Finite Group Databasebeta

← #11750883

Subgroups — #11750883

Order 960.

260 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 63 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#91827C211yesmaximal, characteristic, complemented
2C2×#6715C211yesmaximal, characteristic, complemented
3C2×#6705C211yesmaximal, characteristic, complemented
4#91784C211yesmaximal, characteristic, complemented
5C3×C5×#102C211yesmaximal, characteristic, complemented
6#91105C211yesmaximal, characteristic, complemented
7#91092C211yesmaximal, characteristic, complemented
8#65071—31nomaximal, Hall
9C2×C3×C5×D4C2211yescharacteristic
10C2×#1220—21no—
11C2×D60—21no—
12C2×D60C2211yescharacteristic
13C2×C4×D15C2211yescharacteristic
14C2×C3×C5×C8C2211yescharacteristic
15C3×C5×C4⋊C4C2211yescharacteristic
16#6719—21no—
17#6715—22no—
18#6714—21no—
19C4⋊Dic15C2211yescharacteristic
20C2×C3⋊#168C2211yescharacteristic
21#6705—22no—
22#4782—51nomaximal, Hall
23#4084—31no—
24C2×#686—31no—
25C2×#676—31no—
26#4041—31no—
27C5×#102D311yescharacteristic, complemented
28#3953—31no—
29#3940—31no—
30C23×C3×C5—21no—
31C22×D15—21no—
32C22×D15D411yescharacteristic
33C3×C5×D4—21no—
34C3×C5×D4—21no—
35C2×C3×C4×C5—21no—
36C2×C3×C4×C5C2311yescharacteristic
37#1220—42no—
38C2×Dic15—21no—
39C2×Dic15D411yescharacteristic
40D60—21no—
41D60—21no—
42D60—42no—
43C4×D15—21no—
44C4×D15—21no—
45C3×C5×C8—21no—
46C3⋊#168D412yescomplemented
47#938—51no—
48C2×#213—51no—
49C2×ΓL(1,𝔽25)—51no—
50#895—51no—
51C3×#102D511yescharacteristic, complemented
52#821—51no—
53#808—51no—
54C2×C5×D4C2×D311yescharacteristic
55C2×C22⋊D5—61no—
56C2×D20—31no—
57C2×D20—61no—
58C2×C4×D5—31no—
59C2×C5×C8C2×D311yescharacteristic
60C5×C4⋊C4C2×D311yescharacteristic
61C22⋊Dic5—61no—
62#686—62no—
63#685—61no—
64C4⋊Dic5—31no—
65C2×#168—31no—
66#676—62no—
67#469—151noSylow
68C22×C3×C5—41no—
69C22×C3×C5—41no—
70C22×C3×C5—41no—
71C22×C3×C5C2×D411yescharacteristic
72C2×D15—21no—
73C2×D15—21no—
74C2×D15—21no—
75C2×D15—41no—
76C2×D15—41no—
77C2×D15—41no—
78C3×C4×C5—41no—
79C3×C4×C5C2×D411yescharacteristic
80C3×C4×C5#4111yescharacteristic
81Dic15—21no—
82Dic15—41no—
83C2×C3×D4C2×D511yescharacteristic
84C2×#67—101no—
85C2×D12—51no—
86C2×D12—101no—
87C2×C4×D3—51no—
88C2×C3×C8C2×D511yescharacteristic
89C3×C4⋊C4C2×D511yescharacteristic
90#217—101no—
91#213—102no—
92(C2×D3)⋊C4—101no—
93C4⋊Dic3—51no—
94C2×C3⋊C8—51no—
95ΓL(1,𝔽25)—102no—
96C23×C5—21no—
97C22×D5—31no—
98C22×D5—61no—
99C5×D4—21no—
100C5×D4—21no—
101C2×C4×C5—21no—
102C2×C4×C5C22×D311yescharacteristic
103C22⋊D5—122no—
104C2×Dic5—31no—
105C2×Dic5—61no—
106D20—61no—
107D20—61no—
108D20—122no—
109C4×D5—61no—
110C4×D5—61no—
111C5×C8—21no—
112#168—32no—
113C2×D8—151no—
114C2×M16—151no—
115#121—151no—
116#121—151no—
117#106—151no—
118#102—151no—
119#102D1511yescharacteristic, complemented
120C2×C3×C5—81no—
121C2×C3×C5#12111yescharacteristic
122C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
