Finite Group Databasebeta

← #11747317

Subgroups — #11747317

Order 960.

260 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 62 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#91784C211yesmaximal, characteristic, complemented
2#91466C211yesmaximal, characteristic, complemented
3C2×#6654C211yesmaximal, characteristic, complemented
4C2×#6651C211yesmaximal, characteristic, complemented
5C5×#809C211yesmaximal, characteristic, complemented
6C3×#3940C211yesmaximal, characteristic, complemented
7#90968C211yesmaximal, characteristic, complemented
8#65071—31nomaximal, Hall
9C2×D60—21no—
10C2×D60C2211yescharacteristic
11C2×C4×D15C2211yescharacteristic
12C2×C5×D12C2211yescharacteristic
13C2×#1203—21no—
14C3×C5×C4⋊C4C2211yescharacteristic
15#6714—21no—
16C2×C5×C3⋊C8C2211yescharacteristic
17C3×C4⋊Dic5C2211yescharacteristic
18C2×C3×#168C2211yescharacteristic
19(C2×D3)⋊Dic5—21no—
20#6654—22no—
21#6651—22no—
22#4865—51nomaximal, Hall
23#4084—31no—
24C2×#686—31no—
25C2×#676—31no—
26#4041—31no—
27C5×#102—31no—
28#3953—31no—
29#3940D311yescharacteristic, complemented
30C22×D15—21no—
31C22×D15D411yescharacteristic
32C22×C5×D3—21no—
33C2×C3×C4×C5—21no—
34C2×C3×C4×C5C2311yescharacteristic
35C2×Dic15D411yescharacteristic
36D60—21no—
37D60—21no—
38D60—42no—
39C4×D15—21no—
40C4×D15—21no—
41C5×D12—21no—
42C5×D12—21no—
43C2×C3×Dic5—21no—
44#1203—42no—
45C3×#168D412yescomplemented
46C5×C3⋊C8—21no—
47C2×D24—51no—
48C2×ΓL(1,𝔽25)—51no—
49#895—51no—
50#895—51no—
51C3×#106—51no—
52#809—51no—
53#809D511yescharacteristic, complemented
54C2×C5×D4—31no—
55C2×C22⋊D5—61no—
56C2×D20—31no—
57C2×D20—61no—
58C2×C4×D5—31no—
59C2×C5×C8—31no—
60C5×C4⋊C4C2×D311yescharacteristic
61C22⋊Dic5—61no—
62#686—62no—
63#685—61no—
64C4⋊Dic5C2×D311yescharacteristic
65C2×#168C2×D311yescharacteristic
66#676—62no—
67#469—151noSylow
68C22×C3×C5C2×D411yescharacteristic
69C2×D15—21no—
70C2×D15—21no—
71C2×D15—21no—
72C2×D15—41no—
73C2×D15—41no—
74C2×D15—41no—
75C2×C5×D3—41no—
76C2×C5×D3—41no—
77C2×C5×D3—41no—
78C3×C4×C5—41no—
79C3×C4×C5C2×D411yescharacteristic
80C3×C4×C5#4111yescharacteristic
81Dic15—21no—
82C3×Dic5—41no—
83C2×D12—51no—
84C2×D12—101no—
85C2×D12—101no—
86C2×D12C2×D511yescharacteristic
87C2×C4×D3—51no—
88C2×C3×C8—51no—
89C3×C4⋊C4—51no—
90C3×C4⋊C4C2×D511yescharacteristic
91(C2×D3)⋊C4—101no—
92(C2×D3)⋊C4—101no—
93C2×C3⋊C8C2×D511yescharacteristic
94D24—102no—
95ΓL(1,𝔽25)—102no—
96C23×C5—61no—
97C22×D5—31no—
98C22×D5—61no—
99C5×D4—61no—
100C5×D4—61no—
101C2×C4×C5—21no—
102C2×C4×C5C22×D311yescharacteristic
103C22⋊D5—122no—
104C2×Dic5—21no—
105C2×Dic5—31no—
106D20—61no—
107D20—61no—
108D20—122no—
109C4×D5—61no—
110C4×D5—61no—
111C5×C8—61no—
112#168D1212yescomplemented
113C2×D8—151no—
114C2×M16—151no—
115#121—151no—
116#121—151no—
117#106—51no—
118#102—31no—
119#102—151no—
120C2×C3×C5#12111yescharacteristic
121C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
122C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
