Finite Group Databasebeta

← #14315913

Subgroups — #14315913

Order 1920.

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

normal subgroups only

This group has 308 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×#65731C211yesmaximal, characteristic, complemented
2#11751684C211yesmaximal, characteristic, complemented
3#11748278C211yesmaximal, characteristic
4#11746777C211yesmaximal, characteristic, complemented
5#11746472C211yesmaximal, characteristic, complemented
6#11746465C211yesmaximal, characteristic, complemented
7#11746452C211yesmaximal, characteristic, complemented
8#10604132—31nomaximal, Hall
9C3×D4×AGL(1,𝔽5)—21no—
10#91914—21no—
11C3×D5×D8C2211yescharacteristic
12#91271C2211yescharacteristic
13#91224C2211yescharacteristic
14#91219C2211yescharacteristic
15C3×#4007—21no—
16C3×#3993C2211yescharacteristic
17C3×#3992C2211yescharacteristic
18#91158—21no—
19#91110C411yescharacteristic, complemented
20C5×#827C411yescharacteristic, complemented
21#90940C411yescharacteristic, complemented
22#90938C411yescharacteristic, complemented
23#90934C2211yescharacteristic
24#70918—51nomaximal, Hall
25#65741—31no—
26#65731D311yescharacteristic, complemented
27#65203—31no—
28#64907—31no—
29#64906—31no—
30#64847—31no—
31#64845—31no—
32C22×C3×AGL(1,𝔽5)—41no—
33C3×D4×D5—21no—
34#6773—21no—
35#6758—21no—
36C3×C22⋊AGL(1,𝔽5)—41no—
37C3×C4⋊AGL(1,𝔽5)—21no—
38C3×C4×AGL(1,𝔽5)D411yescharacteristic
39C3×D5⋊C8D411yescharacteristic
40#6740—41no—
41#6738—41no—
42C3×C5×D8C2×C411yescharacteristic
43D120C2×C411yescharacteristic, complemented
44C5×Dic12C2×C411yescharacteristic, complemented
45C3×#686—21no—
46C3×D40C2×C411yescharacteristic
47C3×C8×D5C2311yescharacteristic
48#6660—21no—
49C3⋊#674—21no—
50C3⋊#672C2×C411yescharacteristic, complemented
51C5×C3⋊C16C2×C411yescharacteristic, complemented
52C3×#442—51no—
53#5147—51no—
54#4717—51no—
55#4563—51no—
56#4488—51no—
57#4487—51no—
58#4466—51no—
59#4133—61no—
60D4×AGL(1,𝔽5)—21no—
61#4065—31no—
62D5×D8C2×D311yescharacteristic
63#4010—61no—
64#4007—21no—
65#3995—31no—
66#3993C2×D311yescharacteristic
67#3992C2×D311yescharacteristic
68#3990—31no—
69C5×SD32—31no—
70#3960—31no—
71#3958—31no—
72D80—31no—
73#3930—31no—
74AGL(1,ℤ/16)—151noSylow
75C22×C3×D5—41no—
76C2×C3×AGL(1,𝔽5)—21no—
77C2×C3×AGL(1,𝔽5)—41no—
78C2×C3×AGL(1,𝔽5)—82no—
79C3×C5×D4—21no—
80D60—21no—
81C5×Dic6—21no—
82C3×C22⋊D5—41no—
83C3×D20—21no—
84C3×C4×D5C2×D411yescharacteristic
85#1202—41no—
86#1200—41no—
87C3⋊#170—41no—
88C3×#170—21no—
89C3×C5×C8C22×C411yescharacteristic
90C3×#168#4111yescharacteristic
