Finite Group Databasebeta

← #11747967

Subgroups — #11747967

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×#6706C211yesmaximal, characteristic, complemented
2#91428C211yesmaximal, characteristic, complemented
3#91364C211yesmaximal, characteristic, complemented
4C2×#6653C211yesmaximal, characteristic
5C5×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C3×#3953C211yesmaximal, characteristic, complemented
7#90974C211yesmaximal, characteristic, complemented
8#65133—31nomaximal, Hall
9C2×D60C2211yescharacteristic
10C2×Dic30C2211yescharacteristic
11C2×C3×D20C2211yescharacteristic
12C2×#1200—21no—
13C2×C3×C5×C8C2211yescharacteristic
14#6706—22no—
15C4×C5×Dic3C2211yescharacteristic
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×C4⋊Dic5C2211yescharacteristic
18#6667—21no—
19#6665—21no—
20#6665—21no—
21#6653—22no—
22#4787—51nomaximal, Hall
23C2×D40—31no—
24C2×#677—31no—
25#4021—31no—
26C4×D20—31no—
27C5×C4⋊C8—31no—
28#3953D311yescharacteristic, complemented
29#3948—31no—
30C22×D15—21no—
31C22×C3×D5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15—21no—
34D60—21no—
35D60D412yes—
36Dic30—21no—
37Dic30—21no—
38C2×C5×Dic3D411yescharacteristic
39C2×C5×Dic3D411yescharacteristic
40C2×C3×Dic5—21no—
41C3×D20—21no—
42C3×D20—21no—
43#1200—42no—
44C3×C5×C8—21no—
45C5×C3⋊C8—21no—
46#936—51no—
47C2×#213—51no—
48C2×#204—51no—
49#893—51no—
50C3×#102—51no—
51Dic3⋊C8D511yescharacteristic, complemented
52#810—51no—
53C2×D20—31no—
54C2×D20C2×D311yescharacteristic
55C2×C4×D5—61no—
56C2×Dic10—31no—
57C2×C5×C8—31no—
58C2×C5×C8C2×D311yescharacteristic
59C42×C5—31no—
60#685—61no—
61#685—61no—
62#685—61no—
63C4⋊Dic5C2×D311yescharacteristic
64D40—62no—
65#677—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×C5C2×D411yescharacteristic
75C3×C4×C5#4111yescharacteristic
76Dic15—41no—
77C3×Dic5—41no—
78C5×Dic3—21no—
79C5×Dic3—21no—
80C2×C3×D4—51no—
81C2×D12—51no—
82C2×C4×D3—101no—
83C2×Dic6—51no—
84C2×C3×C8C2×D511yescharacteristic
85C3×C4⋊C4—51no—
86#217—101no—
87#217—101no—
88#213—102no—
89(C2×D3)⋊C4—101no—
90C4×Dic3C2×D511yescharacteristic
91C2×C3⋊C8C2×D511yescharacteristic
92#204—102no—
93C22×D5—21no—
94C22×D5—61no—
95C2×C4×C5—31no—
96C2×C4×C5—31no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—21no—
99C2×Dic5—61no—
100D20—21no—
101D20—21no—
102D20—32no—
103D20—61no—
104C4×D5—122no—
105Dic10—61no—
106Dic10—61no—
107C5×C8—21no—
108C5×C8—61no—
109C2×SD16—151no—
110C2×D8—151no—
111#124—151no—
112C4×D4—151no—
113C4⋊C8—31no—
114#103—151no—
115#102—51no—
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×D4—101no—
124C3×D4—101no—
125C2×C3×C4—101no—
126C2×C3×C4C22×D511yescharacteristic
127C2×Dic3—101no—
128C2×Dic3D2011yescharacteristic
129C2×Dic3D2011yescharacteristic
130D12—52no—
131D12—101no—
132C4×D3—202no—
133Dic6—101no—
134Dic6—101no—
135C3×C8—21no—
136C3⋊C8—21no—
137C22×C5D3×D411yescharacteristic
138C2×D5—41no—
139C2×D5—41no—
140C2×D5—41no—
141C2×D5—62no—
142C2×D5—121no—
143C2×D5—121no—
144C4×C5—61no—
145C4×C5—61no—
146C4×C5#23511yescharacteristic
147C4×C5D3×D411yescharacteristic
148Dic5—41no—
149Dic5—121no—
150C2×Q8—151no—
151C2×D4—51no—
152C2×D4—151no—
153C22×C4—301no—
154SD16—302no—
155D8—302no—
156C2×C8—31no—
157C2×C8D3×D511yescharacteristic
158C4⋊C4—51no—
159C22⋊C4—301no—
160C22⋊C4—301no—
161C22⋊C4—301no—
162C42—31no—
163C3×C5#46311yescharacteristic, complemented, Hall
164C22×C3—201no—
165C22×C3—201no—
166C22×C3—201no—
167C22×C3C2×D2011yescharacteristic
168C2×D3—102no—
169C2×D3—201no—
170C2×D3—201no—
171C3×C4—201no—
172C3×C4D4×D511yescharacteristic
173C3×C4#71311yescharacteristic
174Dic3—21no—
175Dic3—21no—
176Dic3—201no—
177C2×C5#88411yescharacteristic
178C2×C5#91111yescharacteristic
179C2×C5#91611yescharacteristic
180D5—81no—
181D5—122no—
182C23—101no—
183C23—301no—
184Q8—301no—
185Q8—301no—
186D4—101no—
187D4—101no—
188D4—152no—
189D4—301no—
190C2×C4—31no—
191C2×C4—31no—
192C2×C4—101no—
193C2×C4—301no—
194C2×C4—602no—
195C2×C4C2×D3×D511yescharacteristic
196C8—21no—
197C8—61no—
198C2×C3—401no—
199C2×C3#404111yescharacteristic
200C2×C3#405011yescharacteristic
201C2×C3#405411yescharacteristic
202D3—202no—
203C5#478711yescharacteristic, complemented, Sylow
204C22—201no—
205C22—201no—
206C22—201no—
207C22—302no—
208C22—601no—
209C22—601no—
210C22D3×D2011yescharacteristic
211C4—61no—
212C4—61no—
213C4—201no—
214C4—601no—
215C4#677311yescharacteristic
216C4#679011yescharacteristic
217C3#6513311yescharacteristic, complemented, Sylow
218C2—401no—
219C2—602no—
220C2#9125411yescharacteristic
221C2#9127211yescharacteristic
222C2#9145911yescharacteristic
subgroupG/H
centerC22D3×D20
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×C8C22
socleC22×C3×C5C2×D4
prime radicalC2×#6653C2
hypercenterC2×C8D3×D5
hypocenterC3×C5#463
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×#6706C2semidirect
2. #91428C2semidirect
3. #91364C2semidirect
5. C5×Dic3⋊C8C2semidirect
6. C3×#3953C2semidirect
7. #90974C2semidirect
28. #3953D3semidirect
51. Dic3⋊C8D5semidirect
163. C3×C5#463semidirect
203. C5#4787semidirect
217. C3#65133semidirect

Maximal subgroups

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

subgroupindex
C2×#67062
#914282
#913642
C2×#66532
C5×Dic3⋊C82
C3×#39532
#909742
#651333
#47875