Finite Group Databasebeta

← #11747929

Subgroups — #11747929

Order 960.

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

normal subgroups only

This group has 240 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
1C2×#6705C211yesmaximal, characteristic, complemented
2#91466C211yesmaximal, characteristic
3#91390C211yesmaximal, characteristic, complemented
4C2×#6656C211yesmaximal, characteristic, complemented
5C5×#821C211yesmaximal, characteristic, complemented
6C3×#3948C211yesmaximal, characteristic, complemented
7#90989C211yesmaximal, characteristic, complemented
8#65069—31nomaximal, Hall
9C2×C4×D15C2211yescharacteristic
10C2×C5×D12C2211yescharacteristic
11C2×C3×Dic10C2211yescharacteristic
12C2×#1203—21no—
13C2×C3×C5×C8C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15#6705—22no—
16C5×C4⋊Dic3C2211yescharacteristic
17C3×C4⋊Dic5C2211yescharacteristic
18Dic3⋊Dic5—21no—
19#6667—21no—
20(C2×D3)⋊Dic5—21no—
21#6656—22no—
22#4812—51nomaximal, Hall
23#4084—31no—
24C2×#687—31no—
25C2×#676—31no—
26#4043—31no—
27C5×#102—31no—
28#3948D311yescharacteristic, complemented
29#3939—31no—
30C22×D15D411yescharacteristic
31C22×C5×D3—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15D411yescharacteristic
34C4×D15—21no—
35C4×D15—21no—
36C2×C5×Dic3—21no—
37C5×D12—21no—
38C5×D12—21no—
39C2×C3×Dic5—21no—
40C2×C3×Dic5—21no—
41C3×Dic10—21no—
42C3×Dic10—21no—
43#1203—42no—
44C3×C5×C8—21no—
45C3⋊#168D412yescomplemented
46#946—51no—
47C2×#215—51no—
48C2×ΓL(1,𝔽25)—51no—
49#895—51no—
50C3×#103—51no—
51#821D511yescharacteristic, complemented
52#807—51no—
53C2×C5×D4—31no—
54C2×C22⋊D5—61no—
55C2×C4×D5—31no—
56C2×Dic10C2×D311yescharacteristic
57C2×C5×C8C2×D311yescharacteristic
58C5×C4⋊C4—31no—
59C22⋊Dic5—61no—
60#687—62no—
61#685—61no—
62C4⋊Dic5—61no—
63C4⋊Dic5C2×D311yescharacteristic
64C2×#168—31no—
65#676—62no—
66#468—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×D15—21no—
69C2×D15—21no—
70C2×D15—21no—
71C2×C5×D3—41no—
72C2×C5×D3—41no—
73C2×C5×D3—41no—
74C3×C4×C5C2×D411yescharacteristic
75C3×C4×C5#4111yescharacteristic
76Dic15—21no—
77C3×Dic5—41no—
78C3×Dic5—41no—
79C5×Dic3—41no—
80C2×C3×Q8—51no—
81C2×D12—101no—
82C2×D12C2×D511yescharacteristic
83C2×C4×D3—51no—
84C2×C3×C8C2×D511yescharacteristic
85C3×C4⋊C4—51no—
86#215—102no—
87(C2×D3)⋊C4—101no—
88(C2×D3)⋊C4—101no—
89C4⋊Dic3C2×D511yescharacteristic
90Dic3⋊C4—101no—
91C2×C3⋊C8—51no—
92ΓL(1,𝔽25)—102no—
93C23×C5—61no—
94C22×D5—31no—
95C5×D4—61no—
96C5×D4—61no—
97C2×C4×C5—61no—
98C2×C4×C5C22×D311yescharacteristic
99C22⋊D5—122no—
100C2×Dic5—21no—
101C2×Dic5—21no—
102C2×Dic5—31no—
103C4×D5—61no—
104C4×D5—61no—
105Dic10—21no—
106Dic10—21no—
107C5×C8—21no—
108#168—32no—
109C2×SD16—151no—
110C2×M16—151no—
111C22⋊Q8—151no—
112#121—151no—
113#107—151no—
114#103—51no—
115#102—31no—
