Finite Group Databasebeta

← #14318551

Subgroups — #14318551

Order 1920.

268 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 68 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#11748057C211yesmaximal, characteristic, complemented
2#11747904C211yesmaximal, characteristic
3#11746337C211yesmaximal, characteristic, complemented
4C5×#4513C211yesmaximal, characteristic, complemented
5C3×#64734C211yesmaximal, characteristic, complemented
6#11745933C211yesmaximal, characteristic, complemented
7#11745920C211yesmaximal, characteristic, complemented
8#10600106—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10C2×C3×#676C2211yescharacteristic
11#91450—21no—
12D5×#208—21no—
13C3×C5×M32C2211yescharacteristic
14#91103C2211yescharacteristic
15C5×#819C2211yescharacteristic
16C5×#817C2211yescharacteristic
17C3×#3944C2211yescharacteristic
18#90991—21no—
19#90969—21no—
20#69116—51nomaximal, Hall
21#65182—31no—
22#65154—31no—
23C5×#365—31no—
24#64736—31no—
25#64734D311yescharacteristic, complemented
26#64715—31no—
27#64707—31no—
28C2×D60—21no—
29C2×C3×C4×D5D411yescharacteristic
30C2×#1202—41no—
31C2×C3×C5×C8C2311yescharacteristic
32#6710—21no—
33D120—21no—
34D120—21no—
35C5×C4⋊Dic3—21no—
36C5×#208—21no—
37C2×C3×#168D411yescharacteristic
38C3×#676—21no—
39C3×#676—21no—
40#6667—41no—
41#6649—41no—
42D5×C3⋊C8—41no—
43C3×C5×C16—21no—
44C3×#672—21no—
45#5135—51no—
46#5125—51no—
47C3×#349—51no—
48#4516—51no—
49#4516—51no—
50#4513—51no—
51#4513D511yescharacteristic, complemented
52D5×M16—61no—
53C2×D40—31no—
54C2×#676C2×D311yescharacteristic
55#4041—61no—
56C5×M32C2×D311yescharacteristic
57C5×#108—31no—
58C5×#106—31no—
59#3954—61no—
60#3951—31no—
61#3944C2×D311yescharacteristic
62#3941—61no—
63#2238—151noSylow
64C22×D15—41no—
65C22×C3×D5SD1611yescharacteristic
66C2×C3×C4×C5C2×D411yescharacteristic
67D60—41no—
68D60—41no—
69C2×C5×Dic3—41no—
70C2×C3×Dic5SD1611yescharacteristic
71C3×C4×D5—21no—
72C3×C4×D5—21no—
73#1202—82no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—41no—
77C3×#168—21no—
78C5×C3⋊C8—41no—
79C2×C3×M16—51no—
80#930—101no—
81C2×#208—101no—
82C2×D24—51no—
83C3×M32—51no—
84C3×M32C2×D511yescharacteristic
85#821—101no—
86#819—51no—
87#819—101no—
88#819C2×D511yescharacteristic
89#817C2×D511yescharacteristic
90C2×D20—61no—
91C2×D20—121no—
92C2×C4×D5D1211yescharacteristic
93C5×M16—61no—
94C2×C5×C8C22×D311yescharacteristic
95C5×C4⋊C4—61no—
96#685—121no—
97#681—61no—
98C2×#168D1211yescharacteristic
99D40—61no—
100D40—61no—
101#676—21no—
102#676—21no—
103#676—121no—
104C8×D5—121no—
105C5×C16—21no—
106#672—21no—
107#469—151no—
108#430—151no—
109#365—31no—
110#365—151no—
111#361—151no—
112#361—151no—
113#349—51no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×D15—81no—
116C2×D15—81no—
117C2×D15—81no—
118C2×C3×D5—21no—
119C2×C3×D5—41no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122C3×Dic5—21no—
123C5×Dic3—81no—
124C22×C3×C4—51no—
125C2×#67—201no—
126C2×D12—101no—
127C3×M16—101no—
128C3×M16—101no—
129C2×C3×C8—51no—
130C2×C3×C8C22×D511yescharacteristic
131(C2×D3)⋊C4—201no—
132C4⋊Dic3—21no—
133#208—21no—
134#208—101no—
135#208—201no—
