Finite Group Databasebeta

← #14287902

Subgroups — #14287902

Order 1920.

640 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756403C211yesmaximal, characteristic, complemented
2C3×C5×#450C211yesmaximal, characteristic, complemented
3#11751324C211yesmaximal, characteristic, complemented
4#11751318C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic, complemented
7#11746289C211yesmaximal, characteristic, complemented
8#10601770—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—21no—
11C2×C3×C5×SD16—21no—
12C3×C5×C22⋊Q8C2211yescharacteristic
13C2×#6719—21no—
14#91836—21no—
15C2×#6715—21no—
16#91819C2211yescharacteristic
17C2×#6714C2211yescharacteristic
18#91787—21no—
19#91784—21no—
20#91783—21no—
21#91771—21no—
22#91770—21no—
23C3×C5×#102—21no—
24C3×C5×C22⋊C8C2211yescharacteristic
25#91116—21no—
26#91115C2211yescharacteristic
27#91114C2211yescharacteristic
28#70977—51nomaximal, Hall
29#65978—31no—
30C5×#450D311yescharacteristic, complemented
31#65512—31no—
32#65506—31no—
33#64758—31no—
34#64690—31no—
35#64688—31no—
36C24×C3×C5—21no—
37C23×D15D411yescharacteristic
38C2×C3×C5×Q8D411yescharacteristic, complemented
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—42no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×#1220—21no—
44C2×#1220—42no—
45C2×#1220—42no—
46C2×#1220—42no—
47C22×Dic15—21no—
48C22×Dic15D411yescharacteristic
49C2×D60—21no—
50C2×D60—21no—
51C2×D60D411yescharacteristic, complemented
52C2×C4×D15—21no—
53C3×C5×SD16—42no—
54C2×C3×C5×C8—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C4⋊C4D411yescharacteristic, complemented
57C3×C5×C22⋊C4—21no—
58#6719—42no—
59#6715—42no—
60#6714—21no—
61#6714—21no—
62#6714—21no—
63#6714—21no—
64#6714—21no—
65#6714—21no—
66C4⋊Dic15D411yescharacteristic, complemented
67#6712—21no—
68C4×Dic15—21no—
69C2×C3⋊#168—21no—
70#5644—51no—
71C3×#450D511yescharacteristic, complemented
72#5223—51no—
73#5217—51no—
74#4538—51no—
75#4470—51no—
76#4468—51no—
77C22×C5×D4C2×D311yescharacteristic
78C22×C22⋊D5—61no—
79C2×C5×SD16—21no—
80C5×C22⋊Q8C2×D311yescharacteristic
81C2×C22⋊Dic5—61no—
82#4093—61no—
83C2×#686—61no—
84#4076—31no—
85C2×#685—31no—
86#4044—61no—
87#4041—61no—
88#4040—61no—
89#4028—61no—
90#4027—61no—
91C5×#102—21no—
92C5×C22⋊C8C2×D311yescharacteristic
93#3964—61no—
94#3963—31no—
95C22⋊#168—31no—
96#1600—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5C2×D411yescharacteristic
105C22×D15—21no—
106C22×D15—21no—
107C22×D15—21no—
108C22×D15—21no—
109C22×D15—41no—
110C22×D15—41no—
111C3×C5×Q8—41no—
112C3×C5×D4—22no—
113C3×C5×D4—22no—
114C3×C5×D4—41no—
115C3×C5×D4—41no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—41no—
119C2×C3×C4×C5C2×D411yescharacteristic
120C2×C3×C4×C5C2×D411yescharacteristic
121#1220—48no—
122#1220—41no—
123#1220—41no—
124C2×Dic15—22no—
125C2×Dic15—21no—
126C2×Dic15—21no—
127C2×Dic15—41no—
128C2×Dic15—41no—
129C2×Dic15—41no—
130D60—41no—
131D60—81no—
132D60—81no—
133C4×D15—81no—
134C3×C5×C8—41no—
135C3⋊#168—41no—
136C22×C3×D4C2×D511yescharacteristic
137C22×#67—101no—
138C2×C3×SD16—21no—
139C3×C22⋊Q8C2×D511yescharacteristic
140C2×#217—101no—
141#947—101no—
142C2×#213—101no—
143#930—51no—
144C2×(C2×D3)⋊C4—51no—
145#898—101no—
146#895—101no—
147#894—101no—
148#882—101no—
149#67⋊C4—101no—
150C3×#102—21no—
151C3×C22⋊C8C2×D511yescharacteristic
152#832—101no—
153C3⋊#95—51no—
154#830—51no—
155C24×C5—21no—
156C23×D5—31no—
157C2×C5×Q8#6711yescharacteristic, complemented
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—42no—
161C22×C4×C5C22×D311yescharacteristic
162C2×C22⋊D5—61no—
163C2×C22⋊D5—122no—
164C2×C22⋊D5—122no—
165C2×C22⋊D5—122no—
166C22×Dic5—31no—
167C22×Dic5—61no—
168C2×D20—31no—
169C2×D20—61no—
170C2×D20—61no—
171C2×C4×D5—61no—
172C5×SD16—42no—
173C2×C5×C8—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4#6711yescharacteristic, complemented
