Finite Group Databasebeta

← #11747310

Subgroups — #11747310

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×#4038C211yesmaximal, characteristic, complemented
2#91449C211yesmaximal, characteristic
3#91091C211yesmaximal, characteristic, complemented
4C5×#809C211yesmaximal, characteristic, complemented
5#90987C211yesmaximal, characteristic, complemented
6#90966C211yesmaximal, characteristic, complemented
7#90955C211yesmaximal, characteristic, complemented
8#65068—31nomaximal, Hall
9C2×C5×D12C2211yescharacteristic
10C2×C3×C4×D5C2211yescharacteristic
11C2×#1201—21no—
12C3×C5×C4⋊C4C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×#685—21no—
17C3×C4⋊Dic5C2211yescharacteristic
18C3×C4×Dic5—21no—
19(C2×D3)⋊Dic5—21no—
20#5003—51nomaximal, Hall
21#4084—31no—
22#4038D311yescharacteristic, complemented
23C5×#102—31no—
24#3964—31no—
25#3952—31no—
26#3949—31no—
27#3939—31no—
28C22×C5×D3—21no—
29C22×C3×D5D411yescharacteristic
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C5×D12—21no—
34C5×D12—21no—
35C2×C3×Dic5—21no—
36C2×C3×Dic5D411yescharacteristic
37C3×C4×D5—21no—
38C3×C4×D5—21no—
39#1201—42no—
40C3⋊#168—21no—
41C5×C3⋊C8—21no—
42C3×#117—51no—
43#930—51no—
44#830—51no—
45#809—51no—
46#809D511yescharacteristic, complemented
47#808—51no—
48#807—51no—
49C2×C5×D4—31no—
50C2×C22⋊D5—61no—
51C2×C4×D5C2×D311yescharacteristic
52C2×C5×C8—31no—
53C5×C4⋊C4C2×D311yescharacteristic
54C22⋊Dic5—61no—
55#685—21no—
56C4⋊Dic5—31no—
57C4⋊Dic5C2×D311yescharacteristic
58C4×Dic5—21no—
59C2×#168—31no—
60#482—151noSylow
61C22×C3×C5C2×D411yescharacteristic
62C2×C5×D3—41no—
63C2×C5×D3—41no—
64C2×C5×D3—41no—
65C2×C3×D5—21no—
66C2×C3×D5—21no—
67C2×C3×D5—21no—
68C3×C4×C5—41no—
69C3×C4×C5#4111yescharacteristic
70C3×C4×C5#4111yescharacteristic
71Dic15—41no—
72C3×Dic5—21no—
73C3×Dic5—41no—
74C22×C3×C4—51no—
75C2×#67—101no—
76C2×D12C2×D511yescharacteristic
77C3×C4⋊C4—51no—
78C3×C4⋊C4C2×D511yescharacteristic
79C3×C22⋊C4—101no—
80C3×C42—101no—
81(C2×D3)⋊C4—101no—
82C4⋊Dic3—51no—
83C2×C3⋊C8—51no—
84C2×C3⋊C8C2×D511yescharacteristic
85C23×C5—61no—
86C22×D5#6711yescharacteristic
87C5×D4—61no—
88C5×D4—61no—
89C2×C4×C5—21no—
90C2×C4×C5C22×D311yescharacteristic
91C22⋊D5—122no—
92C2×Dic5—21no—
93C2×Dic5—61no—
94C2×Dic5#6711yescharacteristic
95C4×D5—21no—
96C4×D5—21no—
97C5×C8—61no—
98#168—61no—
99#121—151no—
100#117—51no—
101#107—151no—
102#106—151no—
103#102—31no—
104#102—151no—
105C22⋊C8—151no—
106C2×C3×C5#12311yescharacteristic
107C2×C3×C5#13511yescharacteristic
108C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
109C3×D5—41no—
110C5×D3—81no—
111C23×C3—51no—
112C22×D3—21no—
113C2×C3×C4—21no—
114C2×C3×C4—51no—
115C2×C3×C4—101no—
116C2×C3×C4—101no—
117C2×C3×C4—101no—
118C2×C3×C4C22×D511yescharacteristic
119#67—202no—
120C2×Dic3—101no—
121D12—21no—
122D12—21no—
123C3⋊C8—21no—
124C3⋊C8—101no—
125C22×C5—121no—
126C22×C5—121no—
127C22×C5—121no—
128C22×C5C2×#6711yescharacteristic
129C2×D5—21no—
130C2×D5—21no—
131C2×D5—21no—
132C4×C5—41no—
133C4×C5#23511yescharacteristic
134C4×C5#23511yescharacteristic
135Dic5—21no—
136Dic5—41no—
137Dic5—121no—
138C2×D4—31no—
139C2×D4—301no—
140C22×C4—51no—
141C2×C8—31no—
142C2×C8—151no—
143C4⋊C4—51no—
144C4⋊C4—151no—
145C4⋊C4D3×D511yescharacteristic
146C22⋊C4—101no—
147C22⋊C4—301no—
148C42—101no—
149C3×C5#48211yescharacteristic, complemented, Hall
150C22×C3—101no—
151C22×C3—101no—
152C22×C3—101no—
153C22×C3D4×D511yescharacteristic
154C2×D3—41no—
155C2×D3—41no—
156C2×D3—41no—
157C3×C4—41no—
158C3×C4—101no—
159C3×C4—201no—
160C3×C4#70911yescharacteristic
161C3×C4#71111yescharacteristic
162Dic3—201no—
163C2×C5—241no—
164C2×C5#92911yescharacteristic
165C2×C5#94911yescharacteristic
166C2×C5#95011yescharacteristic
167D5—41no—
168C23—51no—
169C23—61no—
170D4—61no—
171D4—61no—
172D4—602no—
173C2×C4—21no—
174C2×C4—51no—
175C2×C4—101no—
176C2×C4—101no—
177C2×C4—101no—
178C2×C4—301no—
179C2×C4C2×D3×D511yescharacteristic
180C8—61no—
181C8—301no—
182C2×C3—201no—
183C2×C3#402911yescharacteristic
184C2×C3#405711yescharacteristic
185C2×C3#406211yescharacteristic
186D3—81no—
187C5#500311yescharacteristic, complemented, Sylow
188C22—101no—
189C22—101no—
190C22—101no—
191C22—121no—
192C22—121no—
193C22—121no—
194C22D5×#6711yescharacteristic
195C4—41no—
196C4—101no—
197C4—201no—
198C4—601no—
199C4#677111yescharacteristic
200C4#677211yescharacteristic
201C3#6506811yescharacteristic, complemented, Sylow
202C2—201no—
203C2—241no—
204C2#9144711yescharacteristic
205C2#9147811yescharacteristic
206C2#9151411yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radical#91449C2
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
1. C3×#4038C2semidirect
3. #91091C2semidirect
4. C5×#809C2semidirect
5. #90987C2semidirect
6. #90966C2semidirect
7. #90955C2semidirect
22. #4038D3semidirect
46. #809D5semidirect
149. C3×C5#482semidirect
187. C5#5003semidirect
201. C3#65068semidirect

Maximal subgroups

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

subgroupindex
C3×#40382
#914492
#910912
C5×#8092
#909872
#909662
#909552
#650683
#50035