Finite Group Databasebeta

← #11747207

Subgroups — #11747207

Order 960.

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

normal subgroups only

This group has 212 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×#4041C211yesmaximal, characteristic
2#91358C211yesmaximal, characteristic, complemented
3#91091C211yesmaximal, characteristic, complemented
4C5×#808C211yesmaximal, characteristic, complemented
5#90965C211yesmaximal, characteristic, complemented
6#90964C211yesmaximal, characteristic, complemented
7#90955C211yesmaximal, characteristic, complemented
8#65155—31nomaximal, Hall
9C2×C3×D20—21no—
10C2×C3×D20C2211yescharacteristic
11C2×C3×C4×D5C2211yescharacteristic
12C3×C5×C4⋊C4C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#685—21no—
18#6665—21no—
19Dic3×Dic5—21no—
20#5035—51nomaximal, Hall
21#4041D311yescharacteristic
22#4038—31no—
23C5×#106—31no—
24#3953—31no—
25#3952—31no—
26#3941—31no—
27#3939—31no—
28C22×C3×D5—21no—
29C22×C3×D5D411yescharacteristic
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C2×C5×Dic3—21no—
34C2×C3×Dic5D411yescharacteristic
35C3×D20—21no—
36C3×D20—21no—
37C3×D20—42no—
38C3×C4×D5—21no—
39C3×C4×D5—21no—
40C3⋊#168—21no—
41C5×C3⋊C8—21no—
42C3×#121—51no—
43#926—51no—
44#832—51no—
45#832—51no—
46#830—51no—
47#808D511yescharacteristic, complemented
48#807—51no—
49C2×D20—21no—
50C2×D20C2×D311yescharacteristic
51C2×C4×D5C2×D311yescharacteristic
52C2×C5×C8—31no—
53C5×C4⋊C4—31no—
54C5×C4⋊C4C2×D311yescharacteristic
55#685—21no—
56#685—61no—
57C4⋊Dic5—31no—
58C4×Dic5—61no—
59C2×#168—31no—
60#482—151noSylow
61C22×C3×C5C2×D411yescharacteristic
62C2×C3×D5—21no—
63C2×C3×D5—21no—
64C2×C3×D5—21no—
65C2×C3×D5—41no—
66C2×C3×D5—41no—
67C2×C3×D5—41no—
68C3×C4×C5—41no—
69C3×C4×C5#4111yescharacteristic
70C3×C4×C5#4111yescharacteristic
71Dic15—41no—
72C3×Dic5—21no—
73C5×Dic3—41no—
74C2×C3×D4—51no—
75C2×C3×D4—101no—
76C22×C3×C4—51no—
77C3×C4⋊C4C2×D511yescharacteristic
78C3×C22⋊C4—101no—
79#217—101no—
80C4⋊Dic3—51no—
81C4⋊Dic3C2×D511yescharacteristic
82C4×Dic3—101no—
83C2×C3⋊C8—51no—
84C2×C3⋊C8C2×D511yescharacteristic
85C22×D5—21no—
86C22×D5#6711yescharacteristic
87C2×C4×C5—21no—
88C2×C4×C5—61no—
89C2×C4×C5C22×D311yescharacteristic
90C2×Dic5—61no—
91C2×Dic5#6711yescharacteristic
92D20—21no—
93D20—21no—
94D20—42no—
95C4×D5—21no—
96C4×D5—21no—
97C5×C8—61no—
98#168—61no—
99#121—51no—
100#117—151no—
101#107—151no—
102#106—31no—
103#102—151no—
104#102—151no—
105C22⋊C8—151no—
106C2×C3×C5#12311yescharacteristic
107C2×C3×C5#13511yescharacteristic
108C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
109C3×D5—41no—
110C3×D5—81no—
111C23×C3—51no—
112C23×C3—101no—
113C3×D4—101no—
114C3×D4—101no—
115C3×D4—202no—
116C2×C3×C4—21no—
117C2×C3×C4—51no—
118C2×C3×C4—101no—
119C2×C3×C4—101no—
120C2×C3×C4C22×D511yescharacteristic
121C2×Dic3—21no—
122C2×Dic3—101no—
123C3⋊C8—21no—
124C3⋊C8—101no—
125C22×C5C2×#6711yescharacteristic
126C2×D5—21no—
127C2×D5—21no—
128C2×D5—21no—
129C2×D5—41no—
130C2×D5—41no—
131C2×D5—41no—
132C4×C5—41no—
133C4×C5—121no—
134C4×C5#23711yescharacteristic
135C4×C5#23711yescharacteristic
136Dic5—21no—
137Dic5—121no—
138C2×D4—51no—
139C2×D4—101no—
140C22×C4—51no—
141C2×C8—31no—
142C2×C8—151no—
143C4⋊C4—31no—
144C4⋊C4—151no—
145C4⋊C4D3×D511yescharacteristic
146C22⋊C4—101no—
147C22⋊C4—301no—
148C42—301no—
149C3×C5#48211yescharacteristic, complemented, Hall
150C22×C3—101no—
151C22×C3—101no—
152C22×C3—101no—
153C22×C3—201no—
154C22×C3—201no—
155C22×C3—201no—
156C22×C3D4×D511yescharacteristic
157C3×C4—41no—
158C3×C4—101no—
159C3×C4#70911yescharacteristic
160C3×C4#71311yescharacteristic
161Dic3—41no—
162Dic3—201no—
163C2×C5#93211yescharacteristic
164C2×C5#93511yescharacteristic
165C2×C5#95011yescharacteristic
166D5—41no—
167D5—81no—
168C23—51no—
169C23—101no—
170D4—101no—
171D4—101no—
172D4—202no—
173C2×C4—21no—
174C2×C4—51no—
175C2×C4—61no—
176C2×C4—101no—
177C2×C4—101no—
178C2×C4—301no—
179C2×C4C2×D3×D511yescharacteristic
180C8—61no—
181C8—301no—
182C2×C3—201no—
183C2×C3—401no—
184C2×C3#404011yescharacteristic
185C2×C3#406011yescharacteristic
186C2×C3#406211yescharacteristic
187C5#503511yescharacteristic, complemented, Sylow
188C22—101no—
189C22—101no—
190C22—101no—
191C22—201no—
192C22—201no—
193C22—201no—
194C22D5×#6711yescharacteristic
195C4—41no—
196C4—101no—
197C4—121no—
198C4—601no—
199C4#676511yescharacteristic
200C4#676611yescharacteristic
201C3#6515511yescharacteristic, complemented, Sylow
202C2—201no—
203C2—401no—
204C2#9140711yescharacteristic
205C2#9149111yescharacteristic
206C2#9151411yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC3×#4041C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #91358C2semidirect
3. #91091C2semidirect
4. C5×#808C2semidirect
5. #90965C2semidirect
6. #90964C2semidirect
7. #90955C2semidirect
47. #808D5semidirect
149. C3×C5#482semidirect
187. C5#5035semidirect
201. C3#65155semidirect

Maximal subgroups

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

subgroupindex
C3×#40412
#913582
#910912
C5×#8082
#909652
#909642
#909552
#651553
#50355