Finite Group Databasebeta

← #14288875

Subgroups — #14288875

Order 1920.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752651C211yesmaximal, characteristic, complemented
2C3×#65137C211yesmaximal, characteristic, complemented
3#11747083C211yesmaximal, characteristic, complemented
4#11747039C211yesmaximal, characteristic
5#11746305C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599195—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#874C2211yescharacteristic
11C2×C3×#677—21no—
12C3×#4020C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91435—21no—
15#91423—22no—
16Dic5×D12—21no—
17#91373—21no—
18#91370—21no—
19C2×#6657—21no—
20C2×#6652—22no—
21C3×C5×C4⋊C8C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3953—21no—
25#90965—21no—
26#71031—51nomaximal, Hall
27#66047—31no—
28#65362—31no—
29#65137—31no—
30#65137D311yescharacteristic, complemented
31C5×#331—31no—
32#64704—31no—
33#64704—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×Dic10D411yescharacteristic
42C2×D3×Dic5—22no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C3×#677—42no—
54(C2×D3)⋊Dic5—22no—
55(C2×D3)⋊Dic5—22no—
56(C2×D3)⋊Dic5—22no—
57#6657—42no—
58#6652—44no—
59#5585—51no—
60C3×#460—51no—
61#5075—51no—
62#5073—51no—
63#4535—51no—
64#4485D511yescharacteristic, complemented
65#4484—51no—
66C5×#127—31no—
67#4082—61no—
68#4082—61no—
69#4081—62no—
70D4×Dic5—61no—
71D4×Dic5—61no—
72C2×#686—62no—
73C2×#677—21no—
74C2×#677—61no—
75#4020C2×D311yescharacteristic
76C4×Dic10—31no—
77C4×Dic10C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C5×C4⋊C8C2×D311yescharacteristic
80#3953—21no—
81#3953—61no—
82C4×#168—31no—
83#1620—151noSylow
84C22×C5×D3—22no—
85C22×C3×D5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30—21no—
93C5×D12—42no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—41no—
97C5×D12—41no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—21no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105C3×Dic10—21no—
106C3×Dic10—21no—
107D3×Dic5—82no—
108C3×C5×C8—41no—
109C3⋊#168—22no—
110C5×C3⋊C8—41no—
111C2×C3×SD16—101no—
112C3×#127—51no—
113C3×C4×Q8—51no—
114#947—101no—
115C2×#214—101no—
116C2×#213—102no—
117#894—102no—
118#893—101no—
119#875—101no—
120#874C2×D511yescharacteristic
121C4×D12—101no—
122C4×Dic6—51no—
123C3×C4⋊C8C2×D511yescharacteristic
124C3×#102—101no—
125#832—101no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8—51no—
128C2×C5×D4—32no—
129C2×C5×D4—61no—
130C2×C5×D4—61no—
131C22×Dic5—62no—
132C2×D20—21no—
133C2×D20—21no—
134C2×D20—21no—
135C2×Dic10—31no—
136C2×Dic10#6711yescharacteristic
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C42×C5C22×D311yescharacteristic
140C22⋊Dic5—62no—
141C22⋊Dic5—62no—
142C22⋊Dic5—62no—
143#686—124no—
144C4⋊Dic5—31no—
145C4⋊Dic5#6711yescharacteristic
146#683—21no—
147#683—61no—
148C4×Dic5—21no—
149C4×Dic5—61no—
150C2×#168—61no—
151#677—42no—
152#677—122no—
153#559—151no—
154#493—151no—
155#460—51no—
156#460—151no—
157#331—31no—
158Q8⋊C8—151no—
159Q8⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×C5×D3—42no—
162C2×C5×D3—42no—
163C2×C5×D3—42no—
164C2×C3×D5—81no—
165C2×C3×D5—81no—
166C2×C3×D5—81no—
167C3×C4×C5—21no—
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172Dic15—41no—
173Dic15—41no—
174C3×Dic5—41no—
175C3×Dic5—41no—
176C2×C3×Q8—51no—
177C2×C3×D4—101no—
178C2×C3×D4—101no—
179C2×C3×D4—101no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12D2012yes—
183C2×C4×D3—102no—
184C2×Dic6—51no—
185C3×SD16—202no—
186C2×C3×C8—21no—
187C3×C4⋊C4—51no—
188C3×C4⋊C4—101no—
189C3×C42—101no—
190C3×C42C22×D511yescharacteristic
191#214—202no—
192#213—204no—
193(C2×D3)⋊C4—102no—
194(C2×D3)⋊C4—102no—
195(C2×D3)⋊C4—102no—
196C4⋊Dic3—51no—
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C23×C5—62no—
202C22×D5—41no—
203C5×D4—122no—
204C5×D4—121no—
205C5×D4—121no—
206C5×D4—121no—
207C5×D4—121no—
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×Dic5—21no—
212C2×Dic5—21no—
213C2×Dic5—61no—
214C2×Dic5—61no—
215C2×Dic5—242no—
