Finite Group Databasebeta

← #14292460

Subgroups — #14292460

Order 1920.

336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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#11750932C211yesmaximal, characteristic, complemented
2#11747086C211yesmaximal, characteristic
3#11747081C211yesmaximal, characteristic
4#11746949C211yesmaximal, characteristic, complemented
5C5×#4485C211yesmaximal, characteristic
6C3×#64702C211yesmaximal, characteristic, complemented
7#11745868C211yesmaximal, characteristic, complemented
8#10599205—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#874C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C2×#6659—21no—
13C2×#6656—21no—
14C2×#6656—21no—
15C3×C5×C4⋊C8C2211yescharacteristic
16#91099—21no—
17#91098—21no—
18C4×C3⋊#168C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21#90987—21no—
22#90974—21no—
23#90967—21no—
24#68472—51nomaximal, Hall
25#65365—31no—
26#65364—31no—
27#65140—31no—
28#65120—31no—
29C5×#331—31no—
30#64702D311yescharacteristic, complemented
31#64699—31no—
32C2×Dic30D411yescharacteristic
33C2×C5×D12—21no—
34C2×C5×D12—21no—
35C2×C5×D12—21no—
36C2×C3×Dic10—21no—
37C2×C3×C5×C8—21no—
38C3×C42×C5C2311yescharacteristic
39C4⋊Dic15D411yescharacteristic
40#6712—21no—
41C4×Dic15—21no—
42C2×C3⋊#168D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44C2×C5×C3⋊C8—21no—
45C3×C4⋊Dic5—21no—
46C3×C4⋊Dic5—21no—
47C2×C3×#168—21no—
48#6659—42no—
49#6656—42no—
50#6656—42no—
51#5094—51no—
52#5085—51no—
53#4848—51no—
54#4831—51no—
55C3×#332—51no—
56#4485D511yescharacteristic
57#4479—51no—
58C5×#127—31no—
59C2×#687—61no—
60C2×#687—61no—
61C2×#687—61no—
62#4015C2×D311yescharacteristic
63C4×Dic10—31no—
64C5×C4⋊C8—31no—
65C5×C4⋊C8C2×D311yescharacteristic
66#3964—61no—
67#3949—61no—
68#3948—61no—
69#3947—61no—
70#3946—61no—
71C4⋊#168C2×D311yescharacteristic
72C4×#168—31no—
73#1686—151noSylow
74C22×C5×D3—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5#4111yescharacteristic
78C2×Dic15—21no—
79C2×Dic15—21no—
80Dic30—21no—
81Dic30—21no—
82C5×D12—41no—
83C5×D12—41no—
84C5×D12—41no—
85C5×D12—41no—
86C5×D12—81no—
87C2×C3×Dic5—41no—
88C3×Dic10—41no—
89C3×Dic10—41no—
90C3×C5×C8—41no—
91C3⋊#168—21no—
92C3⋊#168SD1612yescomplemented
93C3×#168—41no—
94C5×C3⋊C8—41no—
95C3×C4⋊Q8—51no—
96C2×#215—101no—
97C2×#215—101no—
98C2×#204—101no—
99#874C2×D511yescharacteristic
100C4×Dic6—51no—
101C3×C4⋊C8—51no—
102C3×C4⋊C8C2×D511yescharacteristic
103#821—101no—
104#815—101no—
105Dic3⋊C8—101no—
106#810—101no—
107#808—101no—
108C4⋊(C3⋊C8)C2×D511yescharacteristic
109C4×C3⋊C8—51no—
110C2×C5×D4—61no—
111C2×C5×D4—61no—
112C2×C5×D4—61no—
113C2×Dic10—21no—
114C2×Dic10—31no—
115C2×C5×C8—21no—
116C2×C5×C8—61no—
117C42×C5C22×D311yescharacteristic
118#687—122no—
119#687—122no—
120#687—122no—
121C4⋊Dic5—21no—
122C4⋊Dic5—21no—
123C4⋊Dic5—31no—
124#683—61no—
125C4×Dic5—61no—
126C2×#168—21no—
127C2×#168—31no—
128C2×#168—31no—
129#492—151no—
130#475—151no—
131#460—151no—
132#446—151no—
133#335—151no—
134#332—51no—
135#331—31no—
136C22×C3×C5#12111yescharacteristic
137C2×C5×D3—81no—
138C2×C5×D3—81no—
139C2×C5×D3—81no—
140C3×C4×C5—21no—
141C3×C4×C5C2×SD1611yescharacteristic
142C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
144C3×C4×C5#13711yescharacteristic
145Dic15—41no—
146Dic15—41no—
147C3×Dic5—81no—
148C2×C3×Q8—101no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×Dic6—51no—
153C2×C3×C8—21no—
154C2×C3×C8—101no—
155C3×C4⋊C4—101no—
156C3×C4⋊C4—101no—
157C3×C42C22×D511yescharacteristic
158#215—202no—
159#215—202no—
160C4⋊Dic3—51no—
161Dic3⋊C4—101no—
162C4×Dic3—101no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—51no—
165C2×C3⋊C8—51no—
166#204—202no—
167C23×C5—121no—
168C5×D4—121no—
