Finite Group Databasebeta

← #11749226

Subgroups — #11749226

Order 960.

248 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 62 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×#6717C211yesmaximal, characteristic, complemented
2C3×#4093C211yesmaximal, characteristic, complemented
3#91418C211yesmaximal, characteristic, complemented
4C2×#6653C211yesmaximal, characteristic
5C5×#835C211yesmaximal, characteristic, complemented
6#90982C211yesmaximal, characteristic, complemented
7#90964C211yesmaximal, characteristic, complemented
8#65108—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×D60C2211yescharacteristic
11C2×C3×D20C2211yescharacteristic
12C2×#1200—21no—
13#6717—22no—
14C2×C3⋊#168C2211yescharacteristic
15C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#685—21no—
18C3×#685—21no—
19C3×C4×Dic5C2211yescharacteristic
20#6667—21no—
21#6653—22no—
22#5057—51nomaximal, Hall
23#4093D311yescharacteristic, complemented
24C2×#688—31no—
25C2×D40—31no—
26#4039—31no—
27C5×#103—31no—
28#3946—31no—
29#3941—31no—
30C22×D15—21no—
31C22×C3×D5—21no—
32C3×C5×Q8—21no—
33C3×C5×Q8—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36D60—21no—
37D60D412yes—
38C2×C5×Dic3—21no—
39C2×C3×Dic5D411yescharacteristic
40C2×C3×Dic5D411yescharacteristic
41C3×D20—21no—
42C3×D20—21no—
43#1200—42no—
44C3⋊#168—21no—
45C5×C3⋊C8—21no—
46C3×#124—51no—
47C2×#215—51no—
48C2×#213—51no—
49C4×D12—51no—
50#835D511yescharacteristic, complemented
51#832—51no—
52C4⋊(C3⋊C8)—51no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×D20—31no—
55C2×D20C2×D311yescharacteristic
56C2×C4×D5—61no—
57C2×C5×C8—31no—
58C5×C4⋊C4—31no—
59#688—62no—
60#685—21no—
61#685—21no—
62#685—61no—
63C4×Dic5C2×D311yescharacteristic
64C2×#168—31no—
65D40—62no—
66#463—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×D15—22no—
69C2×D15—41no—
70C2×D15—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
77C3×Dic5—21no—
78C3×Dic5—21no—
79C5×Dic3—41no—
80C2×C3×Q8C2×D511yescharacteristic
81C2×C3×D4—51no—
82C2×D12—51no—
83C2×C4×D3—101no—
84C3×C22⋊C4—101no—
85C3×C22⋊C4—101no—
86C3×C42—51no—
87#215—102no—
88#213—102no—
89(C2×D3)⋊C4—101no—
90C4⋊Dic3C2×D511yescharacteristic
91C2×C3⋊C8—51no—
92C2×C3⋊C8C2×D511yescharacteristic
93C22×D5—21no—
94C22×D5—61no—
95C5×Q8—21no—
96C5×Q8—21no—
97C2×C4×C5—21no—
98C2×C4×C5—61no—
99C2×C4×C5C22×D311yescharacteristic
100C2×Dic5#6711yescharacteristic
101C2×Dic5#6711yescharacteristic
102D20—21no—
103D20—21no—
104D20—32no—
105D20—61no—
106C4×D5—122no—
107C5×C8—61no—
108#168—61no—
109C2×SD16—151no—
110C2×D8—151no—
111#124—51no—
112C4×D4—151no—
113C4⋊C8—151no—
114#103—31no—
115#102—151no—
116C2×C3×C5#12111yescharacteristic
117C2×C3×C5#13511yescharacteristic
118C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
119D15—42no—
120C3×D5—81no—
121C23×C3—101no—
122C22×D3—101no—
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—21no—
132D12—52no—
133D12—101no—
134C4×D3—202no—
135C3⋊C8—21no—
136C3⋊C8—101no—
137C22×C5C2×#6711yescharacteristic
138C2×D5—41no—
139C2×D5—41no—
140C2×D5—41no—
141C2×D5—62no—
142C2×D5—121no—
143C2×D5—121no—
144C4×C5—41no—
145C4×C5—121no—
146C4×C5D3×D411yescharacteristic
147C4×C5#23711yescharacteristic
148Dic5—21no—
149Dic5—21no—
150C2×Q8D3×D511yescharacteristic
151C2×D4—51no—
152C2×D4—151no—
153C22×C4—301no—
154SD16—302no—
155D8—302no—
156C2×C8—31no—
157C2×C8—151no—
158C4⋊C4—31no—
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—102no—
169C2×D3—201no—
170C2×D3—201no—
171C3×C4—41no—
172C3×C4—101no—
173C3×C4—101no—
174C3×C4#70911yescharacteristic
175C3×C4D4×D511yescharacteristic
176Dic3—41no—
177C2×C5#93811yescharacteristic
178C2×C5#94911yescharacteristic
179C2×C5#95011yescharacteristic
180D5—81no—
181D5—122no—
182C23—101no—
183C23—301no—
184Q8—21no—
185Q8—21no—
186D4—101no—
187D4—101no—
188D4—152no—
189D4—301no—
190C2×C4—21no—
191C2×C4—51no—
192C2×C4—51no—
193C2×C4—61no—
194C2×C4—602no—
195C2×C4C2×D3×D511yescharacteristic
196C8—61no—
197C8—301no—
198C2×C3—401no—
199C2×C3#403011yescharacteristic
200C2×C3#406011yescharacteristic
201C2×C3#406511yescharacteristic
202D3—202no—
203C5#505711yescharacteristic, complemented, Sylow
204C22—201no—
205C22—201no—
206C22—201no—
207C22—302no—
208C22—601no—
209C22—601no—
210C22D5×#6711yescharacteristic
211C4—41no—
212C4—101no—
213C4—101no—
214C4—121no—
215C4#677911yescharacteristic
216C4#679011yescharacteristic
217C3#6510811yescharacteristic, complemented, Sylow
218C2—401no—
219C2—602no—
220C2#9150211yescharacteristic
221C2#9151611yescharacteristic
222C2#9153311yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC2×#6653C2
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×#6717C2semidirect
2. C3×#4093C2semidirect
3. #91418C2semidirect
5. C5×#835C2semidirect
6. #90982C2semidirect
7. #90964C2semidirect
23. #4093D3semidirect
50. #835D5semidirect
163. C3×C5#463semidirect
203. C5#5057semidirect
217. C3#65108semidirect

Maximal subgroups

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

subgroupindex
C2×#67172
C3×#40932
#914182
C2×#66532
C5×#8352
#909822
#909642
#651083
#50575