Finite Group Databasebeta

← #11749224

Subgroups — #11749224

Order 960.

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

normal subgroups only

This group has 248 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
1C2×C5×#215C211yesmaximal, characteristic, complemented
2C3×#4093C211yesmaximal, characteristic, complemented
3Dic5×D12C211yesmaximal, characteristic, complemented
4C2×#6652C211yesmaximal, characteristic
5#91119C211yesmaximal, characteristic, complemented
6#90982C211yesmaximal, characteristic, complemented
7#90965C211yesmaximal, characteristic, complemented
8#65454—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C5×D12C2211yescharacteristic
11C2×C3×D20C2211yescharacteristic
12C2×D3×Dic5—21no—
13C4⋊Dic15C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15C5×#215—22no—
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#685—21no—
18C3×#685—21no—
19C3×C4×Dic5C2211yescharacteristic
20(C2×D3)⋊Dic5—21no—
21#6652—22no—
22#5057—51nomaximal, Hall
23C2×C5×SD16—31no—
24#4093D311yescharacteristic, complemented
25D4×Dic5—31no—
26C2×#686—31no—
27#3967—31no—
28#3953—31no—
29#3946—31no—
30C22×C5×D3—21no—
31C22×C3×D5—21no—
32C3×C5×Q8—21no—
33C3×C5×Q8—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36C2×Dic15—21no—
37C5×D12—21no—
38C5×D12D412yes—
39C2×C3×Dic5D411yescharacteristic
40C2×C3×Dic5D411yescharacteristic
41C3×D20—21no—
42C3×D20—21no—
43D3×Dic5—42no—
44C3⋊#168—21no—
45C5×C3⋊C8—21no—
46C3×#124—51no—
47C2×#215D511yescharacteristic, complemented
48C2×#213—51no—
49C4×D12—51no—
50#835—51no—
51#832—51no—
52C4⋊(C3⋊C8)—51no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×C5×D4—31no—
55C22×Dic5—61no—
56C2×D20C2×D311yescharacteristic
57C5×SD16—62no—
58C2×C5×C8—31no—
59C22⋊Dic5—61no—
60#686—62no—
61#685—21no—
62#685—21no—
63C4⋊Dic5—31no—
64C4×Dic5C2×D311yescharacteristic
65C2×#168—31no—
66#463—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×C5×D3—22no—
69C2×C5×D3—41no—
70C2×C5×D3—41no—
71C2×C3×D5—41no—
72C2×C3×D5—41no—
73C2×C3×D5—41no—
74C3×C4×C5—41no—
75C3×C4×C5C2×D411yescharacteristic
76C3×C4×C5#4111yescharacteristic
77Dic15—41no—
78C3×Dic5—21no—
79C3×Dic5—21no—
80C2×C3×Q8C2×D511yescharacteristic
81C2×C3×D4—51no—
82C2×D12C2×D511yescharacteristic
83C2×C4×D3—101no—
84C3×C22⋊C4—101no—
85C3×C22⋊C4—101no—
86C3×C42—51no—
87#215—22no—
88#213—102no—
89(C2×D3)⋊C4—101no—
90C4⋊Dic3—51no—
91C2×C3⋊C8—51no—
92C2×C3⋊C8C2×D511yescharacteristic
93C23×C5—61no—
94C22×D5—21no—
95C5×Q8—21no—
96C5×Q8—21no—
97C5×D4—32no—
98C5×D4—61no—
99C2×C4×C5—21no—
100C2×C4×C5C22×D311yescharacteristic
101C2×Dic5—61no—
102C2×Dic5—122no—
103C2×Dic5#6711yescharacteristic
104C2×Dic5#6711yescharacteristic
105D20—21no—
106D20—21no—
107C5×C8—61no—
108#168—61no—
109C2×SD16—31no—
110C2×D8—151no—
111#124—51no—