91C2×C3×D8—51no—
92C3×C4×D4—101no—
93#904—51no—
94#901—101no—
95C3×#106—51no—
96C3×#102—101no—
97C3×#97—51no—
98#827—51no—
99#827AGL(1,𝔽5)11yescharacteristic, complemented
100#826—51no—
101#826—51no—
102#819—51no—
103#812—51no—
104#812—51no—
105#805—101no—
106C22×AGL(1,𝔽5)—41no—
107#713—61no—
108D4×D5—21no—
109C22⋊AGL(1,𝔽5)—41no—
110C4⋊AGL(1,𝔽5)—21no—
111C4×AGL(1,𝔽5)#6711yescharacteristic
112#700—61no—
113#700—121no—
114D5⋊C8—121no—
115D5⋊C8#6711yescharacteristic
116C5×Q16—31no—
117C5×D8C4×D311yescharacteristic
118#688—61no—
119#686—21no—
120D40—31no—
121D40C4×D311yescharacteristic
122C8×D5C22×D311yescharacteristic
123#674—61no—
124C5×C16—31no—
125#672—31no—
126#509—151no—
127#444—151no—
128#442—51no—
129#365—151no—
130#361—151no—
131#360—151no—
132#347—151no—
133C22×C3×C5—41no—
134C2×D15—41no—
135C2×C3×D5—41no—
136C2×C3×D5—81no—
137C2×C3×D5—81no—
138C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
139C3×AGL(1,𝔽5)—41no—
140C3×AGL(1,𝔽5)—81no—
141C3×C4×C5C4×D411yescharacteristic
142C3×Dic5AGL(1,ℤ/8)11yescharacteristic
143C5×Dic3—41no—
144C2×C3×D4—101no—
145C22×C3×C4—201no—
146#235—101no—
147C3×D8—51no—
148C3×D8—101no—
149C3×D8C2×AGL(1,𝔽5)11yescharacteristic
150C2×C3×C8—51no—
151C2×C3×C8—51no—
152C3×C4⋊C4—101no—
153C3×C22⋊C4—201no—
154C3×C42—51no—
155#208—101no—
156Dic12C2×AGL(1,𝔽5)11yescharacteristic, complemented
157D24—51no—
158#204—101no—
159ΓL(1,𝔽25)—201no—
160D3×C8—201no—
161C3⋊C16—51no—
162C3⋊C16—101no—
163C3⋊C16C2×AGL(1,𝔽5)11yescharacteristic, complemented
164C22×D5—41no—
165C2×AGL(1,𝔽5)—21no—
166C2×AGL(1,𝔽5)—41no—
167C2×AGL(1,𝔽5)—82no—
168C5×Q8—61no—
169C5×D4—21no—
170C22⋊D5—41no—
171D20—21no—
172D20—61no—
173D20—121no—
174C4×D5—121no—
175C4×D5C2×#6711yescharacteristic
176#170—21no—
177#170—121no—
178C5×C8C2×C4×D311yescharacteristic
179#168#23511yescharacteristic
180#135—151no—
181C2×D8—51no—
182#131—301no—
183C4×D4—101no—
184SD32—31no—
185SD32—151no—
186D16—151no—
187D16—151no—
188M32—151no—
189M32—151no—
190#108—151no—
191#106—51no—
192#104—301no—
193#102—101no—
194#97—51no—
195C2×C3×C5—81no—
196C2×C3×C5#44211yescharacteristic
197D15—81no—
198C3×D5—21no—
199C3×D5—81no—
200C23×C3—201no—
201C3×D4—21no—
202C3×D4—101no—
203C3×D4—201no—
204C2×C3×C4—51no—
205C2×C3×C4—101no—
206C2×C3×C4—201no—
207C2×C3×C4—402no—
208#67—201no—
209D12—101no—
210C4×D3—201no—
211Dic6—21no—
212C3×C8—51no—
213C3×C8—101no—
214C3×C8C22×AGL(1,𝔽5)11yescharacteristic
215C3⋊C8—201no—
216C22×C5—41no—
217C2×D5—41no—
218C2×D5—81no—
219C2×D5—81no—
220C2×D5—121no—
221C2×D5#93211yescharacteristic
222AGL(1,𝔽5)—41no—
223AGL(1,𝔽5)—81no—
