Finite Group Databasebeta

← #11751146

Subgroups — #11751146

Order 960.

192 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 67 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×C5×C22⋊Q8C211yesmaximal, characteristic
2#91815C211yesmaximal, characteristic
3#91119C211yesmaximal, characteristic, complemented
4#91119C211yesmaximal, characteristic, complemented
5#91114C211yesmaximal, characteristic
6#91092C211yesmaximal, characteristic, complemented
7#91091C211yesmaximal, characteristic, complemented
8#65334—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C22×C3×C4×C5C2211yescharacteristic
11C3×C5×C4⋊C4—21no—
12C3×C5×C4⋊C4C2211yescharacteristic
13C3×C5×C22⋊C4—21no—
14#6719—21no—
15C4⋊Dic15C2211yescharacteristic
16C4⋊Dic15C2211yescharacteristic
17C4×Dic15—21no—
18C2×C3⋊#168C2211yescharacteristic
19C2×C3⋊#168C2211yescharacteristic
20#5045—51nomaximal, Hall
21C5×C22⋊Q8D311yescharacteristic
22#4072—31no—
23#3967—31no—
24#3967—31no—
25C22⋊#168—31no—
26#3940—31no—
27#3939—31no—
28C23×C3×C5D411yescharacteristic
29C3×C5×Q8—21no—
30C3×C5×Q8—21no—
31C2×C3×C4×C5—21no—
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5D411yescharacteristic
36C2×C3×C4×C5C2311yescharacteristic
37C2×Dic15—21no—
38C2×Dic15—21no—
39C3⋊#168—21no—
40C3⋊#168—21no—
41C3×C22⋊Q8D511yescharacteristic
42#926—51no—
43#835—51no—
44#835—51no—
45#830—51no—
46#808—51no—
47#807—51no—
48C2×C5×Q8C2×D311yescharacteristic
49C22×C4×C5C2×D311yescharacteristic
50C5×C4⋊C4—21no—
51C5×C4⋊C4C2×D311yescharacteristic
52C5×C22⋊C4—21no—
53C22⋊Dic5—61no—
54C4⋊Dic5—31no—
55C4⋊Dic5—31no—
56C4×Dic5—61no—
57C2×#168—31no—
58C2×#168—31no—
59#485—151noSylow
60C22×C3×C5—21no—
61C22×C3×C5—21no—
62C22×C3×C5—21no—
63C22×C3×C5C2×D411yescharacteristic
64C3×C4×C5—21no—
65C3×C4×C5—41no—
66C3×C4×C5—41no—
67C3×C4×C5#4111yescharacteristic
68C3×C4×C5#4111yescharacteristic
69Dic15—41no—
70Dic15—41no—
71C2×C3×Q8C2×D511yescharacteristic
72C22×C3×C4C2×D511yescharacteristic
73C3×C4⋊C4—21no—
74C3×C4⋊C4C2×D511yescharacteristic
75C3×C22⋊C4—21no—
76#217—101no—
77C4⋊Dic3—51no—
78C4⋊Dic3—51no—
79C4×Dic3—101no—
80C2×C3⋊C8—51no—
81C2×C3⋊C8—51no—
82C23×C5#6711yescharacteristic
83C5×Q8—21no—
84C5×Q8—21no—
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—21no—
89C2×C4×C5#6711yescharacteristic
90C2×C4×C5C22×D311yescharacteristic
91C2×Dic5—61no—
92C2×Dic5—61no—
93#168—61no—
94#168—61no—
95C22⋊Q8D1511yescharacteristic
96#117—151no—
97#107—151no—
98#106—151no—
99#103—151no—
100#103—151no—
101C22⋊C8—151no—
102C2×C3×C5—41no—
103C2×C3×C5#12311yescharacteristic
104C2×C3×C5#13511yescharacteristic
105C2×C3×C5#13711yescharacteristic
106C23×C3C22⋊D511yescharacteristic
107C3×Q8—21no—
108C3×Q8—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4C22⋊D511yescharacteristic
114C2×C3×C4C22×D511yescharacteristic
115C2×Dic3—101no—
116C2×Dic3—101no—
117C3⋊C8—101no—
118C3⋊C8—101no—
119C22×C5—21no—
120C22×C5—21no—
121C22×C5—21no—
122C22×C5C2×#6711yescharacteristic
123C4×C5—21no—
124C4×C5—41no—
125C4×C5—41no—
126C4×C5#23711yescharacteristic
127C4×C5#23711yescharacteristic
128Dic5—121no—
129Dic5—121no—
130C2×Q8C2×D1511yescharacteristic
131C22×C4C2×D1511yescharacteristic
132C2×C8—151no—
133C2×C8—151no—
134C4⋊C4—21no—
135C4⋊C4—151no—
136C4⋊C4—151no—
137C4⋊C4C2×D1511yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—301no—
140C42—301no—
141C3×C5#48511yescharacteristic, complemented, Hall
142C22×C3—21no—
143C22×C3—21no—
144C22×C3—21no—
145C22×C3C2×C22⋊D511yescharacteristic
146C3×C4—21no—
147C3×C4—41no—
148C3×C4—41no—
149C3×C4#71111yescharacteristic
150C3×C4#71111yescharacteristic
151Dic3—201no—
152Dic3—201no—
153C2×C5—41no—
154C2×C5#93511yescharacteristic
155C2×C5#94211yescharacteristic
156C2×C5#95011yescharacteristic
157C23#122011yescharacteristic
158Q8—21no—
159Q8—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—301no—
165C2×C4—301no—
166C2×C4#122011yescharacteristic
167C2×C4C22×D1511yescharacteristic
168C8—301no—
169C8—301no—
170C2×C3—41no—
171C2×C3#408111yescharacteristic
172C2×C3#408811yescharacteristic
173C2×C3#409611yescharacteristic
174C5#504511yescharacteristic, complemented, Sylow
175C22—21no—
176C22—21no—
177C22—21no—
178C22C2×#122011yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—601no—
183C4—601no—
184C4#681911yescharacteristic
185C4#681911yescharacteristic
186C3#6533411yescharacteristic, complemented, Sylow
187C2—41no—
188C2#9182411yescharacteristic
189C2#9183111yescharacteristic
190C2#9183911yescharacteristic
subgroupG/H
centerC22C2×#1220
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×C22⋊Q8C2
socleC22×C3×C5C2×D4
prime radicalC23×C3×C5D4
hypercenterC22⋊Q8D15
hypocenterC3×C5#485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #91119C2semidirect
4. #91119C2semidirect
6. #91092C2semidirect
7. #91091C2semidirect
141. C3×C5#485semidirect
174. C5#5045semidirect
186. C3#65334semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C22⋊Q82
#918152
#911192
#911142
#910922
#910912
#653343
#50455