136C2×C3⋊C8—201no—
137D24—101no—
138D24—101no—
139C3×C16—21no—
140C3×C16—101no—
141C22×D5—121no—
142C22×D5#20411yescharacteristic
143C2×C4×C5—121no—
144C2×C4×C5C2×D1211yescharacteristic
145C2×Dic5#20411yescharacteristic
146D20—121no—
147D20—121no—
148D20—242no—
149C4×D5—21no—
150C4×D5—21no—
151C5×C8—121no—
152C5×C8#23711yescharacteristic
153C5×C8#23711yescharacteristic
154#168—21no—
155#168—121no—
156C2×D8—151no—
157C2×M16—51no—
158C2×M16—301no—
159#121—301no—
160M32—51no—
161M32D3×D511yescharacteristic
162#108—31no—
163#108—151no—
164#108—301no—
165#106—31no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169D15—161no—
170C3×D5—41no—
171C23×C3—51no—
172C22×D3—201no—
173C2×C3×C4—51no—
174C2×C3×C4—101no—
175C2×C3×C4—101no—
176C2×C3×C4D4×D511yescharacteristic
177#67—402no—
178C2×Dic3—41no—
179D12—201no—
180D12—201no—
181C3×C8—101no—
182C3×C8#70911yescharacteristic
183C3×C8#71311yescharacteristic
184C3⋊C8—41no—
185C3⋊C8—201no—
186C22×C5C2×#20411yescharacteristic
187C2×D5—21no—
188C2×D5—41no—
189C2×D5—241no—
190C2×D5—241no—
191C2×D5—241no—
192C4×C5—241no—
193C4×C5#88611yescharacteristic
194C4×C5#90811yescharacteristic
195Dic5—21no—
196C2×D4—301no—
197C2×D4—601no—
198C22×C4—51no—
199D8—301no—
200D8—301no—
201M16—61no—
202M16—101no—
203M16—101no—
204M16—301no—
205M16—601no—
206C2×C8—51no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—61no—
210C22⋊C4—601no—
211C16—21no—
212C16—101no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—101no—
215C22×C3—201no—
216C22×C3D5×SD1611yescharacteristic
217C2×D3—401no—
218C2×D3—401no—
219C2×D3—401no—
220C3×C4—101no—
221C3×C4#404011yescharacteristic
222C3×C4#406011yescharacteristic
223Dic3—81no—
224C2×C5—21no—
225C2×C5#473511yescharacteristic
226D5—41no—
227D5—481no—
228C23—51no—
229C23—601no—
230D4—601no—
231D4—601no—
232D4—1202no—
233C2×C4—51no—
234C2×C4—101no—
235C2×C4—101no—
236C2×C4—121no—
237C2×C4D5×D1211yescharacteristic
238C8—101no—
239C8—121no—
240C8—601no—
241C8#676611yescharacteristic
242C8#677911yescharacteristic
243C2×C3—21no—
244C2×C3—201no—
245C2×C3#6515211yescharacteristic
246D3—801no—
247C5#6911611yescharacteristic, complemented, Sylow
248C22—101no—
249C22—201no—
250C22—1201no—
251C22—1201no—
252C22—1201no—
253C22D5×#20411yescharacteristic
254C4—101no—
255C4—241no—
256C4#9124911yescharacteristic
257C4#9141311yescharacteristic
258C3#1060010611yescharacteristic, complemented, Sylow
259C2—21no—
260C2—201no—
261C2—2401no—
262C2#1174761411yescharacteristic
subgroupG/H
centerC2#11747614
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#481
prime radical#11747904C2
hypercenterM32D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. #11748057C2semidirect
3. #11746337C2semidirect
4. C5×#4513C2semidirect
5. C3×#64734C2semidirect
6. #11745933C2semidirect
7. #11745920C2semidirect
25. #64734D3semidirect
51. #4513D5semidirect
213. C3×C5#2238semidirect
247. C5#69116semidirect
258. C3#10600106semidirect

Maximal subgroups

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

subgroupindex
#117480572
#117479042
#117463372
C5×#45132
C3×#647342
#117459332
#117459202
#106001063
#691165