Finite Group Databasebeta

← #14288856

Subgroups — #14288856

Order 1920.

480 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756344C211yesmaximal, characteristic, complemented
2#11751128C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4#11750796C211yesmaximal, characteristic
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10599051—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91836—21no—
11C2×#6717—21no—
12C2×D120—22no—
13C2×#6706—21no—
14#91783—22no—
15#91782—21no—
16#91764—21no—
17#91763C2211yescharacteristic
18#91763C2211yescharacteristic
19C4×D60—21no—
20C4×Dic30C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23#91105—21no—
24#91093—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68258—51nomaximal, Hall
27#65919—31no—
28#65316—31no—
29#65137—31no—
30#64984—31no—
31C5×Q8⋊C8D311yescharacteristic, complemented
32#64705—31no—
33#64676—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60D412yes—
41C2×C4×D15—22no—
42C2×Dic30D411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49#6717—42no—
50#6714—22no—
51#6714—22no—
52#6714—22no—
53C4⋊Dic15D411yescharacteristic
54#6712—21no—
55C4×Dic15—21no—
56C2×C3⋊#168—21no—
57D120—44no—
58#6706—42no—
59#5585—51no—
60#5027—51no—
61#4848—51no—
62#4695—51no—
63C3×Q8⋊C8D511yescharacteristic, complemented
64#4485—51no—
65#4456—51no—
66C4×C5×Q8C2×D311yescharacteristic
67#4093—61no—
68C2×#688—61no—
69C2×D40—62no—
70C2×#677—61no—
71#4040—62no—
72#4039—61no—
73#4021—61no—
74#4020—31no—
75#4020—31no—
76C4×D20—61no—
77C4×Dic10—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C4×C5×C8C2×D311yescharacteristic
80#3953—61no—
81#3941—61no—
82C4⋊#168—31no—
83#1620—151noSylow
84C22×D15—22no—
85C22×D15—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×Dic15—21no—
94C2×Dic15—21no—
95D60—42no—
96D60—42no—
97D60—41no—
98D60—41no—
99D60—41no—
100D60—41no—
101D60—41no—
102D60—41no—
103D60—41no—
104D60—41no—
105C4×D15—82no—
106Dic30—21no—
107Dic30—21no—
108C3×C5×C8—22no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3×C4×Q8C2×D511yescharacteristic
112#947—101no—
113C2×#215—101no—
114C2×D24—102no—
115C2×#204—101no—
116#894—102no—
117#893—101no—
118#875—101no—
119#874—51no—
120#874—51no—
121C4×D12—101no—
122C4×Dic6—51no—
123C3×C4⋊C8C2×D511yescharacteristic
124C3×C4×C8C2×D511yescharacteristic
125#821—101no—
126#809—101no—
127C4⋊(C3⋊C8)—51no—
128C2×C5×Q8D1211yescharacteristic
129C2×D20—32no—
130C2×D20—61no—
131C2×D20—61no—
132C2×D20—61no—
133C2×D20—61no—
134C2×D20—61no—
135C2×C4×D5—62no—
136C2×Dic10—31no—
137C2×C5×C8—21no—
138C2×C5×C8—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4D1211yescharacteristic
141C42×C5—21no—
142C42×C5C22×D311yescharacteristic
143#688—122no—
144#685—62no—
145#685—62no—
146#685—62no—
147C4⋊Dic5—31no—
148#683—61no—
149C4×Dic5—61no—
150C2×#168—61no—
151D40—124no—
152#677—122no—
153#559—151no—
154#493—151no—
155#460—151no—
156#460—151no—
157#331—151no—
158Q8⋊C8—151no—
159Q8⋊C8D1511yescharacteristic, complemented
160C22×C3×C5#12011yescharacteristic
161C2×D15—42no—
162C2×D15—42no—
163C2×D15—42no—
164C2×D15—81no—
165C2×D15—81no—
166C2×D15—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
174Dic15—41no—
175Dic15—41no—
176C2×C3×Q8D2011yescharacteristic
177C2×D12—52no—
178C2×D12—101no—
179C2×D12—101no—
180C2×D12—101no—
181C2×D12—101no—
182C2×D12—101no—
183C2×C4×D3—102no—
184C2×Dic6—51no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4D2011yescharacteristic
189C3×C42—21no—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192(C2×D3)⋊C4—102no—
193(C2×D3)⋊C4—102no—
194(C2×D3)⋊C4—102no—
195C4⋊Dic3—51no—
196Dic3⋊C4—101no—
197C4×Dic3—101no—
198C2×C3⋊C8—101no—
199D24—204no—
200#204—202no—
201C22×D5—62no—
202C22×D5—121no—
203C5×Q8—21no—
204C5×Q8—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5C2×D1211yescharacteristic
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×Dic5—61no—
211C2×Dic5—61no—
212D20—122no—
213D20—122no—
214D20—121no—
215D20—121no—
216D20—121no—
217D20—121no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—242no—
