Finite Group Databasebeta

← #14291081

Subgroups — #14291081

Order 1920.

416 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 75 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#11756443C211yesmaximal, characteristic
2C3×C5×#489C211yesmaximal, characteristic, complemented
3#11751187C211yesmaximal, characteristic, complemented
4#11751182C211yesmaximal, characteristic, complemented
5#11746361C211yesmaximal, characteristic, complemented
6#11746286C211yesmaximal, characteristic, complemented
7#11746285C211yesmaximal, characteristic, complemented
8#10602038—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#124C2211yescharacteristic
11#91835—21no—
12C2×#6718—21no—
13C2×#6717—21no—
14#91828—21no—
15#91775—21no—
16#91773—21no—
17#91772—21no—
18#91767—21no—
19#91764C2211yescharacteristic
20#91759C2211yescharacteristic
21C3×C5×#103—21no—
22C3×C5×#102—21no—
23C3×C5×#97C2211yescharacteristic
24#91092—21no—
25#91091—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#71245—51nomaximal, Hall
29#66018—31no—
30C5×#489D311yescharacteristic, complemented
31#65375—31no—
32#65369—31no—
33#64760—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×Q8D411yescharacteristic
38C2×C3×C5×D4D411yescharacteristic
39C2×#1220—21no—
40C2×#1220—21no—
41C22×Dic15—21no—
42C2×D60D411yescharacteristic
43C2×C4×D15—21no—
44C2×Dic30D411yescharacteristic
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C22⋊C4—21no—
49C3×C5×C22⋊C4—21no—
50C3×C42×C5C2311yescharacteristic
51#6719—21no—
52#6718—42no—
53#6717—42no—
54#6714—21no—
55#6714—21no—
56#6714—21no—
57C4⋊Dic15—21no—
58C4⋊Dic15D411yescharacteristic
59C4⋊Dic15D411yescharacteristic
60#6712—21no—
61#6712—21no—
62#6712—21no—
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65#5684—51no—
66C3×#489D511yescharacteristic, complemented
67#5086—51no—
68#5081—51no—
69#4540—51no—
70#4465—51no—
71#4464—51no—
72C5×C4⋊Q8C2×D311yescharacteristic
73C5×#124C2×D311yescharacteristic
74#4092—61no—
75C2×#689—61no—
76C2×#688—61no—
77#4085—61no—
78#4032—61no—
79#4030—61no—
80#4029—61no—
81#4024—61no—
82#4021—31no—
83#4016—31no—
84C5×#103—21no—
85C5×#102—21no—
86C5×#97C2×D311yescharacteristic
87#3940—61no—
88#3939—61no—
89#3935—31no—
90#3935—31no—
91#1661—151noSylow
92C23×C3×C5—21no—
93C22×D15—21no—
94C3×C5×Q8—41no—
95C3×C5×Q8—41no—
96C3×C5×Q8—41no—
97C3×C5×D4—41no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103#1220—81no—
104#1220—81no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—81no—
109D60—41no—
110C4×D15—81no—
111Dic30—41no—
112C3×C5×C8—41no—
113C3⋊#168—22no—
114C3⋊#168—22no—
115C3×C4⋊Q8C2×D511yescharacteristic
116C3×#124C2×D511yescharacteristic
117#946—101no—
118C2×#216—101no—
119C2×#215—101no—
120#939—101no—
121#886—101no—
122#884—101no—
123#883—101no—
124#878—101no—
125#875—51no—
126#870—51no—
127C3×#103—21no—
128C3×#102—21no—
129C3×#97C2×D511yescharacteristic
130#808—101no—
131#807—101no—
132#803—51no—
133#803—51no—
134C2×C5×Q8—21no—
135C2×C5×Q8#6711yescharacteristic
136C2×C5×D4#6711yescharacteristic
137C2×C22⋊D5—61no—
138C2×C22⋊D5—61no—
139C22×Dic5—61no—
140C2×D20—31no—
141C2×C4×D5—61no—
142C2×Dic10—31no—
143C2×C5×C8—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C22⋊C4—21no—
147C5×C22⋊C4—21no—
148C42×C5C22×D311yescharacteristic
149C22⋊Dic5—61no—
150#689—122no—
151#688—122no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—31no—
157C4⋊Dic5—61no—
158#683—61no—
159#683—61no—
160#683—61no—
161C2×#168—61no—
162C2×#168—61no—
163#562—151no—
164#501—151no—
165#497—151no—
166#489D1511yescharacteristic, complemented
167#330—151no—
168#329—151no—
169#329—151no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5#12011yescharacteristic
174C2×D15—41no—
175C2×D15—41no—
176C2×D15—41no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—81no—
182Dic15—41no—
183Dic15—41no—
184Dic15—41no—
185C2×C3×Q8—21no—
186C2×C3×Q8C22⋊D511yescharacteristic
187C2×C3×D4C22⋊D511yescharacteristic
188C2×#67—101no—
189C2×#67—101no—
190C22×Dic3—101no—
191C2×D12—51no—
192C2×C4×D3—101no—
193C2×Dic6—51no—
194C2×C3×C8—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C42C22×D511yescharacteristic
200#217—101no—
201#216—202no—
202#215—202no—
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206C4⋊Dic3—51no—
207C4⋊Dic3—51no—