224C4×C5—121no—
225C4×C5C4×#6711yescharacteristic
226Dic5#94911yescharacteristic
227#41—301no—
228C2×D4—101no—
229C22×C4—201no—
230Q16—31no—
231SD16—301no—
232D8—51no—
233D8—101no—
234D8—151no—
235D8D3×AGL(1,𝔽5)11yescharacteristic
236M16—301no—
237M16—601no—
238C2×C8—51no—
239C2×C8—51no—
240C2×C8—601no—
241C4⋊C4—101no—
242C22⋊C4—201no—
243C42—51no—
244C16—31no—
245C16—151no—
246C16—301no—
247C3×C5AGL(1,ℤ/16)11yescharacteristic, complemented, Hall
248C22×C3—41no—
249C22×C3—51no—
250C22×C3—201no—
251C22×C3—401no—
252C22×C3—401no—
253C2×D3—201no—
254C3×C4—51no—
255C3×C4—201no—
256C3×C4—401no—
257C3×C4D4×AGL(1,𝔽5)11yescharacteristic
258Dic3—41no—
259C2×C5—81no—
260C2×C5#501411yescharacteristic
261D5—21no—
262D5—81no—
263D5—241no—
264C23—201no—
265Q8—61no—
266D4—21no—
267D4—101no—
268D4—201no—
269D4—301no—
270D4—601no—
271C2×C4—51no—
272C2×C4—101no—
273C2×C4—201no—
274C2×C4—402no—
275C2×C4—601no—
276C8—51no—
277C8—101no—
278C8—601no—
279C8C2×D3×AGL(1,𝔽5)11yescharacteristic
280C2×C3—81no—
281C2×C3—101no—
282C2×C3—401no—
283C2×C3#6573111yescharacteristic
284D3—401no—
285C5#7091811yescharacteristic, complemented, Sylow
286C22—41no—
287C22—51no—
288C22—201no—
289C22—401no—
290C22—401no—
291C22—601no—
292C4—51no—
293C4—121no—
294C4—201no—
295C4—401no—
296C4AGL(1,𝔽5)×#6711yescharacteristic
297C3#1060413211yescharacteristic, complemented, Sylow
298C2—81no—
299C2—101no—
300C2—401no—
301C2—1201no—
302C2#1175194011yescharacteristic
subgroupG/H
centerC2#11751940
commutatorC3×C5×C8C22×C4
FrattiniC8C2×D3×AGL(1,𝔽5)
FittingC3×C5×D8C2×C4
socleC2×C3×C5#442
prime radical#11748278C2
cosocleC3×C8×D5C23
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5AGL(1,ℤ/16)
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D8

Complements

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

NH ≅ G/Ntype
1. C3×#65731C2semidirect
2. #11751684C2semidirect
4. #11746777C2semidirect
5. #11746472C2semidirect
6. #11746465C2semidirect
7. #11746452C2semidirect
19. #91110C4semidirect
20. C5×#827C4semidirect
21. #90940C4semidirect
22. #90938C4semidirect
26. #65731D3semidirect
43. D120C2×C4semidirect
44. C5×Dic12C2×C4semidirect
50. C3⋊#672C2×C4semidirect
51. C5×C3⋊C16C2×C4semidirect
99. #827AGL(1,𝔽5)semidirect
156. Dic12C2×AGL(1,𝔽5)semidirect
163. C3⋊C16C2×AGL(1,𝔽5)semidirect
247. C3×C5AGL(1,ℤ/16)semidirect
285. C5#70918semidirect
297. C3#10604132semidirect

Maximal subgroups

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

subgroupindex
C3×#657312
#117516842
#117482782
#117467772
#117464722
#117464652
#117464522
#106041323
#709185