223Dic10—61no—
224Dic10—61no—
225C5×C8—22no—
226C5×C8—41no—
227#168—121no—
228C2×SD16—301no—
229C2×SD16—301no—
230C2×D8—302no—
231#127—151no—
232#127—151no—
233#124—301no—
234#124—301no—
235#123—302no—
236C4×Q8—151no—
237C4×Q8C2×D1511yescharacteristic
238C4×D4—301no—
239C4×D4—301no—
240C4⋊C8—151no—
241C4⋊C8C2×D1511yescharacteristic
242#102—301no—
243#102—301no—
244C4×C8C2×D1511yescharacteristic
245C2×C3×C5#44911yescharacteristic
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#45311yescharacteristic
248D15—82no—
249D15—161no—
250C22×D3—102no—
251C22×D3—201no—
252C3×Q8—21no—
253C3×Q8—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4C2×D2011yescharacteristic
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×Dic3—101no—
260C2×Dic3—101no—
261D12—202no—
262D12—202no—
263D12—201no—
264D12—201no—
265D12—201no—
266D12—201no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—201no—
271C4×D3—402no—
272Dic6—101no—
273Dic6—101no—
274C3×C8—22no—
275C3×C8—41no—
276C3⋊C8—201no—
277C22×C5#88211yescharacteristic
278C2×D5—122no—
279C2×D5—122no—
280C2×D5—122no—
281C2×D5—241no—
282C2×D5—241no—
283C2×D5—241no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5—41no—
287C4×C5#90411yescharacteristic
288C4×C5#90811yescharacteristic
289C4×C5#91411yescharacteristic
290C4×C5#91911yescharacteristic
291Dic5—121no—
292Dic5—121no—
293C2×Q8—151no—
294C2×Q8D6011yescharacteristic
295C2×D4—152no—
296C2×D4—301no—
297C2×D4—301no—
298C2×D4—301no—
299C2×D4—301no—
300C2×D4—301no—
301C22×C4—302no—
302SD16—602no—
303SD16—602no—
304D8—604no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—301no—
308C4⋊C4—21no—
309C4⋊C4—151no—
310C4⋊C4—301no—
311C4⋊C4D6011yescharacteristic
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C42—21no—
316C42—301no—
317C42C22×D1511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3#402811yescharacteristic
320C2×D3—202no—
321C2×D3—202no—
322C2×D3—202no—
323C2×D3—401no—
324C2×D3—401no—
325C2×D3—401no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4#405011yescharacteristic
330C3×C4#405411yescharacteristic
331C3×C4#406011yescharacteristic
332C3×C4#406511yescharacteristic
333Dic3—201no—
334Dic3—201no—
335C2×C5#473411yescharacteristic
336C2×C5#481011yescharacteristic
337C2×C5#482211yescharacteristic
338D5—242no—
339D5—481no—
340C23—302no—
341C23—601no—
342Q8—21no—
343Q8—21no—
344Q8—301no—
345Q8—301no—
346D4—602no—
347D4—602no—
348D4—601no—
349D4—601no—
350D4—601no—
351D4—601no—
352D4—601no—
353D4—601no—
354D4—601no—
355D4—601no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—1202no—
361C2×C4C2×D6011yescharacteristic
362C2×C4D4×D1511yescharacteristic
363C2×C4D4×D1511yescharacteristic
364C8—22no—
365C8—41no—
366C8—601no—
367C2×C3#6502311yescharacteristic
368C2×C3#6510011yescharacteristic
369C2×C3#6511111yescharacteristic
370D3—402no—
371D3—801no—
372C5#6825811yescharacteristic, complemented, Sylow
373C22—602no—
374C22—602no—
375C22—602no—
376C22—1201no—
377C22—1201no—
378C22—1201no—
379C22#9177111yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—601no—
384C4—601no—
385C4#9179311yescharacteristic
386C4#9179711yescharacteristic
387C4#9180311yescharacteristic
388C4#9180811yescharacteristic
389C3#1059905111yescharacteristic, complemented, Sylow
390C2—1202no—
391C2—2401no—
392C2#1175083511yescharacteristic
393C2#1175091111yescharacteristic
394C2#1175092311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radical#11750796C2
hypercenterQ8⋊C8D15
hypocenterC3×C5#1620
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #11756344C2semidirect
2. #11751128C2semidirect
3. #11750949C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. #11746306C2semidirect
7. #11746277C2semidirect
31. C5×Q8⋊C8D3semidirect
63. C3×Q8⋊C8D5semidirect
159. Q8⋊C8D15semidirect
318. C3×C5#1620semidirect
372. C5#68258semidirect
389. C3#10599051semidirect

Maximal subgroups

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

subgroupindex
#117563442
#117511282
#117509492
#117507962
C3×C5×Q8⋊C82
#117463062
#117462772
#105990513
#682585