Finite Group Databasebeta

← #14315817

Subgroups — #14315817

Order 1920.

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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×#65739C211yesmaximal, characteristic, complemented
2#11751682C211yesmaximal, characteristic
3#11748300C211yesmaximal, characteristic
4#11746781C211yesmaximal, characteristic, complemented
5#11746472C211yesmaximal, characteristic, complemented
6#11746464C211yesmaximal, characteristic
7#11746452C211yesmaximal, characteristic, complemented
8#10604130—31nomaximal, Hall
9C3×Q8×AGL(1,𝔽5)—21no—
10#91911—21no—
11C3×D5×Q16C2211yescharacteristic
12#91270C2211yescharacteristic
13#91224C2211yescharacteristic
14#91219C2211yescharacteristic
15C3×#4009—21no—
16C3×#3993C2211yescharacteristic
17C3×#3992C2211yescharacteristic
18#91156—21no—
19#91113C411yescharacteristic, complemented
20C5×#828C411yescharacteristic, complemented
21#90947C411yescharacteristic, complemented
22#90941C411yescharacteristic, complemented
23#90934C2211yescharacteristic
24#70917—51nomaximal, Hall
25#65739D311yescharacteristic, complemented
26#65733—31no—
27#65204—31no—
28#64910—31no—
29#64903—31no—
30#64847—31no—
31#64845—31no—
32C3×Q8×D5—21no—
33#6772—21no—
34#6758—21no—
35C3×C4⋊AGL(1,𝔽5)—21no—
36C3×C4⋊AGL(1,𝔽5)—41no—
37C3×C4×AGL(1,𝔽5)—41no—
38C3×C4×AGL(1,𝔽5)D411yescharacteristic
39C3×D5⋊C8D411yescharacteristic
40#6739—41no—
41D3×#170—41no—
42C3×C5×Q16C2×C411yescharacteristic
43Dic60C2×C411yescharacteristic
44C5×D24C2×C411yescharacteristic
45C3×#689—21no—
46C3×Dic20C2×C411yescharacteristic
47C3×C8×D5C2311yescharacteristic
48#6659—21no—
49C3⋊#674—21no—
50C3⋊#672C2×C411yescharacteristic
51C5×C3⋊C16C2×C411yescharacteristic
52C3×#441—51no—
53#5179—51no—
54#4717—51no—
55#4565—51no—
56#4488—51no—
57#4487—51no—
58#4466—51no—
59Q8×AGL(1,𝔽5)—21no—
60#4131—61no—
61D5×Q16C2×D311yescharacteristic
62#4058—31no—
63#4009—21no—
64#4008—61no—
65#3995—31no—
66#3993C2×D311yescharacteristic
67#3992C2×D311yescharacteristic
68#3990—31no—
69C5×SD32—31no—
70#3961—31no—
71#3959—31no—
72Dic40—31no—
73#3930—31no—
74#2180—151noSylow
75C2×C3×AGL(1,𝔽5)—21no—
76C2×C3×AGL(1,𝔽5)—41no—
77C3×C5×Q8—21no—
78Dic30—21no—
79C5×D12—21no—
80C3×C4×D5—41no—
81C3×C4×D5C2×D411yescharacteristic
82C3×Dic10—21no—
83C3×Dic10—41no—
84#1201—41no—
85D3×Dic5—41no—
86C3⋊#170—41no—
87C3×#170—21no—
88C3×C5×C8C22×C411yescharacteristic
89C3×#168#4111yescharacteristic
90C2×C3×Q16—51no—
91C3×C4×Q8—101no—
92#904—51no—
93#901—101no—
94C3×#106—51no—
95C3×#103—101no—
96C3×#97—51no—
97#829—51no—
98#829—51no—
99#828—51no—
100#828AGL(1,𝔽5)11yescharacteristic, complemented
101#819—51no—
102#812—51no—
103#812—51no—
104#805—101no—
105Q8×D5—21no—
106#711—61no—
107#704—121no—
108C2×#170—121no—
109C4⋊AGL(1,𝔽5)—21no—
110C4⋊AGL(1,𝔽5)—41no—
111C4×AGL(1,𝔽5)—41no—
112C4×AGL(1,𝔽5)#6711yescharacteristic
113#700—61no—
114D5⋊C8#6711yescharacteristic
115C5×Q16C4×D311yescharacteristic
116C5×D8—31no—
117#689—21no—
118#687—61no—
119Dic20—31no—
120Dic20C4×D311yescharacteristic
121C8×D5C22×D311yescharacteristic
122#674—61no—
123C5×C16—31no—
124#672—31no—
125#510—151no—
126#444—151no—
127#441—51no—
128#365—151no—
129#362—151no—
130#360—151no—
131#347—151no—
132C2×C5×D3—41no—
133C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
134C3×AGL(1,𝔽5)—41no—
135C3×AGL(1,𝔽5)—81no—
136C3×C4×C5—41no—
137C3×C4×C5C4×D411yescharacteristic
138Dic15—41no—
139C3×Dic5—41no—
140C3×Dic5AGL(1,ℤ/8)11yescharacteristic
141C2×C3×Q8—101no—
142#235—101no—
143C3×Q16—51no—