116C2×C3×C5#12111yescharacteristic
117C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
118C2×C3×C5#13711yescharacteristic
119D15—41no—
120C5×D3—81no—
121C22×D3—21no—
122C22×D3—51no—
123C3×Q8—101no—
124C3×Q8—101no—
125C2×C3×C4—101no—
126C2×C3×C4—101no—
127C2×C3×C4C22×D511yescharacteristic
128C2×Dic3—21no—
129C2×Dic3—51no—
130D12—21no—
131D12—21no—
132D12—202no—
133C4×D3—101no—
134C4×D3—101no—
135C3×C8—21no—
136C3⋊C8—52no—
137C22×C5—121no—
138C22×C5—121no—
139C22×C5—121no—
140C22×C5D3×D411yescharacteristic
141C2×D5—61no—
142C2×D5—61no—
143C2×D5—61no—
144C4×C5—121no—
145C4×C5#23511yescharacteristic
146C4×C5D3×D411yescharacteristic
147Dic5—41no—
148Dic5—41no—
149Dic5—61no—
150C2×Q8—51no—
151C2×D4—31no—
152C2×D4—301no—
153C22×C4—151no—
154SD16—302no—
155M16—302no—
156C2×C8—151no—
157C2×C8D3×D511yescharacteristic
158C4⋊C4—31no—
159C4⋊C4—51no—
160C4⋊C4—301no—
161C22⋊C4—301no—
162C22⋊C4—301no—
163C3×C5#46811yescharacteristic, complemented, Hall
164C22×C3D4×D511yescharacteristic
165C2×D3—41no—
166C2×D3—41no—
167C2×D3—41no—
168C2×D3—101no—
169C2×D3—101no—
170C2×D3—101no—
171C3×C4—201no—
172C3×C4—201no—
173C3×C4#70911yescharacteristic
174C3×C4D4×D511yescharacteristic
175Dic3—41no—
176Dic3—101no—
177C2×C5—241no—
178C2×C5#88411yescharacteristic
179C2×C5#91411yescharacteristic
180C2×C5#91811yescharacteristic
181D5—121no—
182C23—61no—
183C23—151no—
184Q8—101no—
185Q8—101no—
186D4—61no—
187D4—61no—
188D4—602no—
189C2×C4—61no—
190C2×C4—101no—
191C2×C4—101no—
192C2×C4—151no—
193C2×C4—301no—
194C2×C4—301no—
195C2×C4C2×D3×D511yescharacteristic
196C8—21no—
197C8—152no—
198C2×C3#403011yescharacteristic
199C2×C3#405711yescharacteristic
200C2×C3#406111yescharacteristic
201D3—81no—
202D3—201no—
203C5#481211yescharacteristic, complemented, Sylow
204C22—121no—
205C22—121no—
206C22—121no—
207C22—301no—
208C22—301no—
209C22—301no—
210C22#677711yescharacteristic
211C4—121no—
212C4—201no—
213C4—201no—
214C4—301no—
215C4#677111yescharacteristic
216C4#679011yescharacteristic
217C3#6506911yescharacteristic, complemented, Sylow
218C2—241no—
219C2—601no—
220C2#9125711yescharacteristic
221C2#9128011yescharacteristic
222C2#9146111yescharacteristic
subgroupG/H
centerC22#6777
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radical#91466C2
hypercenterC2×C8D3×D5
hypocenterC3×C5#468
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#6705C2semidirect
3. #91390C2semidirect
4. C2×#6656C2semidirect
5. C5×#821C2semidirect
6. C3×#3948C2semidirect
7. #90989C2semidirect
28. #3948D3semidirect
45. C3⋊#168D4semidirect
51. #821D5semidirect
163. C3×C5#468semidirect
203. C5#4812semidirect
217. C3#65069semidirect

Maximal subgroups

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

subgroupindex
C2×#67052
#914662
#913902
C2×#66562
C5×#8212
C3×#39482
#909892
#650693
#48125