123D15—41no—
124D15—81no—
125C5×D3—81no—
126C22×D3—21no—
127C22×D3—51no—
128C22×D3—101no—
129C2×C3×C4—21no—
130C2×C3×C4—101no—
131C2×C3×C4C22×D511yescharacteristic
132C2×Dic3—51no—
133D12—21no—
134D12—21no—
135D12—101no—
136D12—101no—
137D12—202no—
138D12—202no—
139C4×D3—101no—
140C4×D3—101no—
141C3×C8—52no—
142C3⋊C8—21no—
143C22×C5—121no—
144C22×C5—121no—
145C22×C5—121no—
146C22×C5D3×D411yescharacteristic
147C2×D5—61no—
148C2×D5—61no—
149C2×D5—61no—
150C2×D5—121no—
151C2×D5—121no—
152C2×D5—121no—
153C4×C5—41no—
154C4×C5C2×D1211yescharacteristic
155C4×C5#23911yescharacteristic
156Dic5—41no—
157Dic5—61no—
158C2×D4—31no—
159C2×D4—151no—
160C2×D4—301no—
161C2×D4—301no—
162C22×C4—151no—
163D8—302no—
164M16—302no—
165C2×C8—31no—
166C2×C8—51no—
167C4⋊C4—51no—
168C4⋊C4D3×D511yescharacteristic
169C22⋊C4—301no—
170C22⋊C4—301no—
171C3×C5#46911yescharacteristic, complemented, Hall
172C22×C3D4×D511yescharacteristic
173C2×D3—41no—
174C2×D3—41no—
175C2×D3—41no—
176C2×D3—101no—
177C2×D3—101no—
178C2×D3—101no—
179C2×D3—201no—
180C2×D3—201no—
181C2×D3—201no—
182C3×C4—41no—
183C3×C4—201no—
184C3×C4#70911yescharacteristic
185C3×C4D4×D511yescharacteristic
186Dic3—101no—
187C2×C5—241no—
188C2×C5#89511yescharacteristic
189C2×C5#91411yescharacteristic
190C2×C5#91411yescharacteristic
191D5—121no—
192D5—241no—
193C23—61no—
194C23—151no—
195C23—301no—
196D4—61no—
197D4—61no—
198D4—301no—
199D4—301no—
200D4—602no—
201D4—602no—
202C2×C4—21no—
203C2×C4—101no—
204C2×C4—151no—
205C2×C4—301no—
206C2×C4—301no—
207C2×C4C2×D3×D511yescharacteristic
208C8—52no—
209C8—61no—
210C2×C3#403011yescharacteristic
211C2×C3#405711yescharacteristic
212C2×C3#406011yescharacteristic
213D3—81no—
214D3—201no—
215D3—401no—
216C5#486511yescharacteristic, complemented, Sylow
217C22—121no—
218C22—121no—
219C22—121no—
220C22—301no—
221C22—301no—
222C22—301no—
223C22—601no—
224C22—601no—
225C22—601no—
226C22#679011yescharacteristic
227C4—41no—
228C4—201no—
229C4—301no—
230C4#676911yescharacteristic
231C4D5×D1211yescharacteristic
232C3#6507111yescharacteristic, complemented, Sylow
233C2—241no—
234C2—601no—
235C2—1201no—
236C2#9142011yescharacteristic
237C2#9150011yescharacteristic
238C2#9150611yescharacteristic
subgroupG/H
centerC22#6790
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C2×D3×D5
FittingC3×C5×C4⋊C4C22
socleC22×C3×C5C2×D4
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#469
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
1. #91784C2semidirect
2. #91466C2semidirect
3. C2×#6654C2semidirect
4. C2×#6651C2semidirect
5. C5×#809C2semidirect
6. C3×#3940C2semidirect
7. #90968C2semidirect
29. #3940D3semidirect
45. C3×#168D4semidirect
53. #809D5semidirect
112. #168D12semidirect
171. C3×C5#469semidirect
216. C5#4865semidirect
232. C3#65071semidirect

Maximal subgroups

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

subgroupindex
#917842
#914662
C2×#66542
C2×#66512
C5×#8092
C3×#39402
#909682
#650713
#48655