Finite Group Databasebeta

← #14458847

Subgroups — #14458847

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756588C211yesmaximal, characteristic, complemented
2#11756373C211yesmaximal, characteristic, complemented
3C3×C5×#449C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic, complemented
5#11751272C211yesmaximal, characteristic, complemented
6#11751266C211yesmaximal, characteristic, complemented
7#11751257C211yesmaximal, characteristic, complemented
8D8×Dic15C211yesmaximal, characteristic, complemented
9#11751139C211yesmaximal, characteristic, complemented
10#11750912C211yesmaximal, characteristic, complemented
11#11750901C211yesmaximal, characteristic, complemented
12D15×#102C211yesmaximal, characteristic, complemented
13#11750864C211yesmaximal, characteristic, complemented
14#11750838C211yesmaximal, characteristic, complemented
15#11750826C211yesmaximal, characteristic, complemented
16#10611833—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×D4×D15C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic, complemented
20C2×C3×C5×D8C2211yescharacteristic
21C3×C5×#121C2211yescharacteristic, complemented
22#91836C2211yescharacteristic
23#91835C2211yescharacteristic
24#91828—21no—
25#91827—21no—
26#91827C2211yescharacteristic
27#91826—21no—
28#91824—21no—
29D4×Dic15C2211yescharacteristic
30D4×Dic15C2211yescharacteristic, complemented
31C2×#6715C2211yescharacteristic
32#91819C2211yescharacteristic
33#91818—21no—
34C4×#1220C2211yescharacteristic
35C2×#6714—21no—
36#91815C2211yescharacteristic, complemented
37C22×C3⋊#168C2211yescharacteristic, complemented
38C2×C8×D15C2211yescharacteristic
39C4⋊C4×D15C2211yescharacteristic
40#91779C2211yescharacteristic, complemented
41#91770—21no—
42#91768—21no—
43C3×C5×#103C2211yescharacteristic, complemented
44C3×C5×#102C2211yescharacteristic
45C3×C5×C22⋊C8C2211yescharacteristic, complemented
46#91119C2211yescharacteristic, complemented
47#91119C2211yescharacteristic, complemented
48#91116C2211yescharacteristic
49#91116C2211yescharacteristic
50#91116C2211yescharacteristic, complemented
51#91105C2211yescharacteristic
52#91105C2211yescharacteristic
53#91104C2211yescharacteristic
54#91102C2211yescharacteristic, complemented
55#91101C2211yescharacteristic, complemented
56#91098C2211yescharacteristic, complemented
57C8×Dic15C2211yescharacteristic, complemented
58#91093C2211yescharacteristic
59#91091C2211yescharacteristic, complemented
60#80102—51nomaximal, Hall
61#66163—31no—
62#65948—31no—
63C5×#449D311yescharacteristic, complemented
64#65522—31no—
65#65460—31no—
66#65454—31no—
67#65445—31no—
68D8×Dic5—31no—
69#65327—31no—
70#65098—31no—
71#65089—31no—
72D5×#102—31no—
73#65052—31no—
74#65026—31no—
75#65014—31no—
76C23×D15—21no—
77C3×C5×#41—22no—
78C3×C5×#41—41no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C2×C3×C5×D4C2311yescharacteristic
84C22×C3×C4×C5—21no—
85C22×C3×C4×C5C2311yescharacteristic
86C2×#1220—21no—
87C2×#1220—21no—
88C2×#1220—21no—
89C2×#1220D411yescharacteristic
90C22×Dic15—21no—
91C22×Dic15—21no—
92D4×D15—22no—
93D4×D15—41no—
94C2×D60C2311yescharacteristic
95C2×C4×D15—21no—
96C2×C4×D15C2311yescharacteristic
97C3×C5×SD16—41no—
98C3×C5×D8—22no—
99C2×C3×C5×C8C2311yescharacteristic
