Finite Group Databasebeta

← #11748404

Subgroups — #11748404

Order 960.

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

normal subgroups only

This group has 192 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
1C5×#924C211yesmaximal, characteristic
2C3×#4072C211yesmaximal, characteristic
3#91114C211yesmaximal, characteristic
4#90989C211yesmaximal, characteristic, complemented
5#90986C211yesmaximal, characteristic, complemented
6#90972C211yesmaximal, characteristic, complemented
7#90972C211yesmaximal, characteristic, complemented
8#65334—31nomaximal, Hall
9C22×C3×C4×C5C2211yescharacteristic
10C2×C5×Dic6C2211yescharacteristic
11C2×C3⋊#168C2211yescharacteristic
12C2×C3⋊#168C2211yescharacteristic
13C5×#217—21no—
14C5×C4⋊Dic3C2211yescharacteristic
15C5×Dic3⋊C4—21no—
16C3×C22⋊Dic5—21no—
17C3×C4⋊Dic5C2211yescharacteristic
18C3×C4⋊Dic5C2211yescharacteristic
19C3×C4×Dic5—21no—
20#4996—51nomaximal, Hall
21C5×C22⋊Q8—31no—
22#4072D311yescharacteristic
23#3967—31no—
24#3967—31no—
25C22⋊#168—31no—
26#3940—31no—
27#3939—31no—
28C23×C3×C5D411yescharacteristic
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5D411yescharacteristic
32C2×C3×C4×C5C2311yescharacteristic
33C2×C5×Dic3—21no—
34C2×C5×Dic3—21no—
35C5×Dic6—21no—
36C5×Dic6—21no—
37C2×C3×Dic5—21no—
38C2×C3×Dic5—21no—
39C3⋊#168—21no—
40C3⋊#168—21no—
41C3×#117—51no—
42#924D511yescharacteristic
43#830—51no—
44#810—51no—
45#810—51no—
46#808—51no—
47#807—51no—
48C2×C5×Q8—31no—
49C22×C4×C5C2×D311yescharacteristic
50C5×C4⋊C4—31no—
51C5×C4⋊C4—61no—
52C5×C22⋊C4—61no—
53C22⋊Dic5—21no—
54C4⋊Dic5C2×D311yescharacteristic
55C4⋊Dic5C2×D311yescharacteristic
56C4×Dic5—21no—
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#4111yescharacteristic
66C3×C4×C5#4111yescharacteristic
67C3×Dic5—41no—
68C3×Dic5—41no—
69C5×Dic3—41no—
70C5×Dic3—41no—
71C22×C3×C4C2×D511yescharacteristic
72C2×Dic6C2×D511yescharacteristic
73C3×C4⋊C4—51no—
74C3×C4⋊C4—51no—
75C3×C22⋊C4—101no—
76C3×C42—101no—
77#217—21no—
78C4⋊Dic3C2×D511yescharacteristic
79Dic3⋊C4—21no—
80C2×C3⋊C8—51no—
81C2×C3⋊C8—51no—
82C23×C5#6711yescharacteristic
83C5×Q8—61no—
84C5×Q8—61no—
85C2×C4×C5—21no—
86C2×C4×C5—21no—
87C2×C4×C5—61no—
88C2×C4×C5—61no—
89C2×C4×C5#6711yescharacteristic
90C2×C4×C5C22×D311yescharacteristic
91C2×Dic5—21no—
92C2×Dic5—21no—
93#168—61no—
94#168—61no—
95C22⋊Q8—31no—
96#117—51no—
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
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—101no—
110C2×C3×C4—101no—
111C2×C3×C4C22⋊D511yescharacteristic
112C2×C3×C4C22×D511yescharacteristic
113C2×Dic3—21no—
114C2×Dic3—21no—
115Dic6—21no—
116Dic6—21no—
117C3⋊C8—101no—
118C3⋊C8—101no—
119C22×C5—21no—
120C22×C5—21no—
121C22×C5—21no—
122C22×C5C2×#6711yescharacteristic
123C4×C5—21no—
124C4×C5—121no—
125C4×C5—121no—
126C4×C5#23511yescharacteristic
127C4×C5#23511yescharacteristic
128Dic5—41no—
129Dic5—41no—
130C2×Q8—31no—
131C22×C4D3×D511yescharacteristic
132C2×C8—151no—
133C2×C8—151no—
134C4⋊C4—31no—
135C4⋊C4—51no—
136C4⋊C4—51no—
137C4⋊C4—61no—
138C22⋊C4—61no—
139C22⋊C4—101no—
140C42—101no—
141C3×C5#48511yescharacteristic, complemented, Hall
142C22×C3—21no—
143C22×C3—21no—
144C22×C3—21no—
145C22×C3C2×C22⋊D511yescharacteristic
146C3×C4—21no—
147C3×C4—201no—
148C3×C4—201no—
149C3×C4#71111yescharacteristic
150C3×C4#71111yescharacteristic
151Dic3—41no—
152Dic3—41no—
153C2×C5—41no—
154C2×C5#92911yescharacteristic
155C2×C5#95011yescharacteristic
156C2×C5#95111yescharacteristic
157C23#120111yescharacteristic
158Q8—61no—
159Q8—61no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—61no—
163C2×C4—61no—
164C2×C4—101no—
165C2×C4—101no—
166C2×C4#120111yescharacteristic
167C2×C4C2×D3×D511yescharacteristic
168C8—301no—
169C8—301no—
170C2×C3—41no—
171C2×C3#408111yescharacteristic
172C2×C3#408811yescharacteristic
173C2×C3#409611yescharacteristic
174C5#499611yescharacteristic, complemented, Sylow
175C22—21no—
176C22—21no—
177C22—21no—
178C22C2×#120111yescharacteristic
179C4—21no—
180C4—121no—
181C4—121no—
182C4—201no—
183C4—201no—
184C4#678211yescharacteristic
185C4#678211yescharacteristic
186C3#6533411yescharacteristic, complemented, Sylow
187C2—41no—
188C2#9129711yescharacteristic
189C2#9130711yescharacteristic
190C2#9153911yescharacteristic
subgroupG/H
centerC22C2×#1201
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC22×C3×C4×C5C22
socleC22×C3×C5C2×D4
prime radicalC23×C3×C5D4
hypercenterC22×C4D3×D5
hypocenterC3×C5#485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #90989C2semidirect
5. #90986C2semidirect
6. #90972C2semidirect
7. #90972C2semidirect
141. C3×C5#485semidirect
174. C5#4996semidirect
186. C3#65334semidirect

Maximal subgroups

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

subgroupindex
C5×#9242
C3×#40722
#911142
#909892
#909862
#909722
#653343
#49965