Finite Group Databasebeta

← #14292671

Subgroups — #14292671

Order 1920.

320 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 84 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#11751181C211yesmaximal, characteristic, complemented
2C3×#65373C211yesmaximal, characteristic
3#11747062C211yesmaximal, characteristic
4#11747013C211yesmaximal, characteristic
5C5×#4546C211yesmaximal, characteristic, complemented
6#11745868C211yesmaximal, characteristic, complemented
7#11745860C211yesmaximal, characteristic, complemented
8#10599293—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×C4×D20C2211yescharacteristic
12C2×#6657—21no—
13C2×#6649—21no—
14#91092—21no—
15#91092—21no—
16C4×C3⋊#168C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×#3941—21no—
20C3×#3940—21no—
21C3×C4⋊#168C2211yescharacteristic
22#90974—21no—
23#90955—21no—
24#71136—51nomaximal, Hall
25#65373D311yescharacteristic
26#65368—31no—
27#65130—31no—
28#65127—31no—
29C5×#333—31no—
30#64706—31no—
31#64699—31no—
32C2×C3×C5×Q8—21no—
33C2×Dic30—21no—
34C2×C3×D20D411yescharacteristic
35C2×C3×C4×D5—21no—
36C3×C5×C4⋊C4—21no—
37C3×C5×C4⋊C4—21no—
38C3×C42×C5C2311yescharacteristic
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C2×C3⋊#168D411yescharacteristic
42C2×C3⋊#168D411yescharacteristic
43C2×C5×C3⋊C8—21no—
44C2×C5×C3⋊C8—21no—
45C3×#685—21no—
46C3×C4⋊Dic5D411yescharacteristic
47C2×C3×#168—21no—
48#6657—42no—
49#6649—42no—
50C3×#476—51no—
51#5080—51no—
52#5019—51no—
53#5012—51no—
54#4546D511yescharacteristic, complemented
55#4482—51no—
56#4479—51no—
57C5×C4⋊Q8C2×D311yescharacteristic
58C2×#677—61no—
59C2×#676—61no—
60C4×D20C2×D311yescharacteristic
61#4015—31no—
62C5×C4⋊C8—31no—
63C5×C4⋊C8—31no—
64#3952—61no—
65#3948—61no—
66#3941—21no—
67#3940—21no—
68#3940—61no—
69#3940—61no—
70C4⋊#168C2×D311yescharacteristic
71C4×#168—31no—
72#1691—151noSylow
73C22×C3×D5—21no—
74C3×C5×Q8—81no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5#4111yescharacteristic
79C2×Dic15—41no—
80Dic30—41no—
81Dic30—41no—
82C2×C3×Dic5—21no—
83C3×D20—21no—
84C3×D20—21no—
85C3×C4×D5—41no—
86C3×C4×D5—41no—
87C3⋊#168—21no—
88C3⋊#168SD1612yescomplemented
89C3×#168—41no—
90C5×C3⋊C8—41no—
91C5×C3⋊C8—41no—
92C3×C4⋊Q8C2×D511yescharacteristic
93C3×C4×D4—51no—
94C2×#214—101no—
95C2×#208—101no—
96#869—51no—
97C3×#106—101no—
98C3×C4⋊C8—51no—
99C3×#102—101no—
100#830—101no—
101#810—101no—
102#808—101no—
103#808—101no—
104C4⋊(C3⋊C8)C2×D511yescharacteristic
105C4⋊(C3⋊C8)C2×D511yescharacteristic
106C4×C3⋊C8—51no—
107C2×C5×Q8—21no—
108C2×D20#6711yescharacteristic
109C2×C4×D5—21no—
110C2×Dic10—61no—
111C2×C5×C8—61no—
112C2×C5×C8—61no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C42×C5C22×D311yescharacteristic
116#685—21no—
117C4⋊Dic5—61no—
118C4⋊Dic5—61no—
119C4⋊Dic5#6711yescharacteristic
120C2×#168—21no—
121C2×#168—31no—
122C2×#168—31no—
123#677—122no—
124#676—122no—
125#498—151no—
126#476—51no—
127#461—151no—
128#436—151no—
129#335—151no—
130#333—31no—
131#332—151no—
132C22×C3×C5#12111yescharacteristic
133C2×C3×D5—41no—
134C2×C3×D5—41no—
135C2×C3×D5—41no—
136C3×C4×C5—21no—
137C3×C4×C5—81no—
138C3×C4×C5C2×SD1611yescharacteristic
139C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
140C3×C4×C5#13711yescharacteristic
141C3×C4×C5#13711yescharacteristic
142Dic15—81no—
143C3×Dic5—41no—
144C2×C3×Q8—21no—
145C2×C3×D4—51no—
146C22×C3×C4—101no—
147C2×Dic6—101no—
148C2×C3×C8—101no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—51no—
152C3×C22⋊C4—101no—
153C3×C42C22×D511yescharacteristic
154#214—202no—
155C4⋊Dic3—101no—
156C4⋊Dic3—101no—
157#208—202no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—51no—
161C2×C3⋊C8—51no—
162C22×D5—21no—
