Finite Group Databasebeta

← #14288871

Subgroups — #14288871

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
1C3×#65919C211yesmaximal, characteristic, complemented
2#11751128C211yesmaximal, characteristic, complemented
3#11747064C211yesmaximal, characteristic, complemented
4#11747035C211yesmaximal, characteristic
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745852C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10599051—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C2×#6717—21no—
11#91763C2211yescharacteristic
12C3×#4093—21no—
13C3×#4040—22no—
14C3×#4039—21no—
15C3×#4021—21no—
16C3×#4020C2211yescharacteristic
17C3×C4×D20—21no—
18C3×C4×Dic10C2211yescharacteristic
19C2×#6658—21no—
20C2×#6653—22no—
21#91093—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C4×C5×C3⋊C8C2211yescharacteristic
25#90968—21no—
26#71943—51nomaximal, Hall
27#65919D311yescharacteristic, complemented
28#65316—31no—
29#65137—31no—
30#64984—31no—
31C5×Q8⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20D412yes—
41C2×C3×C4×D5—22no—
42C2×C3×Dic10D411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47#6717—42no—
48C2×C3⋊#168—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—22no—
52C3×#685—22no—
53C3×#685—22no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57#6658—42no—
58#6653—44no—
59C3×#559—51no—
60#5073—51no—
61#5027—51no—
62#5027—51no—
63#4544—51no—
64#4535—51no—
65#4535D511yescharacteristic, complemented
66C4×C5×Q8C2×D311yescharacteristic
67#4093—21no—
68C2×#688—61no—
69C2×D40—62no—
70C2×#677—61no—
71#4040—22no—
72#4039—21no—
73#4021—21no—
74#4020—31no—
75#4020C2×D311yescharacteristic
76C4×D20—21no—
77C4×Dic10C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C4×C5×C8—31no—
80#3953—61no—
81#3941—61no—
82C4⋊#168—31no—
83#1620—151noSylow
84C22×D15—41no—
85C22×C3×D5—22no—
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
93D60—42no—
94D60—41no—
95D60—41no—
96D60—41no—
97D60—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×C4×D5—82no—
106C3×Dic10—21no—
107C3×Dic10—21no—
108C3⋊#168—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C3×#127—51no—
112C3×#124—101no—
113C3×#124—101no—
114C3×#123—102no—
115C3×C4×Q8—51no—
116C3×C4×Q8C2×D511yescharacteristic
117C3×C4×D4—101no—
118C3×C4×D4—101no—
119C2×#215—101no—
120C2×#215—101no—
121C2×#213—102no—
122#874—51no—
123#809—101no—
124#809—101no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C4×C3⋊C8C2×D511yescharacteristic
128C2×C5×Q8#6711yescharacteristic
129C2×D20—21no—
130C2×D20—21no—
131C2×D20—61no—
132C2×D20—61no—
133C2×D20—61no—
134C2×D20#6712yes—
135C2×C4×D5—22no—
136C2×Dic10#6711yescharacteristic
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4#6711yescharacteristic
141C42×C5—21no—
142C42×C5C22×D311yescharacteristic
143#688—122no—
144#685—22no—
145#685—22no—
146#685—22no—
147C4⋊Dic5#6711yescharacteristic
148#683—21no—
149C4×Dic5—21no—
150C2×#168—61no—
151D40—124no—
152#677—122no—
153#559—51no—
154#493—151no—
155#460—151no—
156#460—151no—
157#331—151no—
158Q8⋊C8—31no—
159Q8⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×D15—81no—
162C2×D15—81no—
163C2×D15—81no—
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
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
174C3×Dic5—41no—
175C3×Dic5—41no—
176C2×C3×Q8—51no—
177C2×C3×Q8D2011yescharacteristic
178C2×C3×D4—52no—
179C2×C3×D4—101no—
180C2×C3×D4—101no—
181C22×C3×C4—102no—
182C2×D12—101no—
183C2×D12—101no—
184C2×D12—101no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—101no—
188C3×C4⋊C4D2011yescharacteristic
189C3×C22⋊C4—102no—
190C3×C22⋊C4—102no—
191C3×C22⋊C4—102no—
192C3×C42—21no—
193C3×C42—101no—
194C3×C42C22×D511yescharacteristic
195#215—202no—
196#215—202no—
197#213—204no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C22×D5—22no—
202C22×D5—121no—
203C5×Q8—21no—
204C5×Q8—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5C2×#6711yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C2×Dic5—21no—
211C2×Dic5—21no—
212D20—42no—
213D20—41no—
