Finite Group Databasebeta

← #11750989

Subgroups — #11750989

Order 960.

192 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 61 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#91786C211yesmaximal, characteristic
2#91781C211yesmaximal, characteristic
3C3×C5×#107C211yesmaximal, characteristic, complemented
4#91104C211yesmaximal, characteristic
5#91100C211yesmaximal, characteristic, complemented
6#91094C211yesmaximal, characteristic, complemented
7#91092C211yesmaximal, characteristic, complemented
8#65177—31nomaximal, Hall
9C2×C4×D15C2211yescharacteristic
10C2×Dic30C2211yescharacteristic
11C2×C3×C5×C8C2211yescharacteristic
12C3×C5×C4⋊C4C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14#6714—21no—
15#6714—21no—
16C4⋊Dic15—21no—
17C4⋊Dic15C2211yescharacteristic
18C4×Dic15—21no—
19C2×C3⋊#168C2211yescharacteristic
20#4888—51nomaximal, Hall
21#4043—31no—
22#4038—31no—
23C5×#107D311yescharacteristic, complemented
24#3952—31no—
25#3948—31no—
26#3942—31no—
27#3940—31no—
28C22×D15D411yescharacteristic
29C2×C3×C4×C5—21no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33C2×Dic15—21no—
34C2×Dic15D411yescharacteristic
35C4×D15—21no—
36C4×D15—21no—
37Dic30—21no—
38Dic30—21no—
39C3×C5×C8—21no—
40C3⋊#168—21no—
41#897—51no—
42#892—51no—
43C3×#107D511yescharacteristic, complemented
44(C2×D3)⋊C8—51no—
45#816—51no—
46#810—51no—
47#808—51no—
48C2×C4×D5—31no—
49C2×Dic10—31no—
50C2×C5×C8C2×D311yescharacteristic
51C5×C4⋊C4C2×D311yescharacteristic
52C5×C4⋊C4C2×D311yescharacteristic
53#685—61no—
54#685—61no—
55C4⋊Dic5—31no—
56C4⋊Dic5—61no—
57C4×Dic5—61no—
58C2×#168—31no—
59#485—151noSylow
60C22×C3×C5C2×D411yescharacteristic
61C2×D15—21no—
62C2×D15—21no—
63C2×D15—21no—
64C3×C4×C5—41no—
65C3×C4×C5—41no—
66C3×C4×C5#4111yescharacteristic
67C3×C4×C5#4111yescharacteristic
68Dic15—21no—
69Dic15—41no—
70Dic15—41no—
71C2×C4×D3—51no—
72C2×Dic6—51no—
73C2×C3×C8C2×D511yescharacteristic
74C3×C4⋊C4C2×D511yescharacteristic
75C3×C4⋊C4C2×D511yescharacteristic
76(C2×D3)⋊C4—101no—
77(C2×D3)⋊C4—101no—
78C4⋊Dic3—51no—
79C4⋊Dic3—101no—
80C4×Dic3—101no—
81C2×C3⋊C8—51no—
82C22×D5—31no—
83C2×C4×C5—21no—
84C2×C4×C5—21no—
85C2×C4×C5C22×D311yescharacteristic
86C2×Dic5—31no—
87C2×Dic5—61no—
88C2×Dic5—61no—
89C4×D5—61no—
90C4×D5—61no—
91Dic10—61no—
92Dic10—61no—
93C5×C8—21no—
94#168—61no—
95C22⋊Q8—151no—
96#117—151no—
97#107D1511yescharacteristic, complemented
98#106—151no—
99#103—151no—
100#103—151no—
101C22⋊C8—151no—
102C2×C3×C5#12311yescharacteristic
103C2×C3×C5#13511yescharacteristic
104C2×C3×C5#13711yescharacteristic
105D15—41no—
106C22×D3—51no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4C22×D511yescharacteristic
110C2×Dic3—51no—
111C2×Dic3—101no—
112C2×Dic3—101no—
113C4×D3—101no—
114C4×D3—101no—
115Dic6—101no—
116Dic6—101no—
117C3×C8—21no—
118C3⋊C8—101no—
119C22×C5D3×D411yescharacteristic
120C2×D5—61no—
121C2×D5—61no—
122C2×D5—61no—
123C4×C5—41no—
124C4×C5—41no—
125C4×C5#23511yescharacteristic
126C4×C5#23911yescharacteristic
127Dic5—61no—
128Dic5—121no—
129Dic5—121no—
130C2×Q8—151no—
131C22×C4—151no—
132C2×C8—151no—
133C2×C8C2×D1511yescharacteristic
134C4⋊C4—151no—
135C4⋊C4—301no—
136C4⋊C4C2×D1511yescharacteristic
137C4⋊C4C2×D1511yescharacteristic
138C22⋊C4—301no—
139C22⋊C4—301no—
140C42—301no—
141C3×C5#48511yescharacteristic, complemented, Hall
142C22×C3D4×D511yescharacteristic
143C2×D3—101no—
144C2×D3—101no—
145C2×D3—101no—
146C3×C4—41no—
147C3×C4—41no—
148C3×C4#70911yescharacteristic
149C3×C4#71311yescharacteristic
150Dic3—101no—
151Dic3—201no—
152Dic3—201no—
153C2×C5#89411yescharacteristic
154C2×C5#91211yescharacteristic
155C2×C5#91811yescharacteristic
156D5—121no—
157C23—151no—
158Q8—301no—
159Q8—301no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—151no—
163C2×C4—301no—
164C2×C4—301no—
165C2×C4—301no—
166C2×C4—301no—
167C2×C4C22×D1511yescharacteristic
168C8—21no—
169C8—301no—
170C2×C3#404011yescharacteristic
171C2×C3#405811yescharacteristic
172C2×C3#406411yescharacteristic
173D3—201no—
174C5#488811yescharacteristic, complemented, Sylow
175C22—301no—
176C22—301no—
177C22—301no—
178C22D4×D1511yescharacteristic
179C4—41no—
180C4—41no—
181C4—301no—
182C4—601no—
183C4—601no—
184C4#681711yescharacteristic
185C4#682111yescharacteristic
186C3#6517711yescharacteristic, complemented, Sylow
187C2—601no—
188C2#9178311yescharacteristic
189C2#9180111yescharacteristic
190C2#9180711yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#107C2
socleC22×C3×C5C2×D4
prime radicalC22×D15D4
hypercenter#107D15
hypocenterC3×C5#485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. C3×C5×#107C2semidirect
5. #91100C2semidirect
6. #91094C2semidirect
7. #91092C2semidirect
23. C5×#107D3semidirect
43. C3×#107D5semidirect
97. #107D15semidirect
141. C3×C5#485semidirect
174. C5#4888semidirect
186. C3#65177semidirect

Maximal subgroups

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

subgroupindex
#917862
#917812
C3×C5×#1072
#911042
#911002
#910942
#910922
#651773
#48885