Finite Group Databasebeta

← #11750885

Subgroups — #11750885

Order 960.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#91827C211yesmaximal, characteristic
2#91781C211yesmaximal, characteristic, complemented
3C3×C5×#102C211yesmaximal, characteristic, complemented
4#91116C211yesmaximal, characteristic, complemented
5#91104C211yesmaximal, characteristic, complemented
6#91102C211yesmaximal, characteristic, complemented
7#91092C211yesmaximal, characteristic, complemented
8#65073—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10C2×#1220—21no—
11C2×C4×D15C2211yescharacteristic
12C2×C3×C5×C8C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14#6719—21no—
15#6714—21no—
16C4⋊Dic15C2211yescharacteristic
17C4⋊Dic15C2211yescharacteristic
18C4×Dic15—21no—
19C2×C3⋊#168C2211yescharacteristic
20#4784—51nomaximal, Hall
21#4084—31no—
22#4038—31no—
23C5×#102D311yescharacteristic, complemented
24#3964—31no—
25#3952—31no—
26#3950—31no—
27#3940—31no—
28C23×C3×C5—21no—
29C22×D15D411yescharacteristic
30C3×C5×D4—21no—
31C3×C5×D4—21no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5C2311yescharacteristic
34#1220—42no—
35C2×Dic15—21no—
36C2×Dic15—21no—
37C2×Dic15D411yescharacteristic
38C4×D15—21no—
39C4×D15—21no—
40C3×C5×C8—21no—
41C3⋊#168—21no—
42#938—51no—
43#892—51no—
44C3×#102D511yescharacteristic, complemented
45#832—51no—
46(C2×D3)⋊C8—51no—
47#818—51no—
48#808—51no—
49C2×C5×D4C2×D311yescharacteristic
50C2×C22⋊D5—61no—
51C2×C4×D5—31no—
52C2×C5×C8C2×D311yescharacteristic
53C5×C4⋊C4C2×D311yescharacteristic
54C22⋊Dic5—61no—
55#685—61no—
56C4⋊Dic5—31no—
57C4⋊Dic5—31no—
58C4×Dic5—61no—
59C2×#168—31no—
60#482—151noSylow
61C22×C3×C5—41no—
62C22×C3×C5—41no—
63C22×C3×C5—41no—
64C22×C3×C5C2×D411yescharacteristic
65C2×D15—21no—
66C2×D15—21no—
67C2×D15—21no—
68C3×C4×C5—41no—
69C3×C4×C5#4111yescharacteristic
70C3×C4×C5#4111yescharacteristic
71Dic15—21no—
72Dic15—41no—
73Dic15—41no—
74C2×C3×D4C2×D511yescharacteristic
75C2×#67—101no—
76C2×C4×D3—51no—
77C2×C3×C8C2×D511yescharacteristic
78C3×C4⋊C4C2×D511yescharacteristic
79#217—101no—
80(C2×D3)⋊C4—101no—
81C4⋊Dic3—51no—
82C4⋊Dic3—51no—
83C4×Dic3—101no—
84C2×C3⋊C8—51no—
85C23×C5—21no—
86C22×D5—31no—
87C5×D4—21no—
88C5×D4—21no—
89C2×C4×C5—21no—
90C2×C4×C5C22×D311yescharacteristic
91C22⋊D5—122no—
92C2×Dic5—31no—
93C2×Dic5—61no—
94C2×Dic5—61no—
95C4×D5—61no—
96C4×D5—61no—
97C5×C8—21no—
98#168—61no—
99#121—151no—
100#117—151no—
101#107—151no—
102#106—151no—
103#102—151no—
104#102D1511yescharacteristic, complemented
105C22⋊C8—151no—
106C2×C3×C5—81no—
107C2×C3×C5#12311yescharacteristic
108C2×C3×C5#13511yescharacteristic
109C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
110D15—41no—
111C23×C3—21no—
112C22×D3—51no—
113C3×D4—21no—
114C3×D4—21no—
115C2×C3×C4—21no—
116C2×C3×C4C22×D511yescharacteristic
117#67—202no—
118C2×Dic3—51no—
119C2×Dic3—101no—
120C2×Dic3—101no—
121C4×D3—101no—
122C4×D3—101no—
123C3×C8—21no—
124C3⋊C8—101no—
125C22×C5—41no—
126C22×C5—41no—
127C22×C5—41no—
128C22×C5D3×D411yescharacteristic
129C2×D5—61no—
130C2×D5—61no—
131C2×D5—61no—
132C4×C5—41no—
133C4×C5#23511yescharacteristic
134C4×C5#23711yescharacteristic
135Dic5—61no—
136Dic5—121no—
137Dic5—121no—
138C2×D4—301no—
139C2×D4C2×D1511yescharacteristic
140C22×C4—151no—
141C2×C8—151no—
142C2×C8C2×D1511yescharacteristic
143C4⋊C4—151no—
144C4⋊C4—151no—
145C4⋊C4C2×D1511yescharacteristic
146C22⋊C4—301no—
147C22⋊C4—301no—
148C42—301no—
149C3×C5#48211yescharacteristic, complemented, Hall
150C22×C3—41no—
151C22×C3—41no—
152C22×C3—41no—
153C22×C3D4×D511yescharacteristic
154C2×D3—101no—
155C2×D3—101no—
156C2×D3—101no—
157C3×C4—41no—
158C3×C4#70911yescharacteristic
159C3×C4#71111yescharacteristic
160Dic3—101no—
161Dic3—201no—
162Dic3—201no—
163C2×C5—81no—
164C2×C5#88311yescharacteristic
165C2×C5#91211yescharacteristic
166C2×C5#91411yescharacteristic
167D5—121no—
168C23—21no—
169C23—151no—
170D4—21no—
171D4—21no—
172D4—602no—
173C2×C4—21no—
174C2×C4—151no—
175C2×C4—301no—
176C2×C4—301no—
177C2×C4—301no—
178C2×C4—301no—
179C2×C4C22×D1511yescharacteristic
180C8—21no—
181C8—301no—
182C2×C3—81no—
183C2×C3#402911yescharacteristic
184C2×C3#405811yescharacteristic
185C2×C3#406011yescharacteristic
186D3—201no—
187C5#478411yescharacteristic, complemented, Sylow
188C22—41no—
189C22—41no—
190C22—41no—
191C22—301no—
192C22—301no—
193C22—301no—
194C22D4×D1511yescharacteristic
195C4—41no—
196C4—301no—
197C4—601no—
198C4—601no—
199C4#681711yescharacteristic
200C4#681911yescharacteristic
201C3#6507311yescharacteristic, complemented, Sylow
202C2—81no—
203C2—601no—
204C2#9177211yescharacteristic
205C2#9180111yescharacteristic
206C2#9180311yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#102C2
socleC22×C3×C5C2×D4
prime radical#91827C2
hypercenter#102D15
hypocenterC3×C5#482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #91781C2semidirect
3. C3×C5×#102C2semidirect
4. #91116C2semidirect
5. #91104C2semidirect
6. #91102C2semidirect
7. #91092C2semidirect
23. C5×#102D3semidirect
44. C3×#102D5semidirect
104. #102D15semidirect
149. C3×C5#482semidirect
187. C5#4784semidirect
201. C3#65073semidirect

Maximal subgroups

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

subgroupindex
#918272
#917812
C3×C5×#1022
#911162
#911042
#911022
#910922
#650733
#47845