescharacteristic
185C4#678011yescharacteristic
186C3#6510411yescharacteristic, complemented, Sylow
187C2—201no—
188C2#9151411yescharacteristic
189C2#9151511yescharacteristic
190C2#9154811yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC22×C3×D5D4
hypercenterC2×Q8D3×D5
hypocenterC3×C5#485
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
3. #91119C2semidirect
4. C5×#835C2semidirect
5. #90989C2semidirect
6. #90987C2semidirect
44. #835D5semidirect
141. C3×C5#485semidirect
174. C5#5045semidirect
186. C3#65104semidirect

Maximal subgroups

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

subgroupindex
C3×#40922
#913582
#911192
C5×#8352
#909892
#909872
#909552
#651043
#50455