176C5×C22⋊C4—21no—
177C22⋊Dic5—122no—
178#686—122no—
179#685—61no—
180#685—61no—
181#685—61no—
182#685—61no—
183#685—61no—
184#685—61no—
185C4⋊Dic5—31no—
186#683—61no—
187C4×Dic5—61no—
188C2×#168—61no—
189#538—151no—
190#450D1511yescharacteristic, complemented
191#447—151no—
192#392—151no—
193#328—151no—
194#327—151no—
195#323—151no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—42no—
201C22×C3×C5—81no—
202C22×C3×C5—81no—
203C22×C3×C5—81no—
204C22×C3×C5—81no—
205C22×C3×C5#12011yescharacteristic
206C22×C3×C5#13511yescharacteristic
207C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
208C2×D15—42no—
209C2×D15—41no—
210C2×D15—41no—
211C2×D15—41no—
212C2×D15—41no—
213C2×D15—41no—
214C2×D15—41no—
215C2×D15—81no—
216C3×C4×C5—21no—
217C3×C4×C5—21no—
218C3×C4×C5—41no—
219C3×C4×C5—41no—
220Dic15—42no—
221Dic15—41no—
222Dic15—41no—
223C24×C3—21no—
224C23×D3—51no—
225C2×C3×Q8C22⋊D511yescharacteristic, complemented
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C22×C3×C4C22×D511yescharacteristic
230C2×#67—101no—
231C2×#67—202no—
232C2×#67—202no—
233C2×#67—202no—
234C22×Dic3—51no—
235C22×Dic3—101no—
236C2×D12—51no—
237C2×D12—101no—
238C2×D12—101no—
239C2×C4×D3—101no—
240C3×SD16—42no—
241C2×C3×C8—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4C22⋊D511yescharacteristic, complemented
244C3×C22⋊C4—21no—
245#217—202no—
246#213—202no—
247(C2×D3)⋊C4—101no—
248(C2×D3)⋊C4—101no—
249(C2×D3)⋊C4—101no—
250(C2×D3)⋊C4—101no—
251(C2×D3)⋊C4—101no—
252(C2×D3)⋊C4—101no—
253C4⋊Dic3—51no—
254Dic3⋊C4—101no—
255C4×Dic3—101no—
256C2×C3⋊C8—101no—
257C23×C5—22no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5D3×D411yescharacteristic
265C22×D5—61no—
266C22×D5—61no—
267C22×D5—61no—
268C22×D5—61no—
269C22×D5—121no—
270C22×D5—121no—
271C5×Q8—41no—
272C5×D4—22no—
273C5×D4—22no—
274C5×D4—41no—
275C5×D4—41no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—41no—
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5C2×#6711yescharacteristic
281C22⋊D5—128no—
282C22⋊D5—121no—
283C22⋊D5—121no—
284C2×Dic5—62no—
285C2×Dic5—61no—
286C2×Dic5—61no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289C2×Dic5—121no—
290D20—121no—
291D20—241no—
292D20—241no—
293C4×D5—241no—
294C5×C8—41no—
295#168—121no—
296C22×D4—301no—
297C22×D4C2×D1511yescharacteristic
298C2×SD16—21no—
299C2×D8—301no—
300#126—301no—
301#124—301no—
302#123—301no—
303C22⋊Q8C2×D1511yescharacteristic
304#121—151no—
305#121—301no—
306#120—301no—
307C4×D4—301no—
308C2×C22⋊C4—151no—
309C2×C22⋊C4—301no—
310#102—21no—
311#102—301no—
312C22⋊C8—151no—
313C22⋊C8C2×D1511yescharacteristic
314#95—151no—
315C2×C3×C5—21no—
316C2×C3×C5—21no—
317C2×C3×C5—82no—
318C2×C3×C5#44911yescharacteristic
319C2×C3×C5#45311yescharacteristic
320C2×C3×C5B(4,𝔽2)11yescharacteristic
321D15—81no—
322D15—81no—
323C23×C3—22no—
324C23×C3—41no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3D4×D511yescharacteristic
331C22×D3—101no—
332C22×D3—101no—
333C22×D3—101no—
334C22×D3—101no—
335C22×D3—201no—
336C22×D3—201no—
337C3×Q8—41no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—41no—
341C3×D4—41no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—41no—
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C2×C22⋊D511yescharacteristic
347#67—208no—
348#67—201no—
349#67—201no—
350C2×Dic3—102no—
351C2×Dic3—101no—
352C2×Dic3—101no—
353C2×Dic3—201no—
354C2×Dic3—201no—
355C2×Dic3—201no—
356D12—201no—
357D12—401no—
358D12—401no—
359C4×D3—401no—
360C3×C8—41no—
361C3⋊C8—201no—
362C22×C5—21no—
363C22×C5—21no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—42no—
367C22×C5—81no—
368C22×C5—81no—
369C22×C5—81no—
370C22×C5—81no—
371C22×C5#91411yescharacteristic
372C22×C5#91611yescharacteristic
373C22×C5#93711yescharacteristic
374C2×D5—122no—
375C2×D5—121no—
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C2×D5—121no—
