Finite Group Databasebeta

← #14288847

Subgroups — #14288847

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
2C3×C5×#460C211yesmaximal, characteristic, complemented
3#11751176C211yesmaximal, characteristic, complemented
4#11751174C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746305C211yesmaximal, characteristic, complemented
8#10601824—31nomaximal, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12#91836—21no—
13C2×#6716—21no—
14C2×#6715—22no—
15#91783—22no—
16#91782—21no—
17#91764—21no—
18#91763C2211yescharacteristic
19C4×D60—21no—
20C4×Dic30C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#102—21no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71031—51nomaximal, Hall
27#65919—31no—
28C5×#460D311yescharacteristic, complemented
29#65364—31no—
30#65362—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60D412yes—
41C2×C4×D15—22no—
42C2×Dic30D411yescharacteristic
43C3×C5×SD16—42no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C42×C5—21no—
48C3×C42×C5C2311yescharacteristic
49#6716—42no—
50#6715—44no—
51#6714—22no—
52#6714—22no—
53#6714—22no—
54C4⋊Dic15D411yescharacteristic
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5585—51no—
60C3×#460D511yescharacteristic, complemented
61#5075—51no—
62#5073—51no—
63#4535—51no—
64#4485—51no—
65#4484—51no—
66C2×C5×SD16—21no—
67C5×#127C2×D311yescharacteristic
68C4×C5×Q8C2×D311yescharacteristic
69#4093—61no—
70C2×#687—61no—
71C2×#686—62no—
72#4040—62no—
73#4039—61no—
74#4021—61no—
75#4020—31no—
76C4×D20—61no—
77C4×Dic10—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—21no—
80#3964—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1620—151noSylow
84C23×C3×C5—41no—
85C22×D15—22no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C3×C5×D4—42no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—21no—
100D60—42no—
101D60—41no—
102D60—41no—
103D60—41no—
104D60—41no—
105C4×D15—82no—
106Dic30—21no—
107Dic30—21no—
108C3×C5×C8—41no—
109C3⋊#168—22no—
110C3⋊#168—41no—
111C2×C3×SD16—21no—
112C3×#127C2×D511yescharacteristic
113C3×C4×Q8C2×D511yescharacteristic
114#947—101no—
115C2×#214—101no—
116C2×#213—102no—
117#894—102no—
118#893—101no—
119#875—101no—
120#874—51no—
121C4×D12—101no—
122C4×Dic6—51no—
123C3×C4⋊C8C2×D511yescharacteristic
124C3×#102—21no—
125#832—101no—
126C4⋊(C3⋊C8)—51no—
127C4×C3⋊C8—51no—
128C2×C5×Q8#6711yescharacteristic
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×D20—32no—
133C2×D20—61no—
134C2×D20—61no—
135C2×C4×D5—62no—
136C2×Dic10—31no—
137C5×SD16—42no—
138C2×C5×C8—21no—
139C5×C4⋊C4—21no—
140C5×C4⋊C4#6711yescharacteristic
141C42×C5—21no—
142C42×C5C22×D311yescharacteristic
143#687—122no—
144#686—124no—
145#685—62no—
146#685—62no—
147#685—62no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5—61no—
151C2×#168—61no—
152C2×#168—61no—
153#559—151no—
154#493—151no—
155#460—151no—
156#460D1511yescharacteristic, complemented
157#331—151no—
158Q8⋊C8—151no—
159Q8⋊C8—151no—
160C22×C3×C5—81no—
161C22×C3×C5—81no—
162C22×C3×C5—81no—
163C22×C3×C5#12011yescharacteristic
164C2×D15—42no—
165C2×D15—42no—
166C2×D15—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
174Dic15—41no—
175Dic15—41no—
176C2×C3×Q8C22⋊D511yescharacteristic
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×D12—52no—
181C2×D12—101no—
182C2×D12—101no—
183C2×C4×D3—102no—
184C2×Dic6—51no—
185C3×SD16—42no—
186C2×C3×C8—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4C22⋊D511yescharacteristic
189C3×C42—21no—
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—101no—
200C2×C3⋊C8—101no—
201C23×C5—41no—
202C22×D5—62no—
203C5×Q8—21no—
204C5×Q8—21no—
205C5×D4—42no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4—41no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215C2×Dic5—61no—
216C2×Dic5—61no—
217D20—122no—
218D20—121no—
219D20—121no—
220D20—121no—
