Finite Group Databasebeta

← #11747463

Subgroups — #11747463

Order 960.

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

normal subgroups only

This group has 240 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
1C3×#4041C211yesmaximal, characteristic
2#91360C211yesmaximal, characteristic, complemented
3C2×#6657C211yesmaximal, characteristic, complemented
4C2×#6649C211yesmaximal, characteristic, complemented
5#91094C211yesmaximal, characteristic, complemented
6C5×#807C211yesmaximal, characteristic, complemented
7#90964C211yesmaximal, characteristic, complemented
8#65175—31nomaximal, Hall
9C2×Dic30C2211yescharacteristic
10C2×C3×D20—21no—
11C2×C3×D20C2211yescharacteristic
12C2×C3×C4×D5C2211yescharacteristic
13C3×C5×C4⋊C4C2211yescharacteristic
14C2×C3⋊#168C2211yescharacteristic
15C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×#685—21no—
18Dic3⋊Dic5—21no—
19#6665—21no—
20#6657—22no—
21#6649—22no—
22#5042—51nomaximal, Hall
23C2×#677—31no—
24C2×#676—31no—
25#4043—31no—
26#4041D311yescharacteristic
27C5×#107—31no—
28#3942—31no—
29#3941—31no—
30C22×C3×D5—21no—
31C22×C3×D5D411yescharacteristic
32C2×C3×C4×C5—21no—
33C2×C3×C4×C5C2311yescharacteristic
34C2×Dic15—21no—
35Dic30—21no—
36Dic30—21no—
37C2×C5×Dic3—21no—
38C2×C3×Dic5D411yescharacteristic
39C3×D20—21no—
40C3×D20—21no—
41C3×D20—42no—
42C3×C4×D5—21no—
43C3×C4×D5—21no—
44C3⋊#168—21no—
45C5×C3⋊C8D412yescomplemented
46C3×#121—51no—
47C2×#214—51no—
48#924—51no—
49C2×#208—51no—
50#832—51no—
51#810—51no—
52#807D511yescharacteristic, complemented
53C2×D20—21no—
54C2×D20C2×D311yescharacteristic
55C2×C4×D5C2×D311yescharacteristic
56C2×Dic10—31no—
57C2×C5×C8—31no—
58C5×C4⋊C4—31no—
59C5×C4⋊C4C2×D311yescharacteristic
60#685—21no—
61#685—61no—
62C4⋊Dic5—61no—
63C2×#168—31no—
64#677—62no—
65#676—62no—
66#468—151noSylow
67C22×C3×C5C2×D411yescharacteristic
68C2×C3×D5—21no—
69C2×C3×D5—21no—
70C2×C3×D5—21no—
71C2×C3×D5—41no—
72C2×C3×D5—41no—
73C2×C3×D5—41no—
74C3×C4×C5—41no—
75C3×C4×C5C2×D411yescharacteristic
76C3×C4×C5#4111yescharacteristic
77Dic15—41no—
78C3×Dic5—21no—
79C5×Dic3—41no—
80C2×C3×D4—51no—
81C2×C3×D4—101no—
82C22×C3×C4—51no—
83C2×Dic6—51no—
84C3×C4⋊C4C2×D511yescharacteristic
85C3×C22⋊C4—101no—
86#217—101no—
87#214—102no—
88C4⋊Dic3C2×D511yescharacteristic
89Dic3⋊C4—101no—
90#208—102no—
91C2×C3⋊C8—51no—
92C2×C3⋊C8C2×D511yescharacteristic
93C22×D5—21no—
94C22×D5#6711yescharacteristic
95C2×C4×C5—21no—
96C2×C4×C5—61no—
97C2×C4×C5C22×D311yescharacteristic
98C2×Dic5—61no—
99C2×Dic5#6711yescharacteristic
100D20—21no—
101D20—21no—
102D20—42no—
103C4×D5—21no—
104C4×D5—21no—
105Dic10—61no—
106Dic10—61no—
107C5×C8—32no—
108#168—61no—
109C2×SD16—151no—
110C2×M16—151no—
111C22⋊Q8—151no—
112#121—51no—
113#107—31no—
114#103—151no—
115#102—151no—
116C2×C3×C5#12111yescharacteristic
