Finite Group Databasebeta

← #14288868

Subgroups — #14288868

Order 1920.

480 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5585C211yesmaximal, characteristic, complemented
2C3×#65316C211yesmaximal, characteristic, complemented
3#11747068C211yesmaximal, characteristic, complemented
4#11747039C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745853C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10602736—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#947—21no—
11C5×#894—22no—
12C5×#893—21no—
13C5×#875—21no—
14C5×#874C2211yescharacteristic
15C4×C5×D12—21no—
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#688—21no—
18C3×#4020C2211yescharacteristic
19C2×#6655—21no—
20C2×#6652—22no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C3×#3941—21no—
24C3×C4⋊#168C2211yescharacteristic
25#90964—21no—
26#71031—51nomaximal, Hall
27C5×#559—31no—
28#65362—31no—
29#65316—31no—
30#65316D311yescharacteristic, complemented
31#64764—31no—
32Q8⋊#168—31no—
33Q8⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12D412yes—
38C2×C4×C5×D3—22no—
39C2×C5×Dic6D411yescharacteristic
40C2×C3×D20—21no—
41C2×C3×D20—21no—
42C2×C3×D20—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—22no—
50C5×(C2×D3)⋊C4—22no—
51C5×(C2×D3)⋊C4—22no—
52C5×C4⋊Dic3D411yescharacteristic
53C5×Dic3⋊C4—21no—
54C4×C5×Dic3—21no—
55C3×#688—42no—
56C2×C3×#168—21no—
57#6655—42no—
58#6652—44no—
59#5585D511yescharacteristic, complemented
60C3×#460—51no—
61#5075—51no—
62#5073—51no—
63#4535—51no—
64#4485—51no—
65#4484—51no—
66C5×#127—31no—
67C5×#124—61no—
68C5×#124—61no—
69C5×#123—62no—
70C4×C5×Q8—31no—
71C4×C5×Q8C2×D311yescharacteristic
72C4×C5×D4—61no—
73C4×C5×D4—61no—
74C2×#688—21no—
75C2×#688—61no—
76C2×#686—62no—
77#4020C2×D311yescharacteristic
78#3941—21no—
79#3941—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82C4×#168—31no—
83#1620—151noSylow
84C22×C5×D3—22no—
85C22×C3×D5—41no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C5×D12—42no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C5×D12—41no—
100C4×C5×D3—82no—
101C5×Dic6—21no—
102C5×Dic6—21no—
103C3×D20—42no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20—41no—
107C3×D20—41no—
108C3⋊#168—22no—
109C3⋊#168—41no—
110C3×#168—41no—
111C2×C3×SD16—101no—
112C3×#127—51no—
113C3×C4×Q8C2×D511yescharacteristic
114#947—21no—
115C2×#214—101no—
116C2×#213—102no—
117#894—22no—
118#893—21no—
119#875—21no—
120#874C2×D511yescharacteristic
121C4×D12—21no—
122C4×Dic6C2×D511yescharacteristic
123C3×C4⋊C8—51no—
124C3×#102—101no—
125#832—101no—
126C4⋊(C3⋊C8)—51no—
127C4×C3⋊C8—51no—
128C2×C5×Q8—31no—
129C2×C5×Q8#6711yescharacteristic
130C2×C5×D4—32no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133C22×C4×C5—62no—
134C2×D20—21no—
135C2×D20—21no—
136C2×D20—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C22⋊C4—62no—
142C5×C22⋊C4—62no—
143C5×C22⋊C4—62no—
144C42×C5—21no—
145C42×C5—61no—
146C42×C5C22×D311yescharacteristic
147#688—42no—
148#688—122no—
149#686—124no—
150C2×#168—21no—
151C2×#168—61no—
152C2×#168—61no—
153#559—31no—
154#493—151no—
155#460—51no—
156#460—151no—
157#331—151no—
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—41no—
169C3×C4×C5—41no—
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C5×Dic3—41no—
175C5×Dic3—41no—
176C2×C3×Q8C22⋊D511yescharacteristic
177C2×C3×D4—101no—
178C2×C3×D4—101no—
179C2×C3×D4—101no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12C22⋊D512yes—
183C2×C4×D3—22no—
184C2×Dic6C22⋊D511yescharacteristic
185C3×SD16—202no—
186C2×C3×C8—101no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4C22⋊D511yescharacteristic
189C3×C42—21no—
190C3×C42C22×D511yescharacteristic
191#214—202no—
192#213—204no—
193(C2×D3)⋊C4—22no—
194(C2×D3)⋊C4—22no—
195(C2×D3)⋊C4—22no—
196C4⋊Dic3C22⋊D511yescharacteristic
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C23×C5—62no—
202C22×D5—41no—
203C5×Q8—21no—
204C5×Q8—21no—
205C5×Q8—61no—
206C5×Q8—61no—
207C5×D4—122no—
