Finite Group Databasebeta

← #11747472

Subgroups — #11747472

Order 960.

240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 74 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×#4039C211yesmaximal, characteristic
2#91333C211yesmaximal, characteristic, complemented
3C2×#6657C211yesmaximal, characteristic
4#91094C211yesmaximal, characteristic, complemented
5C5×#807C211yesmaximal, characteristic, complemented
6#90964C211yesmaximal, characteristic
7#90952C211yesmaximal, characteristic, complemented
8#65178—31nomaximal, Hall
9C2×Dic30C2211yescharacteristic
10C2×C3×D20C2211yescharacteristic
11C2×C3×C4×D5—21no—
12C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3⋊#168C2211yescharacteristic
14C5×C4⋊Dic3C2211yescharacteristic
15C2×C5×C3⋊C8C2211yescharacteristic
16C3×#685—21no—
17C3×C4×Dic5C2211yescharacteristic
18#6669—21no—
19Dic3×Dic5—21no—
20#6657C414yescomplemented
21#5018—51nomaximal, Hall
22C2×#677—31no—
23#4039D311yescharacteristic
24#4033—31no—
25C5×#107—31no—
26#3947—31no—
27#3942—31no—
28#3941—31no—
29C22×C3×D5—21no—
30C2×C3×C4×C5—21no—
31C2×C3×C4×C5C2311yescharacteristic
32C2×Dic15—21no—
33Dic30—21no—
34Dic30C2×C412yescomplemented
35C2×C5×Dic3—21no—
36C2×C3×Dic5D411yescharacteristic
37C2×C3×Dic5D411yescharacteristic
38C3×D20—21no—
39C3×D20C2×C412yes—
40C3×C4×D5—42no—
41C3⋊#168—21no—
42C5×C3⋊C8C2×C412yescomplemented
43C3×C4×D4—51no—
44C2×#214—51no—
45C4×Dic6—51no—
46#832—51no—
47#810—51no—
48#807D511yescharacteristic, complemented
49#803—51no—
50C2×D20C2×D311yescharacteristic
51C2×C4×D5—21no—
52C2×Dic10—31no—
53C2×C5×C8—31no—
54C5×C4⋊C4—31no—
55C5×C4⋊C4C2×D311yescharacteristic
56#685—21no—
57#683—61no—
58C4×Dic5—61no—
59C4×Dic5C2×D311yescharacteristic
60C2×#168—31no—
61#677—34no—
62#440—151noSylow
63C22×C3×C5C2×D411yescharacteristic
64C2×C3×D5—22no—
65C2×C3×D5—41no—
66C2×C3×D5—41no—
67C3×C4×C5—41no—
68C3×C4×C5C22×C411yescharacteristic
69C3×C4×C5#4111yescharacteristic
70Dic15—22no—
71C3×Dic5—21no—
72C3×Dic5—21no—
73C5×Dic3—41no—
74C2×C3×D4—51no—
75C22×C3×C4—101no—
76C2×Dic6—51no—
77C3×C4⋊C4C2×D511yescharacteristic
78C3×C22⋊C4—101no—
79C3×C42—51no—
80#214—54no—
81C4⋊Dic3C2×D511yescharacteristic
82Dic3⋊C4—101no—
83C4×Dic3—101no—
84C2×C3⋊C8—51no—
85C2×C3⋊C8C2×D511yescharacteristic
86C22×D5—21no—
87C2×C4×C5—21no—
88C2×C4×C5—61no—
89C2×C4×C5C22×D311yescharacteristic
90C2×Dic5—61no—
91C2×Dic5#6711yescharacteristic
92C2×Dic5#6711yescharacteristic
93D20—21no—
94D20C4×D312yes—
95C4×D5—42no—
96Dic10—32no—
97Dic10—61no—
98C5×C8—32no—
99#168—61no—
100C2×SD16—151no—
101C4×Q8—151no—
102C4×D4—51no—
103#107—31no—
104#103—151no—
105#102—151no—
106#97—151no—
107C2×C3×C5C4×D411yescharacteristic
108C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
109C2×C3×C5#13711yescharacteristic
110C3×D5—42no—
111C23×C3—101no—
112C3×D4—52no—
113C3×D4—101no—
114C2×C3×C4—21no—
115C2×C3×C4—51no—
116C2×C3×C4—51no—
117C2×C3×C4—202no—
118C2×C3×C4C22×D511yescharacteristic
119C2×Dic3—21no—
120C2×Dic3—101no—
121Dic6—52no—
122Dic6—101no—
123C3⋊C8—101no—
124C3⋊C8C4×D512yescomplemented
125C22×C5C2×#6711yescharacteristic
126C2×D5—22no—
127C2×D5—41no—
128C2×D5—41no—
129C4×C5—41no—
130C4×C5—121no—
131C4×C5C2×C4×D311yescharacteristic
132C4×C5#23511yescharacteristic
133Dic5—21no—
134Dic5—21no—
135Dic5—62no—
136C2×Q8—151no—
137C2×D4—51no—
138C22×C4—101no—
139SD16—154no—
140C2×C8—31no—
141C2×C8—151no—
142C4⋊C4—31no—
143C4⋊C4—301no—
144C4⋊C4D3×D511yescharacteristic
145C22⋊C4—101no—
146C42—51no—
147C42—301no—
148C3×C5#44011yescharacteristic, complemented, Hall
149C22×C3—102no—
150C22×C3—201no—
151C22×C3—201no—
152C22×C3D4×D511yescharacteristic
153C3×C4—41no—
154C3×C4—101no—
155C3×C4—101no—
156C3×C4C2×C4×D511yescharacteristic
157C3×C4#71311yescharacteristic
158Dic3—41no—
159Dic3—102no—
160C2×C5C4×#6711yescharacteristic
161C2×C5#93211yescharacteristic
162C2×C5#95111yescharacteristic
163D5—42no—
164C23—101no—
165Q8—152no—
166Q8—301no—
167D4—52no—
168D4—101no—
169C2×C4—21no—
170C2×C4—51no—
171C2×C4—51no—
172C2×C4—61no—
173C2×C4—202no—
174C2×C4—301no—
175C2×C4C2×D3×D511yescharacteristic
176C8—32no—
177C8—301no—
178C2×C3—202no—
179C2×C3#403911yescharacteristic
180C2×C3#405711yescharacteristic
181C2×C3#406411yescharacteristic
182C5#501811yescharacteristic, complemented, Sylow
183C22—102no—
184C22—201no—
185C22—201no—
186C22D5×#6711yescharacteristic
187C4—41no—
188C4—101no—
189C4—101no—
190C4—121no—
191C4—302no—
192C4#677311yescharacteristic
193C4C4×D3×D511yescharacteristic
194C3#6517811yescharacteristic, complemented, Sylow
195C2—202no—
196C2#9144411yescharacteristic
197C2#9148911yescharacteristic
198C2#9150811yescharacteristic
subgroupG/H
centerC22D5×#67
commutatorC3×C4×C5C22×C4
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC2×C3×D20C22
cosocleC2×C3×C4×C5C23
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#440
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #91333C2semidirect
4. #91094C2semidirect
5. C5×#807C2semidirect
7. #90952C2semidirect
20. #6657C4semidirect
34. Dic30C2×C4semidirect
42. C5×C3⋊C8C2×C4semidirect
48. #807D5semidirect
124. C3⋊C8C4×D5semidirect
148. C3×C5#440semidirect
182. C5#5018semidirect
194. C3#65178semidirect

Maximal subgroups

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

subgroupindex
C3×#40392
#913332
C2×#66572
#910942
C5×#8072
#909642
#909522
#651783
#50185