123C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
124D15—41no—
125D15—81no—
126C23×C3—21no—
127C22×D3—51no—
128C22×D3—101no—
129C3×D4—21no—
130C3×D4—21no—
131C2×C3×C4—21no—
132C2×C3×C4C22×D511yescharacteristic
133#67—202no—
134C2×Dic3—51no—
135C2×Dic3—101no—
136D12—101no—
137D12—101no—
138D12—202no—
139C4×D3—101no—
140C4×D3—101no—
141C3×C8—21no—
142C3⋊C8—52no—
143C22×C5—41no—
144C22×C5—41no—
145C22×C5—41no—
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×C5#23511yescharacteristic
155C4×C5D3×D411yescharacteristic
156Dic5—61no—
157Dic5—121no—
158C2×D4—151no—
159C2×D4—301no—
160C2×D4—301no—
161C2×D4C2×D1511yescharacteristic
162C22×C4—151no—
163D8—302no—
164M16—302no—
165C2×C8—151no—
166C2×C8C2×D1511yescharacteristic
167C4⋊C4—151no—
168C4⋊C4C2×D1511yescharacteristic
169C22⋊C4—301no—
170C22⋊C4—301no—
171C3×C5#46911yescharacteristic, complemented, Hall
172C22×C3—41no—
173C22×C3—41no—
174C22×C3—41no—
175C22×C3D4×D511yescharacteristic
176C2×D3—101no—
177C2×D3—101no—
178C2×D3—101no—
179C2×D3—201no—
180C2×D3—201no—
181C2×D3—201no—
182C3×C4—41no—
183C3×C4#70911yescharacteristic
184C3×C4D4×D511yescharacteristic
185Dic3—101no—
186Dic3—201no—
187C2×C5—81no—
188C2×C5#88411yescharacteristic
189C2×C5#91111yescharacteristic
190C2×C5#91411yescharacteristic
191D5—121no—
192D5—241no—
193C23—21no—
194C23—151no—
195C23—301no—
196D4—21no—
197D4—21no—
198D4—301no—
199D4—301no—
200D4—602no—
201D4—602no—
202C2×C4—21no—
203C2×C4—151no—
204C2×C4—301no—
205C2×C4—301no—
206C2×C4—301no—
207C2×C4C22×D1511yescharacteristic
208C8—21no—
209C8—152no—
210C2×C3—81no—
211C2×C3#403011yescharacteristic
212C2×C3#405711yescharacteristic
213C2×C3#406011yescharacteristic
214D3—201no—
215D3—401no—
216C5#478211yescharacteristic, complemented, Sylow
217C22—41no—
218C22—41no—
219C22—41no—
220C22—301no—
221C22—301no—
222C22—301no—
223C22—601no—
224C22—601no—
225C22—601no—
226C22D4×D1511yescharacteristic
227C4—41no—
228C4—301no—
229C4—601no—
230C4#681711yescharacteristic
231C4D4×D1511yescharacteristic
232C3#6507111yescharacteristic, complemented, Sylow
233C2—81no—
234C2—601no—
235C2—1201no—
236C2#9177311yescharacteristic
237C2#9180011yescharacteristic
238C2#9180311yescharacteristic
subgroupG/H
centerC22D4×D15
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#102C2
socleC22×C3×C5C2×D4
hypercenter#102D15
hypocenterC3×C5#469
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #91827C2semidirect
2. C2×#6715C2semidirect
3. C2×#6705C2semidirect
4. #91784C2semidirect
5. C3×C5×#102C2semidirect
6. #91105C2semidirect
7. #91092C2semidirect
27. C5×#102D3semidirect
46. C3⋊#168D4semidirect
51. C3×#102D5semidirect
119. #102D15semidirect
171. C3×C5#469semidirect
216. C5#4782semidirect
232. C3#65071semidirect

Maximal subgroups

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

subgroupindex
#918272
C2×#67152
C2×#67052
#917842
C3×C5×#1022
#911052
#910922
#650713
#47825