216D20—42no—
217D20—41no—
218D20—41no—
219D20—41no—
220D20—41no—
221Dic10—21no—
222Dic10—21no—
223Dic10—61no—
224Dic10—61no—
225C5×C8—41no—
226C5×C8—121no—
227#168—62no—
228C2×SD16—101no—
229C2×SD16—301no—
230C2×D8—302no—
231#127—31no—
232#127—51no—
233#124—301no—
234#124—301no—
235#123—302no—
236C4×Q8—51no—
237C4×Q8—151no—
238C4×D4—301no—
239C4×D4—301no—
240C4⋊C8—31no—
241C4⋊C8D3×D511yescharacteristic
242#102—101no—
243#102—301no—
244C4×C8—151no—
245C2×C3×C5#44911yescharacteristic
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#45311yescharacteristic
248C3×D5—161no—
249C5×D3—82no—
250C23×C3—201no—
251C22×D3—22no—
252C3×Q8—101no—
253C3×Q8—101no—
254C3×D4—202no—
255C3×D4—201no—
256C3×D4—201no—
257C3×D4—201no—
258C3×D4—201no—
259C2×C3×C4—101no—
260C2×C3×C4—101no—
261C2×C3×C4C2×D2011yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×Dic3—101no—
265C2×Dic3—101no—
266D12—42no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—41no—
271C4×D3—402no—
272Dic6—101no—
273Dic6—101no—
274C3×C8—41no—
275C3⋊C8—41no—
276C3⋊C8—102no—
277C22×C5—122no—
278C22×C5—122no—
279C22×C5—122no—
280C22×C5#93711yescharacteristic
281C2×D5—81no—
282C2×D5—81no—
283C2×D5—81no—
284C4×C5—21no—
285C4×C5#91411yescharacteristic
286C4×C5#91611yescharacteristic
287C4×C5#93211yescharacteristic
288C4×C5#95011yescharacteristic
289Dic5—41no—
290Dic5—41no—
291Dic5—121no—
292Dic5—121no—
293C2×Q8—51no—
294C2×Q8—151no—
295C2×D4—32no—
296C2×D4—61no—
297C2×D4—61no—
298C2×D4—101no—
299C2×D4—101no—
300C2×D4—101no—
301C22×C4—302no—
302SD16—202no—
303SD16—602no—
304D8—604no—
305C2×C8—21no—
306C2×C8—61no—
307C2×C8—301no—
308C4⋊C4—51no—
309C4⋊C4—101no—
310C4⋊C4—151no—
311C4⋊C4—301no—
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C42—101no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—401no—
320C22×C3—401no—
321C22×C3—401no—
322C22×C3#402811yescharacteristic
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C3×C4—21no—
327C3×C4—201no—
328C3×C4—201no—
329C3×C4#405711yescharacteristic
330C3×C4#405711yescharacteristic
331C3×C4#406211yescharacteristic
332C3×C4#406211yescharacteristic
333Dic3—201no—
334Dic3—201no—
335C2×C5—242no—
336C2×C5#503711yescharacteristic
337C2×C5#517211yescharacteristic
338C2×C5#519811yescharacteristic
339D5—161no—
340C23—62no—
341C23—201no—
342Q8—101no—
343Q8—101no—
344Q8—301no—
345Q8—301no—
346D4—122no—
347D4—121no—
348D4—121no—
349D4—121no—
350D4—121no—
351D4—202no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—201no—
356C2×C4—101no—
357C2×C4—101no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—1202no—
361C2×C4D3×D2011yescharacteristic
362C2×C4#677711yescharacteristic
363C2×C4D5×#6711yescharacteristic
364C8—41no—
365C8—121no—
366C8—302no—
367C2×C3—801no—
368C2×C3#6503611yescharacteristic
369C2×C3#6507011yescharacteristic
370C2×C3#6507011yescharacteristic
371D3—82no—
372C5#7103111yescharacteristic, complemented, Sylow
373C22—122no—
374C22—122no—
375C22—122no—
376C22—401no—
377C22—401no—
378C22—401no—
379C22#9147411yescharacteristic
380C4—21no—
381C4—201no—
382C4—201no—
383C4—601no—
384C4—601no—
385C4#9125711yescharacteristic
386C4#9127611yescharacteristic
387C4#9148911yescharacteristic
388C4#9151411yescharacteristic
389C3#1059919511yescharacteristic, complemented, Sylow
390C2—242no—
391C2—801no—
392C2#1174751011yescharacteristic
393C2#1174788911yescharacteristic
394C2#1174824311yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11747039C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1620
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. #11752651C2semidirect
2. C3×#65137C2semidirect
3. #11747083C2semidirect
5. #11746305C2semidirect
6. C5×#4485C2semidirect
7. #11745840C2semidirect
30. #65137D3semidirect
64. #4485D5semidirect
318. C3×C5#1620semidirect
372. C5#71031semidirect
389. C3#10599195semidirect

Maximal subgroups

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

subgroupindex
#117526512
C3×#651372
#117470832
#117470392
#117463052
C5×#44852
#117458402
#105991953
#710315