163C5×Q8—81no—
164C2×C4×C5—41no—
165C2×C4×C5D3×D411yescharacteristic
166C2×C4×C5#23711yescharacteristic
167C2×C4×C5C2×#6711yescharacteristic
168C2×Dic5—21no—
169C2×Dic5—121no—
170D20—21no—
171D20—21no—
172C4×D5—41no—
173C4×D5—41no—
174Dic10—121no—
175Dic10—121no—
176C5×C8—121no—
177C5×C8—121no—
178#168—32no—
179#168—41no—
180#168—61no—
181C2×SD16—301no—
182C2×M16—301no—
183C4⋊Q8—151no—
184C4⋊Q8D3×D511yescharacteristic
185C4×D4—51no—
186#106—101no—
187#106—301no—
188#106—301no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191C4⋊C8—51no—
192#103—301no—
193#102—101no—
194C22⋊C8—301no—
195C4×C8—151no—
196C2×C3×C5#46111yescharacteristic
197C2×C3×C5#46811yescharacteristic
198C2×C3×C5#47111yescharacteristic
199C3×D5—81no—
200C23×C3—101no—
201C3×Q8—81no—
202C3×D4—101no—
203C3×D4—101no—
204C2×C3×C4—41no—
205C2×C3×C4—101no—
206C2×C3×C4—201no—
207C2×C3×C4—201no—
208C2×C3×C4#70911yescharacteristic
209C2×C3×C4D4×D511yescharacteristic
210C2×C3×C4D4×D511yescharacteristic
211C2×Dic3—201no—
212Dic6—201no—
213Dic6—201no—
214C3×C8—201no—
215C3⋊C8—41no—
216C3⋊C8—41no—
217C3⋊C8—52no—
218C3⋊C8—101no—
219C22×C5#93911yescharacteristic
220C2×D5—41no—
221C2×D5—41no—
222C2×D5—41no—
223C4×C5—21no—
224C4×C5—81no—
225C4×C5D3×SD1611yescharacteristic
226C4×C5#91511yescharacteristic
227C4×C5#94211yescharacteristic
228C4×C5#94911yescharacteristic
229Dic5—41no—
230Dic5—241no—
231C2×Q8—21no—
232C2×Q8—301no—
233C2×D4—51no—
234C22×C4—101no—
235SD16—602no—
236M16—602no—
237C2×C8—61no—
238C2×C8—61no—
239C2×C8—101no—
240C2×C8—151no—
241C2×C8—151no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—51no—
245C4⋊C4—301no—
246C4⋊C4—301no—
247C22⋊C4—101no—
248C42C2×D3×D511yescharacteristic
249C3×C5#169111yescharacteristic, complemented, Hall
250C22×C3—201no—
251C22×C3—201no—
252C22×C3—201no—
253C22×C3#403011yescharacteristic
254C3×C4—21no—
255C3×C4—81no—
256C3×C4—201no—
257C3×C4D5×SD1611yescharacteristic
258C3×C4#406011yescharacteristic
259C3×C4#406411yescharacteristic
260C3×C4#406411yescharacteristic
261Dic3—401no—
262C2×C5#504911yescharacteristic
263C2×C5#516211yescharacteristic
264C2×C5#520011yescharacteristic
265D5—81no—
266C23—101no—
267Q8—81no—
268Q8—601no—
269Q8—601no—
270D4—101no—
271D4—101no—
272C2×C4—41no—
273C2×C4—101no—
274C2×C4—201no—
275C2×C4—201no—
276C2×C4—601no—
277C2×C4#677911yescharacteristic
278C2×C4D5×#6711yescharacteristic
279C2×C4#679011yescharacteristic
280C8—121no—
281C8—121no—
282C8—152no—
283C8—201no—
284C8—301no—
285C2×C3—401no—
286C2×C3#6503711yescharacteristic
287C2×C3#6510111yescharacteristic
288C2×C3#6510711yescharacteristic
289C5#7113611yescharacteristic, complemented, Sylow
290C22—201no—
291C22—201no—
292C22—201no—
293C22#9155011yescharacteristic
294C4—21no—
295C4—81no—
296C4—201no—
297C4—1201no—
298C4#9150211yescharacteristic
299C4#9150511yescharacteristic
300C4#9151511yescharacteristic
301C4#9152211yescharacteristic
302C3#1059929311yescharacteristic, complemented, Sylow
303C2—401no—
304C2#1174913111yescharacteristic
305C2#1174922911yescharacteristic
306C2#1174927311yescharacteristic
subgroupG/H
centerC22#91550
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#121
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1691
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11751181C2semidirect
5. C5×#4546C2semidirect
6. #11745868C2semidirect
7. #11745860C2semidirect
54. #4546D5semidirect
88. C3⋊#168SD16semidirect
249. C3×C5#1691semidirect
289. C5#71136semidirect
302. C3#10599293semidirect

Maximal subgroups

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

subgroupindex
#117511812
C3×#653732
#117470622
#117470132
C5×#45462
#117458682
#117458602
#105992933
#711365