Finite Group Databasebeta

← #11747340

Subgroups — #11747340

Order 960.

208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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×D5×C4⋊C4C211yesmaximal, characteristic
2#91359C211yesmaximal, characteristic
3#91091C211yesmaximal, characteristic, complemented
4C5×#810C211yesmaximal, characteristic, complemented
5#90990C211yesmaximal, characteristic, complemented
6#90972C211yesmaximal, characteristic, complemented
7#90955C211yesmaximal, characteristic
8#65098—31nomaximal, Hall
9C2×C5×Dic6C2211yescharacteristic
10C2×C3×C4×D5—21no—
11C2×C3×C4×D5C2211yescharacteristic
12C3×C5×C4⋊C4C2211yescharacteristic
13C4⋊Dic15C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×C4⋊Dic5C2211yescharacteristic
17C3×#683—21no—
18#6669—21no—
19#6665—21no—
20#4970—51nomaximal, Hall
21#4092—31no—
22D5×C4⋊C4D311yescharacteristic
23C5×#103—31no—
24#3967—31no—
25#3952—31no—
26#3950—31no—
27#3939—31no—
28C22×C3×D5D411yescharacteristic
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5C2311yescharacteristic
31C2×Dic15—21no—
32C2×C5×Dic3—21no—
33C5×Dic6—21no—
34C5×Dic6—21no—
35C2×C3×Dic5—21no—
36C2×C3×Dic5D411yescharacteristic
37C3×C4×D5—21no—
38C3×C4×D5—21no—
39C3×C4×D5—42no—
40C3⋊#168—21no—
41C5×C3⋊C8—21no—
42C2×C3×C4⋊C4—51no—
43#924—51no—
44#830—51no—
45#810—51no—
46#810D511yescharacteristic, complemented
47#807—51no—
48#807—51no—
49C2×C5×Q8—31no—
50C2×C4×D5—21no—
51C2×C4×D5C2×D311yescharacteristic
52C2×C5×C8—31no—
53C5×C4⋊C4C2×D311yescharacteristic
54#685—61no—
55C4⋊Dic5—31no—
56C4⋊Dic5C2×D311yescharacteristic
57#683—21no—
58#683—61no—
59C2×#168—31no—
60#484—151noSylow
61C22×C3×C5C2×D411yescharacteristic
62C2×C3×D5—21no—
63C2×C3×D5—21no—
64C2×C3×D5Q1612yes—
65C3×C4×C5—41no—
66C3×C4×C5#4111yescharacteristic
67C3×C4×C5#4111yescharacteristic
68Dic15—41no—
69C3×Dic5—21no—
70C3×Dic5—41no—
71C5×Dic3—41no—
72C22×C3×C4—51no—
73C22×C3×C4—101no—
74C2×Dic6C2×D511yescharacteristic
75C3×C4⋊C4—51no—
76C3×C4⋊C4—101no—
77C3×C4⋊C4C2×D511yescharacteristic
78#217—101no—
79C4⋊Dic3—51no—
80Dic3⋊C4—101no—
81C2×C3⋊C8—51no—
82C2×C3⋊C8C2×D511yescharacteristic
83C22×D5#6711yescharacteristic
84C5×Q8—61no—
85C5×Q8—61no—
86C2×C4×C5—21no—
87C2×C4×C5—61no—
88C2×C4×C5C22×D311yescharacteristic
89C2×Dic5—21no—
90C2×Dic5—61no—
91C2×Dic5#6711yescharacteristic
92C4×D5—21no—
93C4×D5—21no—
94C4×D5—42no—
95C5×C8—61no—
96#168—61no—
97C22⋊Q8—151no—
98C2×C4⋊C4—51no—
99#107—151no—
100#107—151no—
101#103—31no—
102#103—151no—
103C22⋊C8—151no—
104C2×C3×C5#12311yescharacteristic
105C2×C3×C5C2×Q1611yescharacteristic
106C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
107C3×D5—22no—
108C23×C3—51no—
109C2×C3×C4—21no—
110C2×C3×C4—51no—
111C2×C3×C4—101no—
112C2×C3×C4—101no—
113C2×C3×C4—101no—
114C2×C3×C4—202no—
115C2×C3×C4C22×D511yescharacteristic
116C2×Dic3—21no—
117C2×Dic3—101no—
118Dic6—21no—
119Dic6—21no—
120C3⋊C8—21no—
121C3⋊C8—101no—
122C22×C5C2×#6711yescharacteristic
123C2×D5—21no—
124C2×D5—21no—
125C2×D5#21612yes—
126C4×C5—41no—
127C4×C5—121no—
128C4×C5#23511yescharacteristic
129C4×C5#23511yescharacteristic
130Dic5—21no—
131Dic5—41no—
132Dic5—121no—
133C2×Q8—31no—
134C22×C4—51no—
135C22×C4—101no—
136C2×C8—31no—
137C2×C8—151no—
138C4⋊C4—51no—
139C4⋊C4—101no—
140C4⋊C4—151no—
141C4⋊C4—301no—
142C4⋊C4D3×D511yescharacteristic
143C22⋊C4—301no—
144C3×C5#48411yescharacteristic, complemented, Hall
145C22×C3—52no—
146C22×C3—101no—
147C22×C3—101no—
148C22×C3D4×D511yescharacteristic
149C3×C4—41no—
150C3×C4—101no—
151C3×C4—201no—
152C3×C4#70911yescharacteristic
153C3×C4#71111yescharacteristic
154Dic3—41no—
155Dic3—201no—
156C2×C5#92911yescharacteristic
157C2×C5#93211yescharacteristic
158C2×C5C2×#21611yescharacteristic
159D5—22no—
160C23—51no—
161Q8—61no—
162Q8—61no—
163C2×C4—21no—
164C2×C4—51no—
165C2×C4—61no—
166C2×C4—101no—
167C2×C4—101no—
168C2×C4—101no—
169C2×C4—202no—
170C2×C4—301no—
171C2×C4C2×D3×D511yescharacteristic
172C8—61no—
173C8—301no—
174C2×C3—102no—
175C2×C3#402911yescharacteristic
176C2×C3#406011yescharacteristic
177C2×C3D5×Q1611yescharacteristic
178C5#497011yescharacteristic, complemented, Sylow
179C22—52no—
180C22—101no—
181C22—101no—
182C22D5×#6711yescharacteristic
183C4—41no—
184C4—101no—
185C4—121no—
186C4—201no—
187C4—601no—
188C4#677111yescharacteristic
189C4#677211yescharacteristic
190C3#6509811yescharacteristic, complemented, Sylow
191C2—102no—
192C2#9144711yescharacteristic
193C2#9149111yescharacteristic
194C2D5×#21611yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC22×C3×D5D4
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#484
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
3. #91091C2semidirect
4. C5×#810C2semidirect
5. #90990C2semidirect
6. #90972C2semidirect
46. #810D5semidirect
144. C3×C5#484semidirect
178. C5#4970semidirect
190. C3#65098semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊C42
#913592
#910912
C5×#8102
#909902
#909722
#909552
#650983
#49705