117C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
118C2×C3×C5#13711yescharacteristic
119C3×D5—41no—
120C3×D5—81no—
121C23×C3—51no—
122C23×C3—101no—
123C3×D4—101no—
124C3×D4—101no—
125C3×D4—202no—
126C2×C3×C4—21no—
127C2×C3×C4—51no—
128C2×C3×C4—101no—
129C2×C3×C4—101no—
130C2×C3×C4C22×D511yescharacteristic
131C2×Dic3—21no—
132C2×Dic3—101no—
133Dic6—101no—
134Dic6—101no—
135C3⋊C8—101no—
136C3⋊C8D2012yescomplemented
137C22×C5C2×#6711yescharacteristic
138C2×D5—21no—
139C2×D5—21no—
140C2×D5—21no—
141C2×D5—41no—
142C2×D5—41no—
143C2×D5—41no—
144C4×C5—41no—
145C4×C5—121no—
146C4×C5D3×D411yescharacteristic
147C4×C5#23711yescharacteristic
148Dic5—21no—
149Dic5—121no—
150C2×Q8—151no—
151C2×D4—51no—
152C2×D4—101no—
153C22×C4—51no—
154SD16—302no—
155M16—302no—
156C2×C8—31no—
157C2×C8—151no—
158C4⋊C4—31no—
159C4⋊C4—301no—
160C4⋊C4D3×D511yescharacteristic
161C22⋊C4—101no—
162C22⋊C4—301no—
163C3×C5#46811yescharacteristic, complemented, Hall
164C22×C3—101no—
165C22×C3—101no—
166C22×C3—101no—
167C22×C3—201no—
168C22×C3—201no—
169C22×C3—201no—
170C22×C3D4×D511yescharacteristic
171C3×C4—41no—
172C3×C4—101no—
173C3×C4C2×D2011yescharacteristic
174C3×C4#71311yescharacteristic
175Dic3—41no—
176Dic3—201no—
177C2×C5#93211yescharacteristic
178C2×C5#93911yescharacteristic
179C2×C5#95111yescharacteristic
180D5—41no—
181D5—81no—
182C23—51no—
183C23—101no—
184Q8—301no—
185Q8—301no—
186D4—101no—
187D4—101no—
188D4—202no—
189C2×C4—21no—
190C2×C4—51no—
191C2×C4—61no—
192C2×C4—101no—
193C2×C4—101no—
194C2×C4—301no—
195C2×C4C2×D3×D511yescharacteristic
196C8—32no—
197C8—301no—
198C2×C3—201no—
199C2×C3—401no—
200C2×C3#404111yescharacteristic
201C2×C3#405711yescharacteristic
202C2×C3#406411yescharacteristic
203C5#504211yescharacteristic, complemented, Sylow
204C22—101no—
205C22—101no—
206C22—101no—
207C22—201no—
208C22—201no—
209C22—201no—
210C22D5×#6711yescharacteristic
211C4—41no—
212C4—101no—
213C4—121no—
214C4—601no—
215C4#676611yescharacteristic
216C4D3×D2011yescharacteristic
217C3#6517511yescharacteristic, complemented, Sylow
218C2—201no—
219C2—401no—
220C2#9140911yescharacteristic
221C2#9148911yescharacteristic
222C2#9150811yescharacteristic
subgroupG/H
centerC22D5×#67
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
prime radicalC3×#4041C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#468
LCSG ▷ C2×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. #91360C2semidirect
3. C2×#6657C2semidirect
4. C2×#6649C2semidirect
5. #91094C2semidirect
6. C5×#807C2semidirect
7. #90964C2semidirect
45. C5×C3⋊C8D4semidirect
52. #807D5semidirect
136. C3⋊C8D20semidirect
163. C3×C5#468semidirect
203. C5#5042semidirect
217. C3#65175semidirect

Maximal subgroups

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

subgroupindex
C3×#40412
#913602
C2×#66572
C2×#66492
#910942
C5×#8072
#909642
#651753
#50425