Finite Group Databasebeta

← #11749366

Subgroups — #11749366

Order 960.

228 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 68 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×C5×#216C211yesmaximal, characteristic, complemented
2C3×#4092C211yesmaximal, characteristic
3#91359C211yesmaximal, characteristic
4C2×D5×C3⋊C8C211yesmaximal, characteristic
5#91119C211yesmaximal, characteristic, complemented
6#90990C211yesmaximal, characteristic, complemented
7#90972C211yesmaximal, characteristic, complemented
8#65477—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×C5×Dic6C2211yescharacteristic
11C2×C3×C4×D5C2211yescharacteristic
12C4⋊Dic15C2211yescharacteristic
13C2×C3⋊#168C2211yescharacteristic
14C5×#216—22no—
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×#685—21no—
17C3×C4⋊Dic5C2211yescharacteristic
18C3×#683—21no—
19#6669—21no—
20#6665—21no—
21D5×C3⋊C8—22no—
22#5051—51nomaximal, Hall
23C2×C5×Q16—31no—
24#4092—31no—
25#4092D311yescharacteristic
26C2×C8×D5—31no—
27#3967—31no—
28#3967—31no—
29#3950—31no—
30C22×C3×D5D411yescharacteristic
31C3×C5×Q8—21no—
32C3×C5×Q8—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15—21no—
36C2×C5×Dic3—21no—
37C5×Dic6—21no—
38C5×Dic6—21no—
39C2×C3×Dic5—21no—
40C2×C3×Dic5D411yescharacteristic
41C3×C4×D5—21no—
42C3×C4×D5—21no—
43C3⋊#168—21no—
44C5×C3⋊C8D412yes—
45C3×C22⋊Q8—51no—
46C2×#216D511yescharacteristic, complemented
47#924—51no—
48C22×C3⋊C8—51no—
49#835—51no—
50#810—51no—
51#807—51no—
52C2×C5×Q8—31no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×C4×D5C2×D311yescharacteristic
55C5×Q16—62no—
56C2×C5×C8—31no—
57#685—21no—
58#685—61no—
59C4⋊Dic5—31no—
60C4⋊Dic5C2×D311yescharacteristic
61#683—21no—
62#683—61no—
63C2×#168—31no—
64C8×D5—62no—
65#467—151noSylow
66C22×C3×C5C2×D411yescharacteristic
67C2×C3×D5—21no—
68C2×C3×D5—21no—
69C2×C3×D5Q1612yescomplemented
70C3×C4×C5—41no—
71C3×C4×C5C2×D411yescharacteristic
72C3×C4×C5#4111yescharacteristic
73Dic15—41no—
74C3×Dic5—21no—
75C3×Dic5—41no—
76C5×Dic3—41no—
77C2×C3×Q8C2×D511yescharacteristic
78C22×C3×C4—51no—
79C2×Dic6C2×D511yescharacteristic
80C3×C4⋊C4—51no—
81C3×C4⋊C4—101no—
82C3×C22⋊C4—101no—
83#217—101no—
84#216—22no—
85C4⋊Dic3—51no—
86Dic3⋊C4—101no—
87C2×C3⋊C8—51no—
88C2×C3⋊C8—102no—
89C2×C3⋊C8C2×D511yescharacteristic
90C22×D5#6711yescharacteristic
91C5×Q8—21no—
92C5×Q8—21no—
93C5×Q8—61no—
94C5×Q8—61no—
95C2×C4×C5—21no—
96C2×C4×C5—61no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—21no—
99C2×Dic5—61no—
100C2×Dic5#6711yescharacteristic
101C4×D5—21no—
102C4×D5—21no—
103C5×C8—32no—
104#168—61no—
105C2×Q16—31no—
106C22×C8—151no—
107C22⋊Q8—51no—
108C22⋊Q8—151no—
109#107—151no—
110#103—151no—
111#103—151no—
112C2×C3×C5#12111yescharacteristic
113C2×C3×C5C2×Q1611yescharacteristic
114C2×C3×C5#13511yescharacteristic
115C3×D5—22no—
116C23×C3—51no—
117C3×Q8—21no—
118C3×Q8—21no—
119C2×C3×C4—21no—
120C2×C3×C4—51no—
121C2×C3×C4—101no—
122C2×C3×C4—101no—
123C2×C3×C4—101no—
124C2×C3×C4C22×D511yescharacteristic
125C2×Dic3—21no—
126C2×Dic3—101no—
127Dic6—21no—
128Dic6—21no—
129C3⋊C8—101no—
130C3⋊C8C22⋊D512yes—
131C22×C5C2×#6711yescharacteristic
132C2×D5—21no—
133C2×D5—21no—
134C2×D5#21612yescomplemented
135C4×C5—41no—
136C4×C5—121no—
137C4×C5D3×D411yescharacteristic
138C4×C5#23711yescharacteristic
139Dic5—21no—
140Dic5—41no—
141Dic5—121no—
142C2×Q8—31no—
143C2×Q8D3×D511yescharacteristic
144C22×C4—51no—
145Q16—62no—
146C2×C8—31no—
147C2×C8—151no—
148C2×C8—302no—
149C4⋊C4—51no—
150C4⋊C4—101no—
151C4⋊C4—151no—
152C4⋊C4—301no—
153C22⋊C4—101no—
154C22⋊C4—301no—
155C3×C5#46711yescharacteristic, complemented, Hall
156C22×C3—52no—
157C22×C3—101no—
158C22×C3—101no—
159C22×C3D4×D511yescharacteristic
160C3×C4—41no—
161C3×C4—101no—
162C3×C4—201no—
163C3×C4#71111yescharacteristic
164C3×C4C2×C22⋊D511yescharacteristic
165Dic3—41no—
166Dic3—201no—
167C2×C5#93911yescharacteristic
168C2×C5C2×#21611yescharacteristic
169C2×C5#95011yescharacteristic
170D5—22no—
171C23—51no—
172Q8—21no—
173Q8—21no—
174Q8—61no—
175Q8—61no—
176C2×C4—21no—
177C2×C4—51no—
178C2×C4—61no—
179C2×C4—101no—
180C2×C4—101no—
181C2×C4—101no—
182C2×C4—301no—
183C2×C4C2×D3×D511yescharacteristic
184C8—32no—
185C8—301no—
186C2×C3—102no—
187C2×C3D5×Q1611yescharacteristic
188C2×C3#406511yescharacteristic
189C2×C3#408411yescharacteristic
190C5#505111yescharacteristic, complemented, Sylow
191C22—52no—
192C22—101no—
193C22—101no—
194C22D5×#6711yescharacteristic
195C4—41no—
196C4—101no—
197C4—121no—
198C4—201no—
199C4—601no—
200C4#678011yescharacteristic
201C4D3×C22⋊D511yescharacteristic
202C3#6547711yescharacteristic, complemented, Sylow
203C2—102no—
204C2D5×#21611yescharacteristic
205C2#9151611yescharacteristic
206C2#9154911yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC2×C3×C5×Q8C22
socleC22×C3×C5C2×D4
prime radicalC22×C3×D5D4
hypercenterC2×Q8D3×D5
hypocenterC3×C5#467
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×C5×#216C2semidirect
5. #91119C2semidirect
6. #90990C2semidirect
7. #90972C2semidirect
46. C2×#216D5semidirect
69. C2×C3×D5Q16semidirect
134. C2×D5#216semidirect
155. C3×C5#467semidirect
190. C5#5051semidirect
202. C3#65477semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#2162
C3×#40922
#913592
C2×D5×C3⋊C82
#911192
#909902
#909722
#654773
#50515