Finite Group Databasebeta

← #11750912

Subgroups — #11750912

Order 960.

208 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 63 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#91835C211yesmaximal, characteristic
2C4⋊C4×D15C211yesmaximal, characteristic
3C3×C5×#103C211yesmaximal, characteristic, complemented
4#91119C211yesmaximal, characteristic, complemented
5#91104C211yesmaximal, characteristic
6#91102C211yesmaximal, characteristic, complemented
7#91091C211yesmaximal, characteristic, complemented
8#65098—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C4×D15—21no—
11C2×C4×D15C2211yescharacteristic
12C2×C3×C5×C8C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14#6714—21no—
15C4⋊Dic15C2211yescharacteristic
16C4⋊Dic15C2211yescharacteristic
17#6712—21no—
18#6712—21no—
19C2×C3⋊#168C2211yescharacteristic
20#4811—51nomaximal, Hall
21#4092—31no—
22D5×C4⋊C4—31no—
23C5×#103D311yescharacteristic, complemented
24#3967—31no—
25#3952—31no—
26#3950—31no—
27#3939—31no—
28C22×D15D411yescharacteristic
29C3×C5×Q8—21no—
30C3×C5×Q8—21no—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5C2311yescharacteristic
34C2×Dic15—21no—
35C2×Dic15—21no—
36C2×Dic15D411yescharacteristic
37C4×D15—21no—
38C4×D15—21no—
39C4×D15—42no—
40C3×C5×C8—21no—
41C3⋊#168—21no—
42#946—51no—
43D3×C4⋊C4—51no—
44C3×#103D511yescharacteristic, complemented
45#835—51no—
46(C2×D3)⋊C8—51no—
47#818—51no—
48#807—51no—
49C2×C5×Q8C2×D311yescharacteristic
50C2×C4×D5—31no—
51C2×C4×D5—61no—
52C2×C5×C8C2×D311yescharacteristic
53C5×C4⋊C4C2×D311yescharacteristic
54#685—61no—
55C4⋊Dic5—31no—
56C4⋊Dic5—31no—
57#683—61no—
58#683—61no—
59C2×#168—31no—
60#484—151noSylow
61C22×C3×C5C2×D411yescharacteristic
62C2×D15—21no—
63C2×D15—21no—
64C2×D15Q1612yes—
65C3×C4×C5—41no—
66C3×C4×C5—41no—
67C3×C4×C5#4111yescharacteristic
68C3×C4×C5#4111yescharacteristic
69Dic15—21no—
70Dic15—41no—
71Dic15—41no—
72C2×C3×Q8C2×D511yescharacteristic
73C2×C4×D3—51no—
74C2×C4×D3—101no—
75C2×C3×C8C2×D511yescharacteristic
76C3×C4⋊C4C2×D511yescharacteristic
77(C2×D3)⋊C4—101no—
78C4⋊Dic3—51no—
79C4⋊Dic3—51no—
80Dic3⋊C4—101no—
81Dic3⋊C4—101no—
82C2×C3⋊C8—51no—
83C22×D5—31no—
84C5×Q8—21no—
85C5×Q8—21no—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5C22×D311yescharacteristic
89C2×Dic5—31no—
90C2×Dic5—61no—
91C2×Dic5—61no—
92C4×D5—61no—
93C4×D5—61no—
94C4×D5—122no—
95C5×C8—21no—
96#168—61no—
97C22⋊Q8—151no—
98C2×C4⋊C4—151no—
99#107—151no—
100#107—151no—
101#103—151no—
102#103D1511yescharacteristic, complemented
103C22⋊C8—151no—
104C2×C3×C5#12311yescharacteristic
105C2×C3×C5C2×Q1611yescharacteristic
106C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
107D15—22no—
108C22×D3—51no—
109C3×Q8—21no—
110C3×Q8—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4C22×D511yescharacteristic
114C2×Dic3—51no—
115C2×Dic3—101no—
116C2×Dic3—101no—
117C4×D3—101no—
118C4×D3—101no—
119C4×D3—202no—
120C3×C8—21no—
121C3⋊C8—101no—
122C22×C5D3×D411yescharacteristic
123C2×D5—32no—
124C2×D5—61no—
125C2×D5—61no—
126C4×C5—41no—
127C4×C5—41no—
128C4×C5#23511yescharacteristic
129C4×C5#23711yescharacteristic
130Dic5—61no—
131Dic5—121no—
132Dic5—121no—
133C2×Q8C2×D1511yescharacteristic
134C22×C4—151no—
135C22×C4—301no—
136C2×C8—151no—
137C2×C8C2×D1511yescharacteristic
138C4⋊C4—151no—
139C4⋊C4—151no—
140C4⋊C4—301no—
141C4⋊C4—301no—
142C4⋊C4C2×D1511yescharacteristic
143C22⋊C4—301no—
144C3×C5#48411yescharacteristic, complemented, Hall
145C22×C3D4×D511yescharacteristic
146C2×D3—52no—
147C2×D3—101no—
148C2×D3—101no—
149C3×C4—41no—
150C3×C4—41no—
151C3×C4#70911yescharacteristic
152C3×C4#71111yescharacteristic
153Dic3—101no—
154Dic3—201no—
155Dic3—201no—
156C2×C5#88311yescharacteristic
157C2×C5#91411yescharacteristic
158C2×C5D3×Q1611yescharacteristic
159D5—62no—
160C23—151no—
161Q8—21no—
162Q8—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—151no—
166C2×C4—301no—
167C2×C4—301no—
168C2×C4—301no—
169C2×C4—301no—
170C2×C4—602no—
171C2×C4C22×D1511yescharacteristic
172C8—21no—
173C8—301no—
174C2×C3#402911yescharacteristic
175C2×C3#406011yescharacteristic
176C2×C3D5×Q1611yescharacteristic
177D3—102no—
178C5#481111yescharacteristic, complemented, Sylow
179C22—152no—
180C22—301no—
181C22—301no—
182C22D4×D1511yescharacteristic
183C4—41no—
184C4—41no—
185C4—301no—
186C4—601no—
187C4—601no—
188C4#681711yescharacteristic
189C4#681911yescharacteristic
190C3#6509811yescharacteristic, complemented, Sylow
191C2—302no—
192C2#9177211yescharacteristic
193C2#9180311yescharacteristic
194C2Q16×D1511yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#103C2
socleC22×C3×C5C2×D4
prime radicalC22×D15D4
hypercenter#103D15
hypocenterC3×C5#484
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. C3×C5×#103C2semidirect
4. #91119C2semidirect
6. #91102C2semidirect
7. #91091C2semidirect
23. C5×#103D3semidirect
44. C3×#103D5semidirect
102. #103D15semidirect
144. C3×C5#484semidirect
178. C5#4811semidirect
190. C3#65098semidirect

Maximal subgroups

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

subgroupindex
#918352
C4⋊C4×D152
C3×C5×#1032
#911192
#911042
#911022
#910912
#650983
#48115