Finite Group Databasebeta

← #11749352

Subgroups — #11749352

Order 960.

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

normal subgroups only

This group has 200 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
1C3×#4093C211yesmaximal, characteristic
2#91468C211yesmaximal, characteristic, complemented
3#91119C211yesmaximal, characteristic, complemented
4C5×#835C211yesmaximal, characteristic, complemented
5#90965C211yesmaximal, characteristic
6#90964C211yesmaximal, characteristic
7#90952C211yesmaximal, characteristic, complemented
8#65084—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C3×D20C2211yescharacteristic
11C2×#1204—21no—
12C4⋊Dic15C2211yescharacteristic
13C2×C3⋊#168C2211yescharacteristic
14C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×#685—21no—
17C3×#685—21no—
18C3×C4×Dic5C2211yescharacteristic
19#6668—21no—
20#5055—51nomaximal, Hall
21#4093D311yescharacteristic
22#4034—31no—
23C5×#103—31no—
24#3967—31no—
25#3953—31no—
26#3947—31no—
27#3941—31no—
28C22×C3×D5—21no—
29C3×C5×Q8—21no—
30C3×C5×Q8—21no—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5C2311yescharacteristic
33C2×Dic15—21no—
34C2×C5×Dic3—21no—
35C2×C3×Dic5D411yescharacteristic
36C2×C3×Dic5D411yescharacteristic
37C3×D20—21no—
38C3×D20—21no—
39#1204—42no—
40C3⋊#168—21no—
41C5×C3⋊C8—21no—
42C3×#124—51no—
43#869—51no—
44#835—51no—
45#835D511yescharacteristic, complemented
46#832—51no—
47#832—51no—
48#803—51no—
49C2×C5×Q8C2×D311yescharacteristic
50C2×D20C2×D311yescharacteristic
51C2×Dic10—61no—
52C2×C5×C8—31no—
53C5×C4⋊C4—31no—
54#685—21no—
55#685—21no—
56C4⋊Dic5—31no—
57#683—61no—
58C4×Dic5C2×D311yescharacteristic
59C2×#168—31no—
60#489—151noSylow
61C22×C3×C5C2×D411yescharacteristic
62C2×C3×D5—41no—
63C2×C3×D5—41no—
64C2×C3×D5—41no—
65C3×C4×C5—41no—
66C3×C4×C5#4111yescharacteristic
67C3×C4×C5#4111yescharacteristic
68Dic15—41no—
69C3×Dic5—21no—
70C3×Dic5—21no—
71C5×Dic3—41no—
72C2×C3×Q8C2×D511yescharacteristic
73C2×C3×D4—51no—
74C2×Dic6—101no—
75C3×C22⋊C4—101no—
76C3×C22⋊C4—101no—
77C3×C42—51no—
78C4⋊Dic3—51no—
79C4⋊Dic3—101no—
80C4⋊Dic3C2×D511yescharacteristic
81C2×C3⋊C8—51no—
82C2×C3⋊C8C2×D511yescharacteristic
83C22×D5—21no—
84C5×Q8—21no—
85C5×Q8—21no—
86C2×C4×C5—21no—
87C2×C4×C5—61no—
88C2×C4×C5C22×D311yescharacteristic
89C2×Dic5—61no—
90C2×Dic5#6711yescharacteristic
91C2×Dic5#6711yescharacteristic
92D20—21no—
93D20—21no—
94Dic10—122no—
95C5×C8—61no—
96#168—61no—
97C4⋊Q8—151no—
98#124—51no—
99#103—31no—
100#103—151no—
101#102—151no—
102#102—151no—
103#97—151no—
104C2×C3×C5#12411yescharacteristic
105C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
106C2×C3×C5#13711yescharacteristic
107C3×D5—81no—
108C23×C3—101no—
109C3×Q8—21no—
110C3×Q8—21no—
111C3×D4—101no—
112C3×D4—101no—
113C2×C3×C4—21no—
114C2×C3×C4—51no—
115C2×C3×C4—51no—
116C2×C3×C4C22×D511yescharacteristic
117C2×Dic3—21no—
118C2×Dic3—101no—
119Dic6—202no—
120C3⋊C8—21no—
121C3⋊C8—101no—
122C22×C5C2×#6711yescharacteristic
123C2×D5—41no—
124C2×D5—41no—
125C2×D5—41no—
126C4×C5—41no—
127C4×C5—121no—
128C4×C5#23711yescharacteristic
129C4×C5#23711yescharacteristic
130Dic5—21no—
131Dic5—21no—
132Dic5—121no—
133C2×Q8—301no—
134C2×Q8D3×D511yescharacteristic
135C2×D4—51no—
136C2×C8—31no—
137C2×C8—151no—
138C4⋊C4—31no—
139C4⋊C4—151no—
140C4⋊C4—301no—
141C22⋊C4—101no—
142C22⋊C4—101no—
143C42—51no—
144C3×C5#48911yescharacteristic, complemented, Hall
145C22×C3—201no—
146C22×C3—201no—
147C22×C3—201no—
148C22×C3D4×D511yescharacteristic
149C3×C4—41no—
150C3×C4—101no—
151C3×C4—101no—
152C3×C4#70911yescharacteristic
153C3×C4#71111yescharacteristic
154Dic3—41no—
155Dic3—201no—
156C2×C5#93611yescharacteristic
157C2×C5#94911yescharacteristic
158C2×C5#95111yescharacteristic
159D5—81no—
160C23—101no—
161Q8—21no—
162Q8—21no—
163Q8—602no—
164D4—101no—
165D4—101no—
166C2×C4—21no—
167C2×C4—51no—
168C2×C4—51no—
169C2×C4—61no—
170C2×C4—301no—
171C2×C4C2×D3×D511yescharacteristic
172C8—61no—
173C8—301no—
174C2×C3—401no—
175C2×C3#403111yescharacteristic
176C2×C3#406011yescharacteristic
177C2×C3#406411yescharacteristic
178C5#505511yescharacteristic, complemented, Sylow
179C22—201no—
180C22—201no—
181C22—201no—
182C22D5×#6711yescharacteristic
183C4—41no—
184C4—101no—
185C4—101no—
186C4—121no—
187C4—601no—
188C4#677911yescharacteristic
189C4#678011yescharacteristic
190C3#6508411yescharacteristic, complemented, Sylow
191C2—401no—
192C2#9150211yescharacteristic
193C2#9150811yescharacteristic
194C2#9153411yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC2×C3×D20C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#489
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
2. #91468C2semidirect
3. #91119C2semidirect
4. C5×#835C2semidirect
7. #90952C2semidirect
45. #835D5semidirect
144. C3×C5#489semidirect
178. C5#5055semidirect
190. C3#65084semidirect

Maximal subgroups

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

subgroupindex
C3×#40932
#914682
#911192
C5×#8352
#909652
#909642
#909522
#650843
#50555