Finite Group Databasebeta

← #14315789

Subgroups — #14315789

Order 1920.

284 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 76 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#11748071C211yesmaximal, characteristic
2#11747888C211yesmaximal, characteristic, complemented
3#11747550C211yesmaximal, characteristic
4#11746333C211yesmaximal, characteristic, complemented
5C5×#4517C211yesmaximal, characteristic, complemented
6C3×#64738C211yesmaximal, characteristic
7#11745935C211yesmaximal, characteristic, complemented
8#10600057—31nomaximal, Hall
9C2×C5×Dic12C2211yescharacteristic
10C3×#4050C2211yescharacteristic
11#91344—21no—
12#91284—21no—
13C3×C5×M32C2211yescharacteristic
14#91099C2211yescharacteristic
15#91096C2211yescharacteristic
16C5×#819C2211yescharacteristic
17C3×#3949C2211yescharacteristic
18#90976—21no—
19#90972—21no—
20#90946C412yescomplemented
21#90940C412yescomplemented
22#69248—51nomaximal, Hall
23#65473—31no—
24#65468—31no—
25#65183—31no—
26C5×#362—31no—
27#64738D311yescharacteristic
28#64732—31no—
29#64714—31no—
30C2×C5×Dic6—21no—
31C3×#709—21no—
32C2×C3×C5×C8C2311yescharacteristic
33C4×Dic15D411yescharacteristic
34C2×C3⋊#168D411yescharacteristic
35C5×#208—21no—
36C5×Dic12—21no—
37C5×Dic12C2×C412yes—
38C3×C4⋊Dic5—21no—
39C3×Dic20C2×C411yescharacteristic
40C3×D40C2×C411yescharacteristic
41C3×#677—21no—
42Dic3⋊Dic5—41no—
43Dic3×Dic5—41no—
44#6649—41no—
45D5×C3⋊C8—41no—
46C3×C5×C16—21no—
47C3⋊#672C2×C412yes—
48#5197—51no—
49#5195—51no—
50#4853—51no—
51C3×#360—51no—
52#4517D511yescharacteristic, complemented
53#4512—51no—
54#4487—51no—
55C2×C5×Q16—31no—
56Q8×Dic5—61no—
57#4053—61no—
58#4050C2×D311yescharacteristic
59C5×M32C2×D311yescharacteristic
60C5×#108—31no—
61#3967—61no—
62#3961—32no—
63#3960—32no—
64#3957—61no—
65#3949C2×D311yescharacteristic
66#3947—31no—
67#3944—31no—
68#2180—151noSylow
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×Dic15—21no—
71C2×C5×Dic3—41no—
72C5×Dic6—22no—
73C5×Dic6—41no—
74C3×C22⋊D5—41no—
75C2×C3×Dic5—41no—
76C3×D20—21no—
77C3×C4×D5—41no—
78C3×Dic10—21no—
79C3×C5×C8C22×C411yescharacteristic
80C3×C5×C8#4111yescharacteristic
81C3⋊#168—21no—
82C5×C3⋊C8—41no—
83C3×#135—51no—
84#948—101no—
85C2×Dic12C2×D511yescharacteristic
86#887—101no—
87C3×M32C2×D511yescharacteristic
88C3×#106—51no—
89#837—101no—
90#829—52no—
91#827—52no—
92#819C2×D511yescharacteristic
93#815—51no—
94#812—51no—
95#810—101no—
96C2×C5×Q8—61no—
97#709—21no—
98C5×Q16—32no—
99C5×Q16—61no—
100C5×M16—61no—
101C2×C5×C8C22×D311yescharacteristic
102C4⋊Dic5—21no—
103C4⋊Dic5—121no—
104C4×Dic5—31no—
105C4×Dic5—121no—
106C2×#168—31no—
107Dic20C4×D311yescharacteristic
108D40C4×D311yescharacteristic
109#677—21no—
110#676—121no—
111C8×D5—121no—
112C5×C16—21no—
113#672—32no—
114#510—151no—
115#444—151no—
116#441—151no—
117#365—151no—
118#362—31no—
119#360—51no—
120#347—151no—
121C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
122C2×C3×D5—41no—
123C3×C4×C5C4×D411yescharacteristic
124C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
125Dic15—41no—
126C3×Dic5—41no—
127C3×Dic5—81no—
128C5×Dic3—42no—
129C3×#41—101no—
130C2×Dic6—21no—
131C3×Q16—51no—
132C3×SD16—101no—