221D20—121no—
222C4×D5—242no—
223Dic10—61no—
224Dic10—61no—
225C5×C8—41no—
226#168—62no—
227#168—121no—
228C2×SD16—21no—
229C2×SD16—301no—
230C2×D8—302no—
231#127—151no—
232#127C2×D1511yescharacteristic
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—21no—
243#102—301no—
244C4×C8—151no—
245C2×C3×C5—161no—
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#44911yescharacteristic
248C2×C3×C5#45311yescharacteristic
249D15—82no—
250C23×C3—41no—
251C22×D3—102no—
252C3×Q8—21no—
253C3×Q8—21no—
254C3×D4—42no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—41no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4C2×C22⋊D511yescharacteristic
264C2×Dic3—101no—
265C2×Dic3—101no—
266D12—202no—
267D12—201no—
268D12—201no—
269D12—201no—
270D12—201no—
271C4×D3—402no—
272Dic6—101no—
273Dic6—101no—
274C3×C8—41no—
275C3⋊C8—102no—
276C3⋊C8—201no—
277C22×C5—81no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5#93711yescharacteristic
281C2×D5—122no—
282C2×D5—122no—
283C2×D5—122no—
284C4×C5—21no—
285C4×C5—41no—
286C4×C5—41no—
287C4×C5#91411yescharacteristic
288C4×C5#91611yescharacteristic
289C4×C5#93211yescharacteristic
290C4×C5#95011yescharacteristic
291Dic5—121no—
292Dic5—121no—
293C2×Q8—151no—
294C2×Q8#122011yescharacteristic
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—152no—
299C2×D4—301no—
300C2×D4—301no—
301C22×C4—302no—
302SD16—42no—
303SD16—602no—
304D8—604no—
305C2×C8—21no—
306C2×C8—301no—
307C2×C8—301no—
308C4⋊C4—21no—
309C4⋊C4—151no—
310C4⋊C4—301no—
311C4⋊C4#122011yescharacteristic
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C42—21no—
316C42—301no—
317C42C22×D1511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3#408311yescharacteristic
323C2×D3—202no—
324C2×D3—202no—
325C2×D3—202no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4#406011yescharacteristic
330C3×C4#406211yescharacteristic
331C3×C4#407811yescharacteristic
332C3×C4#409611yescharacteristic
333Dic3—201no—
334Dic3—201no—
335C2×C5—161no—
336C2×C5#503711yescharacteristic
337C2×C5#517211yescharacteristic
338C2×C5#519811yescharacteristic
339D5—242no—
340C23—41no—
341C23—302no—
342Q8—21no—
343Q8—21no—
344Q8—301no—
345Q8—301no—
346D4—42no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351D4—602no—
352D4—601no—
353D4—601no—
354D4—601no—
355D4—601no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—1202no—
361C2×C4D4×D1511yescharacteristic
362C2×C4D4×D1511yescharacteristic
363C2×C4C2×#122011yescharacteristic
364C8—41no—
365C8—302no—
366C8—601no—
367C2×C3—161no—
368C2×C3#6532611yescharacteristic
369C2×C3#6546111yescharacteristic
370C2×C3#6548711yescharacteristic
371D3—402no—
372C5#7103111yescharacteristic, complemented, Sylow
373C22—81no—
374C22—81no—
375C22—81no—
376C22—602no—
377C22—602no—
378C22—602no—
379C22#9182611yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—601no—
384C4—601no—
385C4#9180311yescharacteristic
386C4#9180511yescharacteristic
387C4#9182111yescharacteristic
388C4#9183911yescharacteristic
389C3#1060182411yescharacteristic, complemented, Sylow
390C2—161no—
391C2—1202no—
392C2#1175113811yescharacteristic
393C2#1175127311yescharacteristic
394C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#460C2
socleC22×C3×C5#120
prime radical#11751174C2
hypercenter#460D15
hypocenterC3×C5#1620
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #11756344C2semidirect
2. C3×C5×#460C2semidirect
3. #11751176C2semidirect
5. #11746356C2semidirect
6. #11746306C2semidirect
7. #11746305C2semidirect
28. C5×#460D3semidirect
60. C3×#460D5semidirect
156. #460D15semidirect
318. C3×C5#1620semidirect
372. C5#71031semidirect
389. C3#10601824semidirect

Maximal subgroups

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

subgroupindex
#117563442
C3×C5×#4602
#117511762
#117511742
#117463562
#117463062
#117463052
#106018243
#710315