208C5×D4—121no—
209C5×D4—121no—
210C5×D4—121no—
211C5×D4—121no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—61no—
215C2×C4×C5—61no—
216C2×C4×C5—242no—
217C2×C4×C5D3×D411yescharacteristic
218C2×C4×C5D3×D411yescharacteristic
219C2×C4×C5C2×#6711yescharacteristic
220D20—42no—
221D20—41no—
222D20—41no—
223D20—41no—
224D20—41no—
225#168—41no—
226#168—62no—
227#168—121no—
228C2×SD16—101no—
229C2×SD16—301no—
230C2×D8—302no—
231#127—31no—
232#127—51no—
233#124—61no—
234#124—61no—
235#123—62no—
236C4×Q8—31no—
237C4×Q8D3×D511yescharacteristic
238C4×D4—61no—
239C4×D4—61no—
240C4⋊C8—51no—
241C4⋊C8—151no—
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—21no—
253C3×Q8—21no—
254C3×D4—202no—
255C3×D4—201no—
256C3×D4—201no—
257C3×D4—201no—
258C3×D4—201no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4C2×C22⋊D511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263C2×C3×C4C2×C22⋊D511yescharacteristic
264C2×Dic3—21no—
265C2×Dic3—21no—
266D12—42no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—41no—
271C4×D3—82no—
272Dic6—21no—
273Dic6—21no—
274C3×C8—201no—
275C3⋊C8—102no—
276C3⋊C8—201no—
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—41no—
286C4×C5—41no—
287C4×C5—121no—
288C4×C5—121no—
289C4×C5#91411yescharacteristic
290C4×C5#91611yescharacteristic
291C4×C5#93211yescharacteristic
292C4×C5#95011yescharacteristic
293C2×Q8—31no—
294C2×Q8#120111yescharacteristic
295C2×D4—32no—
296C2×D4—61no—
297C2×D4—61no—
298C2×D4—101no—
299C2×D4—101no—
300C2×D4—101no—
301C22×C4—62no—
302SD16—202no—
303SD16—602no—
304D8—604no—
305C2×C8—101no—
306C2×C8—301no—
307C2×C8—301no—
308C4⋊C4—21no—
309C4⋊C4—31no—
310C4⋊C4—61no—
311C4⋊C4#120111yescharacteristic
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C42—21no—
316C42—61no—
317C42C2×D3×D511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—401no—
320C22×C3—401no—
321C22×C3—401no—
322C22×C3#409911yescharacteristic
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4#409511yescharacteristic
330C3×C4#409511yescharacteristic
331C3×C4#409611yescharacteristic
332C3×C4#409611yescharacteristic
333Dic3—41no—
334Dic3—41no—
335C2×C5—242no—
336C2×C5#503711yescharacteristic
337C2×C5#517211yescharacteristic
338C2×C5#519811yescharacteristic
339D5—161no—
340C23—62no—
341C23—201no—
342Q8—21no—
343Q8—21no—
344Q8—61no—
345Q8—61no—
346D4—122no—
347D4—121no—
348D4—121no—
349D4—121no—
350D4—121no—
351D4—202no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—201no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—242no—
361C2×C4C2×#120111yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4D3×C22⋊D511yescharacteristic
364C8—201no—
365C8—302no—
366C8—601no—
367C2×C3—801no—
368C2×C3#6552711yescharacteristic
369C2×C3#6552711yescharacteristic
370C2×C3#6553011yescharacteristic
371D3—82no—
372C5#7103111yescharacteristic, complemented, Sylow
373C22—122no—
374C22—122no—
375C22—122no—
376C22—401no—
377C22—401no—
378C22—401no—
379C22#9156811yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—121no—
384C4—121no—
385C4#9129711yescharacteristic
386C4#9129811yescharacteristic
387C4#9150411yescharacteristic
388C4#9151711yescharacteristic
389C3#1060273611yescharacteristic, complemented, Sylow
390C2—242no—
391C2—801no—
392C2#1174851711yescharacteristic
393C2#1174928111yescharacteristic
394C2#1174941911yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747039C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1620
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. C5×#5585C2semidirect
2. C3×#65316C2semidirect
3. #11747068C2semidirect
5. #11746356C2semidirect
6. #11745853C2semidirect
7. #11745842C2semidirect
30. #65316D3semidirect
59. #5585D5semidirect
318. C3×C5#1620semidirect
372. C5#71031semidirect
389. C3#10602736semidirect

Maximal subgroups

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

subgroupindex
C5×#55852
C3×#653162
#117470682
#117470392
#117463562
#117458532
#117458422
#106027363
#710315