133C3×D8—51no—
134C2×C3×C8C22×D511yescharacteristic
135C3×C4⋊C4—101no—
136Dic3⋊C4—201no—
137C4×Dic3—51no—
138C4×Dic3—201no—
139#208—21no—
140#208—201no—
141C2×C3⋊C8—51no—
142C2×C3⋊C8—201no—
143Dic12—21no—
144Dic12C4×D512yes—
145C3×C16—21no—
146C3⋊C16—52no—
147C5×Q8—62no—
148C5×Q8—121no—
149C2×C4×C5—121no—
150C2×C4×C5D3×D411yescharacteristic
151C22⋊D5—41no—
152C2×Dic5—41no—
153C2×Dic5—61no—
154D20—21no—
155C4×D5—41no—
156Dic10—21no—
157C5×C8—121no—
158C5×C8C2×C4×D311yescharacteristic
159C5×C8#23711yescharacteristic
160#168—61no—
161#135—51no—
162C2×Q16—31no—
163#131—301no—
164C4×Q8—301no—
165Q32—152no—
166SD32—152no—
167M32—151no—
168M32D3×D511yescharacteristic
169#108—31no—
170#106—51no—
171#104—301no—
172#103—301no—
173#97—151no—
174C2×C3×C5—21no—
175C2×C3×C5#44211yescharacteristic
176C3×D5—81no—
177C3×Q8—101no—
178C3×D4—101no—
179C3×D4—201no—
180C2×C3×C4—201no—
181C2×C3×C4—201no—
182C2×C3×C4D4×D511yescharacteristic
183C2×Dic3—41no—
184C2×Dic3—101no—
185Dic6—22no—
186Dic6—41no—
187C3×C8C2×C4×D511yescharacteristic
188C3×C8#71111yescharacteristic
189C3⋊C8—41no—
190C3⋊C8—101no—
191C22×C5#91111yescharacteristic
192C2×D5—41no—
193C4×C5—122no—
194C4×C5#67⋊C411yescharacteristic
195C4×C5#91411yescharacteristic
196Dic5—41no—
197Dic5—81no—
198Dic5—121no—
199#41—101no—
200C2×Q8—61no—
201Q16—32no—
202Q16—51no—
203Q16—61no—
204SD16—101no—
205D8—51no—
206M16—61no—
207M16—601no—
208C2×C8—151no—
209C2×C8—601no—
210C2×C8C2×D3×D511yescharacteristic
211C4⋊C4—101no—
212C4⋊C4—601no—
213C42—151no—
214C42—601no—
215C16—21no—
216C16—152no—
217C3×C5#218011yescharacteristic, complemented, Hall
218C22×C3—201no—
219C22×C3#406011yescharacteristic
220C3×C4—201no—
221C3×C4—401no—
222C3×C4#402711yescharacteristic
223C3×C4#405711yescharacteristic
224Dic3—42no—
225Dic3—201no—
226C2×C5—21no—
227C2×C5#478511yescharacteristic
228D5—81no—
229Q8—62no—
230Q8—101no—
231Q8—121no—
232D4—101no—
233D4—201no—
234C2×C4—121no—
235C2×C4—201no—
236C2×C4—201no—
237C2×C4—301no—
238C2×C4#677711yescharacteristic
239C8—121no—
240C8—301no—
241C8C4×D3×D511yescharacteristic
242C8#678011yescharacteristic
243C2×C3—21no—
244C2×C3—401no—
245C2×C3#6507411yescharacteristic
246C5#6924811yescharacteristic, complemented, Sylow
247C22—201no—
248C22#9125811yescharacteristic
249C4—122no—
250C4—201no—
251C4—401no—
252C4—601no—
253C4#9125711yescharacteristic
254C4#9144211yescharacteristic
255C3#1060005711yescharacteristic, complemented, Sylow
256C2—21no—
257C2—401no—
258C2#1174773411yescharacteristic
subgroupG/H
centerC2#11747734
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#442
prime radicalC3×#4050C22
cosocleC2×C3×C5×C8C23
hypercenterM32D3×D5
hypocenterC3×C5#2180
LCSG ▷ 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
2. #11747888C2semidirect
4. #11746333C2semidirect
5. C5×#4517C2semidirect
7. #11745935C2semidirect
20. #90946C4semidirect
21. #90940C4semidirect
52. #4517D5semidirect
217. C3×C5#2180semidirect
246. C5#69248semidirect
255. C3#10600057semidirect

Maximal subgroups

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

subgroupindex
#117480712
#117478882
#117475502
#117463332
C5×#45172
C3×#647382
#117459352
#106000573
#692485