208C4⋊Dic3—101no—
209Dic3⋊C4—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212C2×C3⋊C8—101no—
213C2×C3⋊C8—101no—
214C23×C5—21no—
215C22×D5—61no—
216C5×Q8—41no—
217C5×Q8—41no—
218C5×Q8—41no—
219C5×D4—41no—
220C2×C4×C5—21no—
221C2×C4×C5—41no—
222C2×C4×C5D3×D411yescharacteristic
223C2×C4×C5D3×D411yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C22⋊D5—241no—
226C22⋊D5—241no—
227C2×Dic5—61no—
228C2×Dic5—61no—
229C2×Dic5—61no—
230C2×Dic5—241no—
231D20—121no—
232C4×D5—241no—
233Dic10—121no—
234C5×C8—41no—
235#168—62no—
236#168—62no—
237C2×Q16—301no—
238C2×SD16—301no—
239C4⋊Q8C2×D1511yescharacteristic
240#125—151no—
241#124—151no—
242#124C2×D1511yescharacteristic
243#123—301no—
244#123—301no—
245C22⋊Q8—301no—
246C22⋊Q8—301no—
247#121—301no—
248#121—301no—
249#107—301no—
250#106—301no—
251#103—21no—
252#102—21no—
253#97—151no—
254#97—151no—
255#97C2×D1511yescharacteristic
256C2×C3×C5—81no—
257C2×C3×C5#45311yescharacteristic
258C2×C3×C5#45511yescharacteristic
259C2×C3×C5#45611yescharacteristic
260D15—81no—
261C23×C3—21no—
262C22×D3—101no—
263C3×Q8—41no—
264C3×Q8—41no—
265C3×Q8—41no—
266C3×D4—41no—
267C2×C3×C4—21no—
268C2×C3×C4—41no—
269C2×C3×C4D4×D511yescharacteristic
270C2×C3×C4D4×D511yescharacteristic
271C2×C3×C4C2×C22⋊D511yescharacteristic
272#67—401no—
273#67—401no—
274C2×Dic3—101no—
275C2×Dic3—101no—
276C2×Dic3—101no—
277C2×Dic3—401no—
278D12—201no—
279C4×D3—401no—
280Dic6—201no—
281C3×C8—41no—
282C3⋊C8—102no—
283C3⋊C8—102no—
284C22×C5—41no—
285C22×C5—41no—
286C22×C5—41no—
287C22×C5#93711yescharacteristic
288C2×D5—121no—
289C2×D5—121no—
290C2×D5—121no—
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—21no—
294C4×C5—41no—
295C4×C5—81no—
296Dic5—121no—
297Dic5—121no—
298Dic5—121no—
299C2×Q8—21no—
300C2×Q8—151no—
301C2×Q8#122011yescharacteristic
302C2×D4—151no—
303C2×D4—301no—
304C2×D4—301no—
305C2×D4#122011yescharacteristic
306C22×C4—301no—
307C22×C4—301no—
308Q16—602no—
309SD16—602no—
310C2×C8—21no—
311C2×C8—301no—
312C2×C8—301no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—151no—
316C4⋊C4—151no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—301no—
324C22⋊C4—301no—
325C22⋊C4—301no—
326C22⋊C4—301no—
327C42C22×D1511yescharacteristic
328C3×C5#166111yescharacteristic, complemented, Hall
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3#408311yescharacteristic
333C2×D3—201no—
334C2×D3—201no—
335C2×D3—201no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—41no—
340C3×C4—81no—
341Dic3—201no—
342Dic3—201no—
343Dic3—201no—
344C2×C5—81no—
345C2×C5#506111yescharacteristic
346C2×C5#519811yescharacteristic
347C2×C5#520511yescharacteristic
348D5—241no—
349C23—21no—
350C23—301no—
351Q8—41no—
352Q8—41no—
353Q8—41no—
354Q8—601no—
355D4—41no—
356D4—601no—
357D4—1201no—
358D4—1201no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—301no—
362C2×C4—301no—
363C2×C4—301no—
364C2×C4—1201no—
365C2×C4—1201no—
366C2×C4D4×D1511yescharacteristic
367C2×C4D4×D1511yescharacteristic
368C2×C4C2×#122011yescharacteristic
369C8—41no—
370C8—302no—
371C8—302no—
372C2×C3—81no—
373C2×C3#6535011yescharacteristic
374C2×C3#6548711yescharacteristic
375C2×C3#6549411yescharacteristic
376D3—401no—
377C5#7124511yescharacteristic, complemented, Sylow
378C22—41no—
379C22—41no—
380C22—41no—
381C22—601no—
382C22—601no—
383C22—601no—
384C22#9182611yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—81no—
390C4—601no—
391C4—601no—
392C4—601no—
393C3#1060203811yescharacteristic, complemented, Sylow
394C2—81no—
395C2—1201no—
396C2#1175116211yescharacteristic
397C2#1175129911yescharacteristic
398C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#489C2
socleC22×C3×C5#120
prime radical#11756443C2
hypercenter#489D15
hypocenterC3×C5#1661
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. C3×C5×#489C2semidirect
3. #11751187C2semidirect
4. #11751182C2semidirect
5. #11746361C2semidirect
6. #11746286C2semidirect
7. #11746285C2semidirect
30. C5×#489D3semidirect
66. C3×#489D5semidirect
166. #489D15semidirect
328. C3×C5#1661semidirect
377. C5#71245semidirect
393. C3#10602038semidirect

Maximal subgroups

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

subgroupindex
#117564432
C3×C5×#4892
#117511872
#117511822
#117463612
#117462862
#117462852
#106020383
#712455