169C5×D4—121no—
170C5×D4—121no—
171C5×D4—121no—
172C5×D4—241no—
173C2×C4×C5#23511yescharacteristic
174C2×C4×C5D3×D411yescharacteristic
175C2×C4×C5D3×D411yescharacteristic
176C2×Dic5—41no—
177C2×Dic5—61no—
178C2×Dic5—61no—
179Dic10—41no—
180Dic10—41no—
181Dic10—61no—
182Dic10—61no—
183C5×C8—41no—
184C5×C8—121no—
185#168—32no—
186#168—41no—
187#168—61no—
188C2×SD16—301no—
189C2×SD16—301no—
190C2×SD16—301no—
191C4⋊Q8—51no—
192#127—31no—
193C4×Q8—151no—
194#106—301no—
195C4⋊C8—31no—
196C4⋊C8—51no—
197C4⋊C8—301no—
198C4⋊C8D3×D511yescharacteristic
199#103—301no—
200#102—301no—
201#97—301no—
202C4×C8—151no—
203C2×C3×C5#46011yescharacteristic
204C2×C3×C5#46811yescharacteristic
205C2×C3×C5#47111yescharacteristic
206C5×D3—161no—
207C22×D3—41no—
208C3×Q8—201no—
209C3×Q8—201no—
210C2×C3×C4—201no—
211C2×C3×C4#70911yescharacteristic
212C2×C3×C4D4×D511yescharacteristic
213C2×C3×C4D4×D511yescharacteristic
214C2×Dic3—101no—
215C2×Dic3—101no—
216D12—41no—
217D12—41no—
218D12—41no—
219D12—41no—
220D12—81no—
221Dic6—101no—
222Dic6—101no—
223C3×C8—41no—
224C3×C8—201no—
225C3⋊C8—41no—
226C3⋊C8—52no—
227C3⋊C8—101no—
228C22×C5—241no—
229C22×C5—241no—
230C22×C5—241no—
231C22×C5#88411yescharacteristic
232C4×C5—21no—
233C4×C5#91111yescharacteristic
234C4×C5D3×SD1611yescharacteristic
235C4×C5#91411yescharacteristic
236C4×C5#91811yescharacteristic
237Dic5—81no—
238Dic5—121no—
239Dic5—121no—
240C2×Q8—101no—
241C2×Q8—151no—
242C2×D4—61no—
243C2×D4—61no—
244C2×D4—61no—
245SD16—602no—
246SD16—602no—
247SD16—602no—
248C2×C8—21no—
249C2×C8—61no—
250C2×C8—101no—
251C2×C8—151no—
252C2×C8—151no—
253C4⋊C4—101no—
254C4⋊C4—101no—
255C4⋊C4—151no—
256C4⋊C4—301no—
257C42—301no—
258C42C2×D3×D511yescharacteristic
259C3×C5#168611yescharacteristic, complemented, Hall
260C22×C3#403011yescharacteristic
261C2×D3—81no—
262C2×D3—81no—
263C2×D3—81no—
264C3×C4—21no—
265C3×C4—401no—
266C3×C4#405711yescharacteristic
267C3×C4#405711yescharacteristic
268C3×C4D5×SD1611yescharacteristic
269C3×C4#406111yescharacteristic
270Dic3—201no—
271Dic3—201no—
272C2×C5—481no—
273C2×C5#475411yescharacteristic
274C2×C5#476211yescharacteristic
275C2×C5#481211yescharacteristic
276C23—121no—
277Q8—201no—
278Q8—201no—
279Q8—301no—
280Q8—301no—
281D4—121no—
282D4—121no—
283D4—121no—
284D4—121no—
285D4—241no—
286C2×C4—201no—
287C2×C4—301no—
288C2×C4—301no—
289C2×C4#677111yescharacteristic
290C2×C4#677711yescharacteristic
291C2×C4#679011yescharacteristic
292C8—41no—
293C8—121no—
294C8—152no—
295C8—201no—
296C8—301no—
297C2×C3#6503711yescharacteristic
298C2×C3#6505111yescharacteristic
299C2×C3#6506911yescharacteristic
300D3—161no—
301C5#6847211yescharacteristic, complemented, Sylow
302C22—241no—
303C22—241no—
304C22—241no—
305C22#9146111yescharacteristic
306C4—21no—
307C4—401no—
308C4—601no—
309C4—601no—
310C4#9125711yescharacteristic
311C4#9128011yescharacteristic
312C4#9148211yescharacteristic
313C4#9150511yescharacteristic
314C3#1059920511yescharacteristic, complemented, Sylow
315C2—481no—
316C2#1174740811yescharacteristic
317C2#1174792911yescharacteristic
318C2#1174819911yescharacteristic
subgroupG/H
centerC22#91461
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC5×#874C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1686
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11750932C2semidirect
4. #11746949C2semidirect
6. C3×#64702C2semidirect
7. #11745868C2semidirect
30. #64702D3semidirect
92. C3⋊#168SD16semidirect
259. C3×C5#1686semidirect
301. C5#68472semidirect
314. C3#10599205semidirect

Maximal subgroups

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

subgroupindex
#117509322
#117470862
#117470812
#117469492
C5×#44852
C3×#647022
#117458682
#105992053
#684725