112C4×D4—151no—
113C4⋊C8—151no—
114#103—151no—
115#102—151no—
116C2×C3×C5#12111yescharacteristic
117C2×C3×C5#13511yescharacteristic
118C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
119C3×D5—81no—
120C5×D3—42no—
121C23×C3—101no—
122C22×D3—21no—
123C3×Q8—21no—
124C3×Q8—21no—
125C3×D4—101no—
126C3×D4—101no—
127C2×C3×C4—21no—
128C2×C3×C4—51no—
129C2×C3×C4—51no—
130C2×C3×C4C22×D511yescharacteristic
131C2×Dic3—101no—
132D12—21no—
133D12C22⋊D512yes—
134C4×D3—202no—
135C3⋊C8—21no—
136C3⋊C8—101no—
137C22×C5—62no—
138C22×C5—121no—
139C22×C5—121no—
140C22×C5C2×#6711yescharacteristic
141C2×D5—41no—
142C2×D5—41no—
143C2×D5—41no—
144C4×C5—41no—
145C4×C5D3×D411yescharacteristic
146C4×C5#23711yescharacteristic
147Dic5—21no—
148Dic5—21no—
149Dic5—121no—
150C2×Q8D3×D511yescharacteristic
151C2×D4—31no—
152C2×D4—51no—
153C22×C4—301no—
154SD16—62no—
155D8—302no—
156C2×C8—31no—
157C2×C8—151no—
158C4⋊C4—151no—
159C22⋊C4—101no—
160C22⋊C4—101no—
161C22⋊C4—301no—
162C42—51no—
163C3×C5#46311yescharacteristic, complemented, Hall
164C22×C3—201no—
165C22×C3—201no—
166C22×C3—201no—
167C22×C3D4×D511yescharacteristic
168C2×D3—22no—
169C2×D3—41no—
170C2×D3—41no—
171C3×C4—41no—
172C3×C4—101no—
173C3×C4—101no—
174C3×C4#71111yescharacteristic
175C3×C4C2×C22⋊D511yescharacteristic
176Dic3—201no—
177C2×C5—122no—
178C2×C5#93811yescharacteristic
179C2×C5#94911yescharacteristic
180C2×C5#95011yescharacteristic
181D5—81no—
182C23—61no—
183C23—101no—
184Q8—21no—
185Q8—21no—
186D4—32no—
187D4—61no—
188D4—101no—
189D4—101no—
190C2×C4—21no—
191C2×C4—51no—
192C2×C4—51no—
193C2×C4—301no—
194C2×C4—602no—
195C2×C4C2×D3×D511yescharacteristic
196C8—61no—
197C8—301no—
198C2×C3—401no—
199C2×C3#406011yescharacteristic
200C2×C3#406211yescharacteristic
201C2×C3#408511yescharacteristic
202D3—42no—
203C5#505711yescharacteristic, complemented, Sylow
204C22—62no—
205C22—121no—
206C22—121no—
207C22—201no—
208C22—201no—
209C22—201no—
210C22D5×#6711yescharacteristic
211C4—41no—
212C4—101no—
213C4—101no—
214C4—601no—
215C4#678011yescharacteristic
216C4D3×C22⋊D511yescharacteristic
217C3#6545411yescharacteristic, complemented, Sylow
218C2—122no—
219C2—401no—
220C2#9150211yescharacteristic
221C2#9151411yescharacteristic
222C2#9156511yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC2×#6652C2
hypercenterC2×Q8D3×D5
hypocenterC3×C5#463
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×#215C2semidirect
2. C3×#4093C2semidirect
3. Dic5×D12C2semidirect
5. #91119C2semidirect
6. #90982C2semidirect
7. #90965C2semidirect
24. #4093D3semidirect
47. C2×#215D5semidirect
163. C3×C5#463semidirect
203. C5#5057semidirect
217. C3#65454semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#2152
C3×#40932
Dic5×D122
C2×#66522
#911192
#909822
#909652
#654543
#50575