Finite Group Databasebeta

← #11751140

Subgroups — #11751140

Order 960.

260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 69 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×C5×#121C211yesmaximal, characteristic, complemented
2C2×#6715C211yesmaximal, characteristic, complemented
3#91819C211yesmaximal, characteristic, complemented
4C2×#6710C211yesmaximal, characteristic, complemented
5#91116C211yesmaximal, characteristic, complemented
6#91093C211yesmaximal, characteristic, complemented
7#91092C211yesmaximal, characteristic, complemented
8#65328—31nomaximal, Hall
9C2×C3×C5×D4—21no—
10C2×C3×C5×D4C2211yescharacteristic
11C22×C3×C4×C5C2211yescharacteristic
12C2×#1220—21no—
13C2×D60C2211yescharacteristic
14C3×C5×C4⋊C4C2211yescharacteristic
15C3×C5×C22⋊C4—21no—
16#6715—22no—
17#6714—21no—
18C4⋊Dic15C2211yescharacteristic
19#6710—22no—
20C2×C3⋊#168C2211yescharacteristic
21C2×C3⋊#168C2211yescharacteristic
22#5039—51nomaximal, Hall
23C5×#121D311yescharacteristic, complemented
24C2×#686—31no—
25#4076—31no—
26C2×#681—31no—
27#3964—31no—
28#3941—31no—
29#3940—31no—
30C23×C3×C5—21no—
31C23×C3×C5D411yescharacteristic
32C22×D15—21no—
33C3×C5×D4—21no—
34C3×C5×D4—21no—
35C3×C5×D4—42no—
36C2×C3×C4×C5—21no—
37C2×C3×C4×C5—21no—
38C2×C3×C4×C5—21no—
39C2×C3×C4×C5D411yescharacteristic
40C2×C3×C4×C5C2311yescharacteristic
41#1220—42no—
42C2×Dic15—21no—
43D60—21no—
44D60—21no—
45C3⋊#168—21no—
46C3⋊#168D412yescomplemented
47C3×#121D511yescharacteristic, complemented
48C2×#213—51no—
49#930—51no—
50C2×#208—51no—
51#832—51no—
52#809—51no—
53#808—51no—
54C2×C5×D4—21no—
55C2×C5×D4C2×D311yescharacteristic
56C22×C4×C5C2×D311yescharacteristic
57C2×C22⋊D5—61no—
58C2×D20—31no—
59C5×C4⋊C4C2×D311yescharacteristic
60C5×C22⋊C4—21no—
61#686—62no—
62#685—61no—
63C4⋊Dic5—31no—
64#681—62no—
65C2×#168—31no—
66C2×#168—31no—
67#469—151noSylow
68C22×C3×C5—21no—
69C22×C3×C5—21no—
70C22×C3×C5—21no—
71C22×C3×C5—41no—
72C22×C3×C5—41no—
73C22×C3×C5—41no—
74C22×C3×C5C2×D411yescharacteristic
75C2×D15—41no—
76C2×D15—41no—
77C2×D15—41no—
78C3×C4×C5—21no—
79C3×C4×C5—41no—
80C3×C4×C5C2×D411yescharacteristic
81C3×C4×C5#4111yescharacteristic
82Dic15—41no—
83C2×C3×D4—21no—
84C2×C3×D4C2×D511yescharacteristic
85C22×C3×C4C2×D511yescharacteristic
86C2×#67—101no—
87C2×D12—51no—
88C3×C4⋊C4C2×D511yescharacteristic
89C3×C22⋊C4—21no—
90#213—102no—
91(C2×D3)⋊C4—101no—
92C4⋊Dic3—51no—
93#208—102no—
94C2×C3⋊C8—51no—
95C2×C3⋊C8—51no—
96C23×C5—21no—
97C23×C5#6711yescharacteristic
98C22×D5—61no—
99C5×D4—21no—
100C5×D4—21no—
101C5×D4—42no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5#6711yescharacteristic
106C2×C4×C5C22×D311yescharacteristic
107C22⋊D5—122no—
108C2×Dic5—61no—
109D20—61no—
110D20—61no—
111#168—32no—
112#168—61no—
113C2×D8—151no—
114C2×M16—151no—
115#121—151no—
116#121D1511yescharacteristic, complemented
117#106—151no—
118#102—151no—
119#102—151no—
120C2×C3×C5—41no—
121C2×C3×C5—81no—
122C2×C3×C5#12111yescharacteristic
123C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