214D20—41no—
215D20—41no—
216D20—41no—
217D20—122no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—82no—
223Dic10—21no—
224Dic10—21no—
225C5×C8—62no—
226C5×C8—121no—
227#168—121no—
228C2×SD16—301no—
229C2×SD16—301no—
230C2×D8—302no—
231#127—51no—
232#127—151no—
233#124—101no—
234#124—101no—
235#123—102no—
236C4×Q8—51no—
237C4×Q8D3×D511yescharacteristic
238C4×D4—101no—
239C4×D4—101no—
240C4⋊C8—31no—
241C4⋊C8—151no—
242#102—301no—
243#102—301no—
244C4×C8—31no—
245C2×C3×C5#44911yescharacteristic
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—161no—
249C3×D5—82no—
250C23×C3—102no—
251C22×D3—201no—
252C3×Q8—21no—
253C3×Q8—21no—
254C3×Q8—101no—
255C3×Q8—101no—
256C3×D4—202no—
257C3×D4—201no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—101no—
264C2×C3×C4—101no—
265C2×C3×C4—402no—
266C2×C3×C4C2×D2011yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268C2×C3×C4D4×D511yescharacteristic
269D12—202no—
270D12—201no—
271D12—201no—
272D12—201no—
273D12—201no—
274C3⋊C8—22no—
275C3⋊C8—41no—
276C3⋊C8—201no—
277C22×C5#95311yescharacteristic
278C2×D5—42no—
279C2×D5—42no—
280C2×D5—42no—
281C2×D5—241no—
282C2×D5—241no—
283C2×D5—241no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5—41no—
287C4×C5#94911yescharacteristic
288C4×C5#94911yescharacteristic
289C4×C5#95011yescharacteristic
290C4×C5#95011yescharacteristic
291Dic5—41no—
292Dic5—41no—
293C2×Q8—51no—
294C2×Q8#120211yescharacteristic
295C2×D4—52no—
296C2×D4—101no—
297C2×D4—101no—
298C2×D4—301no—
299C2×D4—301no—
300C2×D4—301no—
301C22×C4—102no—
302SD16—602no—
303SD16—602no—
304D8—604no—
305C2×C8—61no—
306C2×C8—61no—
307C2×C8—301no—
308C4⋊C4—21no—
309C4⋊C4—51no—
310C4⋊C4—101no—
311C4⋊C4#120211yescharacteristic
312C22⋊C4—102no—
313C22⋊C4—102no—
314C22⋊C4—102no—
315C42—21no—
316C42—101no—
317C42C2×D3×D511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—202no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3#402811yescharacteristic
323C2×D3—401no—
324C2×D3—401no—
325C2×D3—401no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—201no—
330C3×C4—201no—
331C3×C4#405011yescharacteristic
332C3×C4#405411yescharacteristic
333C3×C4#406011yescharacteristic
334C3×C4#406511yescharacteristic
335C2×C5#523811yescharacteristic
336C2×C5#523811yescharacteristic
337C2×C5#524111yescharacteristic
338D5—82no—
339D5—481no—
340C23—102no—
341C23—601no—
342Q8—21no—
343Q8—21no—
344Q8—101no—
345Q8—101no—
346D4—202no—
347D4—201no—
348D4—201no—
349D4—201no—
350D4—201no—
351D4—602no—
352D4—601no—
353D4—601no—
354D4—601no—
355D4—601no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—101no—
359C2×C4—101no—
360C2×C4—402no—
361C2×C4C2×#120211yescharacteristic
362C2×C4D5×#6711yescharacteristic
363C2×C4D5×#6711yescharacteristic
364C8—62no—
365C8—121no—
366C8—601no—
367C2×C3—402no—
368C2×C3#6502311yescharacteristic
369C2×C3#6510011yescharacteristic
370C2×C3#6511111yescharacteristic
371D3—801no—
372C5#7194311yescharacteristic, complemented, Sylow
373C22—202no—
374C22—202no—
375C22—202no—
376C22—1201no—
377C22—1201no—
378C22—1201no—
379C22#9156411yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—201no—
384C4—201no—
385C4#9130111yescharacteristic
386C4#9131111yescharacteristic
387C4#9150211yescharacteristic
388C4#9151611yescharacteristic
389C3#1059905111yescharacteristic, complemented, Sylow
390C2—402no—
391C2—2401no—
392C2#1174851311yescharacteristic
393C2#1174927211yescharacteristic
394C2#1174941811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#11747035C2
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. C3×#65919C2semidirect
2. #11751128C2semidirect
3. #11747064C2semidirect
5. C5×#4535C2semidirect
6. #11745852C2semidirect
7. #11745841C2semidirect
27. #65919D3semidirect
65. #4535D5semidirect
318. C3×C5#1620semidirect
372. C5#71943semidirect
389. C3#10599051semidirect

Maximal subgroups

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

subgroupindex
C3×#659192
#117511282
#117470642
#117470352
C5×#45352
#117458522
#117458412
#105990513
#719435