Finite Group Databasebeta

← #14315829

Subgroups — #14315829

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
1#11751682C211yesmaximal, characteristic
2#11751668C211yesmaximal, characteristic, complemented
3#11746828C211yesmaximal, characteristic
4#11746719C211yesmaximal, characteristic, complemented
5C3×#64845C211yesmaximal, characteristic, complemented
6#11746471C211yesmaximal, characteristic, complemented
7#11746466C211yesmaximal, characteristic
8#10604130—31nomaximal, Hall
9#91911—21no—
10AGL(1,𝔽5)×Dic6—21no—
11#91270C2211yescharacteristic
12D5×Dic12C2211yescharacteristic
13#91224C2211yescharacteristic
14#91222C2211yescharacteristic
15C3×#3992C2211yescharacteristic
16C3×#3990C2211yescharacteristic
17#91156—21no—
18#91154—21no—
19Dic120C411yescharacteristic, complemented
20C5×#800C411yescharacteristic, complemented
21C3×#3930C2211yescharacteristic
22#90948C411yescharacteristic, complemented
23#90944C411yescharacteristic, complemented
24#69090—51nomaximal, Hall
25#65739—31no—
26#65733—31no—
27#65204—31no—
28#64910—31no—
29#64903—31no—
30#64847—31no—
31#64845D311yescharacteristic, complemented
32#6772—21no—
33D5×Dic6—21no—
34C4⋊ΓL(1,𝔽16)—21no—
35#6758—21no—
36C3×C4×AGL(1,𝔽5)D411yescharacteristic
37C3×D5⋊C8D411yescharacteristic
38#6739—41no—
39D3×#170—41no—
40Dic3⋊AGL(1,𝔽5)—41no—
41Dic3×AGL(1,𝔽5)—41no—
42Dic60C2×C411yescharacteristic
43Dic60C2×C411yescharacteristic
44C5×Dic12C2×C411yescharacteristic
45C5×D24C2×C411yescharacteristic
46C3×C8×D5C2311yescharacteristic
47#6663—21no—
48#6659—21no—
49C3×#674—21no—
50C3×C5×C16C2×C411yescharacteristic
51C3×#672C2×C411yescharacteristic
52#4909—51no—
53#4717—51no—
54#4716—51no—
55C3×#347—51no—
56#4518—51no—
57#4517—51no—
58#4513—51no—
59Q8×AGL(1,𝔽5)—61no—
60#4131—61no—
61D5×Q16—31no—
62#4058—31no—
63#4009—61no—
64#4008—61no—
65#3995—31no—
66#3993—31no—
67#3992C2×D311yescharacteristic
68#3990C2×D311yescharacteristic
69C5×SD32—31no—
70#3961—31no—
71#3959—31no—
72Dic40—31no—
73#3930C2×D311yescharacteristic
74#2180—151noSylow
75C2×ΓL(1,𝔽16)—41no—
76C2×C3×AGL(1,𝔽5)—21no—
77Dic30—21no—
78Dic30—21no—
79C5×D12—21no—
80C5×Dic6—21no—
81C3×C4×D5C2×D411yescharacteristic
82#1204—41no—
83#1201—41no—
84D3×Dic5—41no—
85D5×Dic3—41no—
86C3⋊#170—41no—
87C3×#170—21no—
88C3×C5×C8C22×C411yescharacteristic
89C3×#168#4111yescharacteristic
90C2×Dic12—51no—
91#904—51no—
92#901—101no—
93C4×Dic6—101no—
94C3×M32—51no—
95C3×M32—51no—
96C3×#97—51no—
97#819—51no—
98#817—51no—
99#816—101no—
100#805—101no—
101Dic24—51no—
102Dic24—51no—
103#800—51no—
104#800AGL(1,𝔽5)11yescharacteristic, complemented
105Q8×D5—61no—
106#711—61no—
107#704—121no—
108C2×#170—121no—
109C4⋊AGL(1,𝔽5)—61no—
110C4⋊AGL(1,𝔽5)—121no—
111C4×AGL(1,𝔽5)—121no—
112C4×AGL(1,𝔽5)D1211yescharacteristic
113#700—61no—
114D5⋊C8D1211yescharacteristic
115C5×Q16—31no—
116C5×D8—31no—
117#689—61no—
118#687—61no—
119Dic20—31no—
120Dic20—31no—
121C8×D5C22×D311yescharacteristic
122#674—21no—
123C5×C16C4×D311yescharacteristic
124#672C4×D311yescharacteristic
125#510—151no—
126#444—151no—
127#441—151no—
128#365—151no—
129#362—151no—
130#360—151no—
131#347—51no—
132C2×C5×D3—41no—
133C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
134ΓL(1,𝔽16)—81no—
135C3×AGL(1,𝔽5)—41no—
136C3×C4×C5C4×D411yescharacteristic
137Dic15—41no—
138Dic15—41no—
139C3×Dic5AGL(1,ℤ/8)11yescharacteristic