124C2×C3×C5AGL(1,ℤ/8)11yescharacteristic
125D15—81no—
126C23×C3—21no—
127C23×C3C22⋊D511yescharacteristic
128C22×D3—101no—
129C3×D4—21no—
130C3×D4—21no—
131C3×D4—42no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4C22⋊D511yescharacteristic
136C2×C3×C4C22×D511yescharacteristic
137#67—202no—
138C2×Dic3—101no—
139D12—101no—
140D12—101no—
141C3⋊C8—52no—
142C3⋊C8—101no—
143C22×C5—21no—
144C22×C5—21no—
145C22×C5—21no—
146C22×C5—41no—
147C22×C5—41no—
148C22×C5—41no—
149C22×C5C2×#6711yescharacteristic
150C2×D5—121no—
151C2×D5—121no—
152C2×D5—121no—
153C4×C5—21no—
154C4×C5—41no—
155C4×C5D3×D411yescharacteristic
156C4×C5#23711yescharacteristic
157Dic5—121no—
158C2×D4—21no—
159C2×D4—151no—
160C2×D4—301no—
161C2×D4C2×D1511yescharacteristic
162C22×C4C2×D1511yescharacteristic
163D8—302no—
164M16—302no—
165C2×C8—151no—
166C2×C8—151no—
167C4⋊C4—151no—
168C4⋊C4C2×D1511yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—301no—
171C3×C5#46911yescharacteristic, complemented, Hall
172C22×C3—21no—
173C22×C3—21no—
174C22×C3—21no—
175C22×C3—41no—
176C22×C3—41no—
177C22×C3—41no—
178C22×C3C2×C22⋊D511yescharacteristic
179C2×D3—201no—
180C2×D3—201no—
181C2×D3—201no—
182C3×C4—21no—
183C3×C4—41no—
184C3×C4D4×D511yescharacteristic
185C3×C4#71111yescharacteristic
186Dic3—201no—
187C2×C5—41no—
188C2×C5—81no—
189C2×C5#93211yescharacteristic
190C2×C5#93911yescharacteristic
191C2×C5#94911yescharacteristic
192D5—241no—
193C23—21no—
194C23—301no—
195C23#122011yescharacteristic
196D4—21no—
197D4—21no—
198D4—42no—
199D4—301no—
200D4—301no—
201D4—602no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—301no—
206C2×C4#122011yescharacteristic
207C2×C4C22×D1511yescharacteristic
208C8—152no—
209C8—301no—
210C2×C3—41no—
211C2×C3—81no—
212C2×C3#407811yescharacteristic
213C2×C3#408511yescharacteristic
214C2×C3#409511yescharacteristic
215D3—401no—
216C5#503911yescharacteristic, complemented, Sylow
217C22—21no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—601no—
224C22—601no—
225C22—601no—
226C22C2×#122011yescharacteristic
227C4—21no—
228C4—41no—
229C4—601no—
230C4D4×D1511yescharacteristic
231C4#681911yescharacteristic
232C3#6532811yescharacteristic, complemented, Sylow
233C2—41no—
234C2—81no—
235C2—1201no—
236C2#9182111yescharacteristic
237C2#9182811yescharacteristic
238C2#9183811yescharacteristic
subgroupG/H
centerC22C2×#1220
commutator, cosocleC2×C3×C4×C5C23
FrattiniC2×C4C22×D15
FittingC3×C5×#121C2
socleC22×C3×C5C2×D4
hypercenter#121D15
hypocenterC3×C5#469
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×C5×#121C2semidirect
2. C2×#6715C2semidirect
3. #91819C2semidirect
4. C2×#6710C2semidirect
5. #91116C2semidirect
6. #91093C2semidirect
7. #91092C2semidirect
23. C5×#121D3semidirect
46. C3⋊#168D4semidirect
47. C3×#121D5semidirect
116. #121D15semidirect
171. C3×C5#469semidirect
216. C5#5039semidirect
232. C3#65328semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1212
C2×#67152
#918192
C2×#67102
#911162
#910932
#910922
#653283
#50395