380C2×D5—121no—
381C2×D5—241no—
382C4×C5—21no—
383C4×C5—21no—
384C4×C5—41no—
385C4×C5—41no—
386Dic5—122no—
387Dic5—121no—
388Dic5—121no—
389C24—21no—
390C24—151no—
391C2×Q8#122011yescharacteristic, complemented
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—42no—
395C2×D4—151no—
396C2×D4—301no—
397C2×D4—301no—
398C2×D4—301no—
399C2×D4—602no—
400C2×D4—602no—
401C2×D4—602no—
402C22×C4—151no—
403C22×C4—301no—
404C22×C4—301no—
405C22×C4C22×D1511yescharacteristic
406SD16—42no—
407D8—602no—
408C2×C8—21no—
409C2×C8—301no—
410C4⋊C4—21no—
411C4⋊C4—151no—
412C4⋊C4—301no—
413C4⋊C4#122011yescharacteristic, complemented
414C22⋊C4—21no—
415C22⋊C4—301no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C22⋊C4—301no—
419C22⋊C4—301no—
420C22⋊C4—301no—
421C22⋊C4—602no—
422C42—301no—
423C3×C5#160011yescharacteristic, complemented, Hall
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—81no—
430C22×C3—81no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3#406011yescharacteristic
434C22×C3#406211yescharacteristic
435C22×C3#408311yescharacteristic
436C2×D3—202no—
437C2×D3—201no—
438C2×D3—201no—
439C2×D3—201no—
440C2×D3—201no—
441C2×D3—201no—
442C2×D3—201no—
443C2×D3—401no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—41no—
447C3×C4—41no—
448Dic3—202no—
449Dic3—201no—
450Dic3—201no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—82no—
454C2×C5#503211yescharacteristic
455C2×C5#517211yescharacteristic
456C2×C5#519811yescharacteristic
457D5—241no—
458D5—241no—
459C23—22no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—301no—
467C23—301no—
468C23—301no—
469C23—301no—
470C23—601no—
471C23—601no—
472C23D4×D1511yescharacteristic
473Q8—41no—
474D4—22no—
475D4—22no—
476D4—41no—
477D4—41no—
478D4—601no—
479D4—608no—
480D4—601no—
481D4—601no—
482D4—1201no—
483D4—1201no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—302no—
488C2×C4—301no—
489C2×C4—301no—
490C2×C4—601no—
491C2×C4—601no—
492C2×C4—601no—
493C2×C4—1201no—
494C2×C4D4×D1511yescharacteristic
495C2×C4C2×#122011yescharacteristic
496C8—41no—
497C8—601no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—82no—
501C2×C3#6532111yescharacteristic
502C2×C3#6546111yescharacteristic
503C2×C3#6548711yescharacteristic
504D3—401no—
505D3—401no—
506C5#7097711yescharacteristic, complemented, Sylow
507C22—21no—
508C22—21no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—602no—
517C22—601no—
518C22—601no—
519C22—601no—
520C22—601no—
521C22—601no—
522C22—601no—
523C22—1201no—
524C22#9180311yescharacteristic
525C22#9180511yescharacteristic
526C22#9182611yescharacteristic
527C4—21no—
528C4—21no—
529C4—41no—
530C4—41no—
531C4—602no—
532C4—601no—
533C4—601no—
534C3#1060177011yescharacteristic, complemented, Sylow
535C2—21no—
536C2—21no—
537C2—82no—
538C2—1201no—
539C2—1201no—
540C2#1175113311yescharacteristic
541C2#1175127311yescharacteristic
542C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#450C2
socleC22×C3×C5#120
hypercenter#450D15
hypocenterC3×C5#1600
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #11756403C2semidirect
2. C3×C5×#450C2semidirect
3. #11751324C2semidirect
4. #11751318C2semidirect
5. #11746359C2semidirect
6. #11746291C2semidirect
7. #11746289C2semidirect
30. C5×#450D3semidirect
38. C2×C3×C5×Q8D4semidirect
51. C2×D60D4semidirect
56. C3×C5×C4⋊C4D4semidirect
66. C4⋊Dic15D4semidirect
71. C3×#450D5semidirect
157. C2×C5×Q8#67semidirect
175. C5×C4⋊C4#67semidirect
190. #450D15semidirect
225. C2×C3×Q8C22⋊D5semidirect
243. C3×C4⋊C4C22⋊D5semidirect
391. C2×Q8#1220semidirect
413. C4⋊C4#1220semidirect
423. C3×C5#1600semidirect
506. C5#70977semidirect
534. C3#10601770semidirect

Maximal subgroups

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

subgroupindex
#117564032
C3×C5×#4502
#117513242
#117513182
#117463592
#117462912
#117462892
#106017703
#709775