140C5×Dic3—41no—
141#235—101no—
142C2×Dic6—101no—
143C2×C3×C8—51no—
144C2×C3×C8—51no—
145C3×C42—51no—
146C4⋊Dic3—101no—
147Dic3⋊C4—201no—
148C4×Dic3—201no—
149#208—101no—
150Dic12—51no—
151Dic12—51no—
152Dic12—101no—
153Dic12C2×AGL(1,𝔽5)11yescharacteristic
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)—121no—
163C5×Q8—61no—
164C5×D4—61no—
165C22⋊D5—121no—
166C2×Dic5—121no—
167C4×D5—121no—
168C4×D5C2×D1211yescharacteristic
169Dic10—61no—
170Dic10—61no—
171Dic10—121no—
172#170—21no—
173#170—121no—
174C5×C8C2×C4×D311yescharacteristic
175#168#23511yescharacteristic
176#135—151no—
177C2×Q16—151no—
178#131—301no—
179C4×Q8—301no—
180Q32—151no—
181Q32—151no—
182SD32—31no—
183SD32—151no—
184M32—51no—
185M32—51no—
186#108—151no—
187#106—151no—
188#104—301no—
189#103—301no—
190#97—51no—
191C2×C3×C5#44211yescharacteristic
192C3×D5—21no—
193C5×D3—81no—
194C2×C3×C4—51no—
195C2×C3×C4—101no—
196#67—201no—
197C2×Dic3—201no—
198C2×Dic3—201no—
199D12—21no—
200C4×D3—201no—
201Dic6—21no—
202Dic6—101no—
203Dic6—101no—
204Dic6—201no—
205C3×C8—51no—
206C3×C8—101no—
207C3×C8C22×AGL(1,𝔽5)11yescharacteristic
208C3⋊C8—201no—
209C22×C5—121no—
210C2×D5#90811yescharacteristic
211AGL(1,𝔽5)—41no—
212AGL(1,𝔽5)—241no—
213C4×C5—121no—
214C4×C5C4×D1211yescharacteristic
215Dic5—121no—
216Dic5—121no—
217Dic5#90811yescharacteristic
218#41—301no—
219C2×Q8—301no—
220Q16—31no—
221Q16—151no—
222Q16—151no—
223Q16—301no—
224SD16—301no—
225D8—31no—
226M16—301no—
227M16—601no—
228C2×C8—51no—
229C2×C8—51no—
230C2×C8—601no—
231C4⋊C4—301no—
232C4⋊C4—601no—
233C42—51no—
234C42—601no—
235C16—51no—
236C16—101no—
237C16D3×AGL(1,𝔽5)11yescharacteristic
238C3×C5#218011yescharacteristic, complemented, Hall
239C22×C3—51no—
240C2×D3—41no—
241C3×C4—51no—
242C3×C4—201no—
243C3×C4D4×AGL(1,𝔽5)11yescharacteristic
244Dic3—41no—
245Dic3—201no—
246Dic3—201no—
247Dic3—401no—
248C2×C5—241no—
249C2×C5#471111yescharacteristic
250D5—21no—
251Q8—61no—
252Q8—301no—
253Q8—301no—
254Q8—601no—
255D4—61no—
256D4—601no—
257C2×C4—51no—
258C2×C4—101no—
259C2×C4—601no—
260C2×C4—601no—
261C2×C4—601no—
262C8—51no—
263C8—101no—
264C8—601no—
265C8C2×D3×AGL(1,𝔽5)11yescharacteristic
266C2×C3—101no—
267C2×C3#6573111yescharacteristic
268D3—81no—
269C5#6909011yescharacteristic, complemented, Sylow
270C22—51no—
271C22—121no—
272C4—51no—
273C4—121no—
274C4—201no—
275C4—601no—
276C4—601no—
277C4—1201no—
278C4AGL(1,𝔽5)×D1211yescharacteristic
279C3#1060413011yescharacteristic, complemented, Sylow
280C2—101no—
281C2—241no—
282C2#1175166211yescharacteristic
subgroupG/H
centerC2#11751662
commutatorC3×C5×C8C22×C4
FrattiniC8C2×D3×AGL(1,𝔽5)
FittingC3×C5×C16C2×C4
socleC2×C3×C5#442
prime radical#91270C22
cosocleC3×C8×D5C23
hypercenterC16D3×AGL(1,𝔽5)
hypocenterC3×C5#2180
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
2. #11751668C2semidirect
4. #11746719C2semidirect
5. C3×#64845C2semidirect
6. #11746471C2semidirect
19. Dic120C4semidirect
20. C5×#800C4semidirect
22. #90948C4semidirect
23. #90944C4semidirect
31. #64845D3semidirect
104. #800AGL(1,𝔽5)semidirect
238. C3×C5#2180semidirect
269. C5#69090semidirect
279. C3#10604130semidirect

Maximal subgroups

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

subgroupindex
#117516822
#117516682
#117468282
#117467192
C3×#648452
#117464712
#117464662
#106041303
#690905