Finite Group Databasebeta

← #11750919

Subgroups — #11750919

Order 960.

240 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#91833C211yesmaximal, characteristic, complemented
2C2×#6717C211yesmaximal, characteristic
3C2×#6706C211yesmaximal, characteristic
4#91782C211yesmaximal, characteristic
5C3×C5×#103C211yesmaximal, characteristic, complemented
6#91098C211yesmaximal, characteristic, complemented
7#91094C211yesmaximal, characteristic, complemented
8#65107—31nomaximal, Hall
9C2×C3×C5×Q8C2211yescharacteristic
10C2×D60C2211yescharacteristic
11C2×C4×D15—21no—
12C2×Dic30C2211yescharacteristic
13C2×C3×C5×C8C2211yescharacteristic
14C3×C5×C4⋊C4C2211yescharacteristic
15#6717—22no—
16#6714—21no—
17#6712—21no—
18#6712—21no—
19C4×Dic15C2211yescharacteristic
20C2×C3⋊#168C2211yescharacteristic
21#6706—22no—
22#4818—51nomaximal, Hall
23#4090—31no—
24C2×#688—31no—
25C2×#677—31no—
26#4039—31no—
27C5×#103D311yescharacteristic, complemented
28#3946—31no—
29#3942—31no—
30C22×D15—21no—
31C3×C5×Q8—21no—
32C3×C5×Q8—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5—21no—
35C2×C3×C4×C5C2311yescharacteristic
36C2×Dic15—21no—
37C2×Dic15D411yescharacteristic
38C2×Dic15D411yescharacteristic
39D60—21no—
40D60D412yes—
41C4×D15—42no—
42Dic30—21no—
43Dic30—21no—
44C3×C5×C8—21no—
45C3⋊#168—21no—
46#944—51no—
47C2×#215—51no—
48C2×#204—51no—
49#893—51no—
50C3×#103D511yescharacteristic, complemented
51Dic3⋊C8—51no—
52#810—51no—
53C2×C5×Q8C2×D311yescharacteristic
54C2×D20—31no—
55C2×C4×D5—61no—
56C2×Dic10—31no—
57C2×C5×C8C2×D311yescharacteristic
58C5×C4⋊C4C2×D311yescharacteristic
59#688—62no—
60#685—61no—
61#683—61no—
62#683—61no—
63C4×Dic5—31no—
64C2×#168—31no—
65#677—62no—
66#461—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×D15—22no—
69C2×D15—41no—
70C2×D15—41no—
71C3×C4×C5—41no—
72C3×C4×C5—41no—
73C3×C4×C5C2×D411yescharacteristic
74C3×C4×C5#4111yescharacteristic
75Dic15—21no—
76Dic15—41no—
77Dic15SD1612yescomplemented
78C2×C3×Q8C2×D511yescharacteristic
79C2×D12—51no—
80C2×C4×D3—101no—
81C2×Dic6—51no—
82C2×C3×C8C2×D511yescharacteristic
83C3×C4⋊C4C2×D511yescharacteristic
84#215—102no—
85(C2×D3)⋊C4—101no—
86Dic3⋊C4—101no—
87Dic3⋊C4—101no—
88C4×Dic3—51no—
89C2×C3⋊C8—51no—
90#204—102no—
91C22×D5—61no—
92C5×Q8—21no—
93C5×Q8—21no—
94C2×C4×C5—21no—
95C2×C4×C5—21no—
96C2×C4×C5C22×D311yescharacteristic
97C2×Dic5—31no—
98C2×Dic5—31no—
99C2×Dic5—61no—
100D20—32no—
101D20—61no—
102C4×D5—122no—
103Dic10—61no—
104Dic10—61no—
105C5×C8—21no—
106#168—61no—
107C2×SD16—151no—
108C2×SD16—151no—
109C4⋊Q8—151no—
110C4×D4—151no—
111C4⋊C8—151no—
112#103—151no—
113#103D1511yescharacteristic, complemented
114C2×C3×C5#12111yescharacteristic
115C2×C3×C5C2×SD1611yescharacteristic
116C2×C3×C5#13711yescharacteristic
117D15—42no—
118C22×D3—101no—
119C3×Q8—21no—
120C3×Q8—21no—
121C2×C3×C4—21no—
122C2×C3×C4—21no—
123C2×C3×C4C22×D511yescharacteristic
124C2×Dic3—51no—
125C2×Dic3—51no—
126C2×Dic3—101no—
127D12—52no—
128D12—101no—
129C4×D3—202no—
130Dic6—101no—
131Dic6—101no—
132C3×C8—21no—
133C3⋊C8—101no—
134C22×C5D3×D411yescharacteristic
135C2×D5—62no—
136C2×D5—121no—
137C2×D5—121no—
138C4×C5—41no—
139C4×C5—41no—
140C4×C5#23511yescharacteristic
141C4×C5D3×D411yescharacteristic
142Dic5—32no—
143Dic5—61no—
144Dic5—121no—
145C2×Q8—151no—
146C2×Q8C2×D1511yescharacteristic
147C2×D4—151no—
148C22×C4—301no—
149SD16—302no—
150SD16—302no—
151C2×C8—151no—
152C2×C8C2×D1511yescharacteristic
153C4⋊C4—301no—
154C4⋊C4—301no—
155C4⋊C4C2×D1511yescharacteristic
156C22⋊C4—301no—
157C42—151no—
158C3×C5#46111yescharacteristic, complemented, Hall
159C22×C3D4×D511yescharacteristic
160C2×D3—102no—
161C2×D3—201no—
162C2×D3—201no—
163C3×C4—41no—
164C3×C4—41no—
165C3×C4#70911yescharacteristic
166C3×C4D4×D511yescharacteristic
167Dic3—52no—
168Dic3—101no—
169Dic3—201no—
170C2×C5#88411yescharacteristic
171C2×C5D3×SD1611yescharacteristic
172C2×C5#91811yescharacteristic
173D5—122no—
174C23—301no—
175Q8—21no—
176Q8—21no—
177Q8—301no—
178Q8—301no—
179D4—152no—
180D4—301no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—151no—
184C2×C4—151no—
185C2×C4—301no—
186C2×C4—602no—
187C2×C4C22×D1511yescharacteristic
188C8—21no—
189C8—301no—
190C2×C3#403011yescharacteristic
191C2×C3D5×SD1611yescharacteristic
192C2×C3#406411yescharacteristic
193D3—202no—
194C5#481811yescharacteristic, complemented, Sylow
195C22—302no—
196C22—601no—
197C22—601no—
198C22D4×D1511yescharacteristic
199C4—41no—
200C4—41no—
201C4—152no—
202C4—301no—
203C4—601no—
204C4#681711yescharacteristic
205C4D4×D1511yescharacteristic
206C3#6510711yescharacteristic, complemented, Sylow
207C2—602no—
208C2#9177311yescharacteristic
209C2SD16×D1511yescharacteristic
210C2#9180711yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#103C2
socleC22×C3×C5C2×D4
prime radicalC2×D60C22
hypercenter#103D15
hypocenterC3×C5#461
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #91833C2semidirect
5. C3×C5×#103C2semidirect
6. #91098C2semidirect
7. #91094C2semidirect
27. C5×#103D3semidirect
50. C3×#103D5semidirect
77. Dic15SD16semidirect
113. #103D15semidirect
158. C3×C5#461semidirect
194. C5#4818semidirect
206. C3#65107semidirect

Maximal subgroups

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

subgroupindex
#918332
C2×#67172
C2×#67062
#917822
C3×C5×#1032
#910982
#910942
#651073
#48185