144C3×Q16—101no—
145C3×Q16C2×AGL(1,𝔽5)11yescharacteristic
146C2×C3×C8—51no—
147C2×C3×C8—51no—
148C3×C4⋊C4—101no—
149C3×C4⋊C4—201no—
150C3×C42—51no—
151C3×C42—201no—
152#208—101no—
153Dic12—51no—
154D24C2×AGL(1,𝔽5)11yescharacteristic
155#204—101no—
156ΓL(1,𝔽25)—201no—
157D3×C8—201no—
158C3⋊C16—51no—
159C3⋊C16—101no—
160C3⋊C16C2×AGL(1,𝔽5)11yescharacteristic
161C2×AGL(1,𝔽5)—21no—
162C2×AGL(1,𝔽5)—41no—
163C5×Q8—21no—
164C5×D4—61no—
165C22⋊D5—121no—
166C2×Dic5—121no—
167C4×D5—41no—
168C4×D5C2×#6711yescharacteristic
169Dic10—21no—
170Dic10—41no—
171Dic10—61no—
172#170—21no—
173#170—121no—
174C5×C8C2×C4×D311yescharacteristic
175#168#23511yescharacteristic
176#135—151no—
177C2×Q16—51no—
178#131—301no—
179C4×Q8—101no—
180Q32—151no—
181Q32—151no—
182SD32—31no—
183SD32—151no—
184M32—151no—
185M32—151no—
186#108—151no—
187#106—51no—
188#104—301no—
189#103—101no—
190#97—51no—
191C2×C3×C5#44211yescharacteristic
192C3×D5—21no—
193C5×D3—81no—
194C3×Q8—21no—
195C3×Q8—101no—
196C3×Q8—201no—
197C2×C3×C4—51no—
198C2×C3×C4—101no—
199C2×C3×C4—201no—
200C2×C3×C4—201no—
201#67—201no—
202D12—21no—
203C4×D3—201no—
204Dic6—101no—
205C3×C8—51no—
206C3×C8—101no—
207C3×C8C22×AGL(1,𝔽5)11yescharacteristic
208C3⋊C8—201no—
209C22×C5—121no—
210C2×D5#93211yescharacteristic
211AGL(1,𝔽5)—41no—
212AGL(1,𝔽5)—81no—
213C4×C5—41no—
214C4×C5C4×#6711yescharacteristic
215Dic5—41no—
216Dic5—121no—
217Dic5#94911yescharacteristic
218#41—301no—
219C2×Q8—101no—
220Q16—51no—
221Q16—101no—
222Q16—151no—
223Q16D3×AGL(1,𝔽5)11yescharacteristic
224SD16—301no—
225D8—31no—
226M16—301no—
227M16—601no—
228C2×C8—51no—
229C2×C8—51no—
230C2×C8—601no—
231C4⋊C4—101no—
232C4⋊C4—201no—
233C42—51no—
234C42—201no—
235C16—31no—
236C16—151no—
237C16—301no—
238C3×C5#218011yescharacteristic, complemented, Hall
239C22×C3—51no—
240C2×D3—41no—
241C3×C4—41no—
242C3×C4—51no—
243C3×C4—201no—
244C3×C4—201no—
245C3×C4—401no—
246C3×C4D4×AGL(1,𝔽5)11yescharacteristic
247Dic3—201no—
248C2×C5—241no—
249C2×C5#501411yescharacteristic
250D5—21no—
251Q8—21no—
252Q8—101no—
253Q8—201no—
254Q8—301no—
255D4—61no—
256D4—601no—
257C2×C4—51no—
258C2×C4—101no—
259C2×C4—201no—
260C2×C4—201no—
261C2×C4—601no—
262C8—51no—
263C8—101no—
264C8—601no—
265C8C2×D3×AGL(1,𝔽5)11yescharacteristic
266C2×C3—101no—
267C2×C3#6573111yescharacteristic
268D3—81no—
269C5#7091711yescharacteristic, complemented, Sylow
270C22—51no—
271C22—121no—
272C4—41no—
273C4—51no—
274C4—201no—
275C4—201no—
276C4—401no—
277C4—601no—
278C4AGL(1,𝔽5)×#6711yescharacteristic
279C3#1060413011yescharacteristic, complemented, Sylow
280C2—101no—
281C2—241no—
282C2#1175194011yescharacteristic
subgroupG/H
centerC2#11751940
commutatorC3×C5×C8C22×C4
FrattiniC8C2×D3×AGL(1,𝔽5)
FittingC3×C5×Q16C2×C4
socleC2×C3×C5#442
prime radical#91270C22
cosocleC3×C8×D5C23
hypercenterQ16D3×AGL(1,𝔽5)
hypocenterC3×C5#2180
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

Complements

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

NH ≅ G/Ntype
1. C3×#65739C2semidirect
4. #11746781C2semidirect
5. #11746472C2semidirect
7. #11746452C2semidirect
19. #91113C4semidirect
20. C5×#828C4semidirect
21. #90947C4semidirect
22. #90941C4semidirect
25. #65739D3semidirect
100. #828AGL(1,𝔽5)semidirect
238. C3×C5#2180semidirect
269. C5#70917semidirect
279. C3#10604130semidirect

Maximal subgroups

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

subgroupindex
C3×#657392
#117516822
#117483002
#117467812
#117464722
#117464642
#117464522
#106041303
#709175