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103#6719—21no—
104#6719—21no—
105#6719—21no—
106#6719—21no—
107#6719D411yescharacteristic
108#6715—41no—
109#6714—21no—
110#6714—21no—
111#6714—21no—
112#6714—21no—
113#6714D411yescharacteristic
114C4⋊Dic15—21no—
115C4⋊Dic15C2311yescharacteristic
116C4⋊Dic15C2311yescharacteristic
117C4⋊Dic15C2311yescharacteristic
118#6712—21no—
119#6712—21no—
120#6712—21no—
121#6712D411yescharacteristic
122C4×Dic15—21no—
123C4×Dic15C2311yescharacteristic
124C2×C3⋊#168—41no—
125C2×C3⋊#168C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C8×D15—41no—
128#5829—51no—
129#5614—51no—
130C3×#449D511yescharacteristic, complemented
131#5233—51no—
132#5171—51no—
133#5165—51no—
134#5156—51no—
135Dic3×D8—51no—
136#5038—51no—
137#4811—51no—
138#4800—51no—
139D3×#102—51no—
140#4763—51no—
141#4737—51no—
142#67⋊C8—51no—
143C2×C5×#41C2×D311yescharacteristic
144C2×D4×D5—31no—
145C2×C5×SD16C2×D311yescharacteristic, complemented
146C2×C5×D8C2×D311yescharacteristic
147C5×#121C2×D311yescharacteristic, complemented
148#4093—31no—
149#4092—31no—
150#4085—61no—
151#4084—31no—
152#4084—61no—
153#4083—61no—
154#4081—61no—
155D4×Dic5—31no—
156D4×Dic5—31no—
157C2×#686—31no—
158#4076—31no—
159#4075—61no—
160C4×C22⋊D5—31no—
161C2×#685—61no—
162#4072—31no—
163C22×#168—31no—
164C2×C8×D5—31no—
165D5×C4⋊C4—31no—
166#4036—31no—
167#4027—61no—
168#4025—61no—
169C5×#103C2×D311yescharacteristic, complemented
170C5×#102C2×D311yescharacteristic
171C5×C22⋊C8C2×D311yescharacteristic, complemented
172#3967—31no—
173#3967—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3953—31no—
178#3953—31no—
179#3952—31no—
180#3950—31no—
181#3949—31no—
182#3946—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3939—31no—
186#3297—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5C2×D411yescharacteristic
190C22×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—81no—
194C22×D15C2×D411yescharacteristic
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C3×C5×D4—21no—
198C3×C5×D4—21no—
199C3×C5×D4—21no—
200C3×C5×D4—42no—
201C3×C5×D4—81no—
202C3×C5×D4#4112yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—42no—
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2411yescharacteristic
210#1220—22no—
211#1220—42no—
212#1220—42no—
213#1220—81no—
214C2×Dic15—21no—
215C2×Dic15—21no—
216C2×Dic15—21no—
217C2×Dic15—81no—
218C2×Dic15—81no—
219C2×Dic15C2×D411yescharacteristic
220C2×Dic15C2×D411yescharacteristic
221C2×Dic15C2×D411yescharacteristic
222D60—21no—
223D60—21no—
224C4×D15—21no—
225C4×D15—21no—
226C4×D15—81no—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3⋊#168—21no—
230C3⋊#168—21no—
231C2×C3×#41C2×D511yescharacteristic
232C2×D3×D4—51no—
233C2×C3×SD16C2×D511yescharacteristic, complemented
234C2×C3×D8C2×D511yescharacteristic
235C3×#121C2×D511yescharacteristic, complemented
236#947—51no—
237#946—51no—
238#939—101no—
239#938—51no—
240#938—101no—
241#937—101no—
242#935—101no—
243D4×Dic3—51no—
244D4×Dic3—51no—
245C2×#213—51no—
246#930—51no—
247#929—101no—
248C4×#67—51no—
249C2×(C2×D3)⋊C4—101no—
250#926—51no—
251C22×C3⋊C8—51no—
252C2×D3×C8—51no—
253D3×C4⋊C4—51no—
254#890—51no—
255#67⋊C4—101no—
256#879—101no—
257C3×#103C2×D511yescharacteristic, complemented
258C3×#102C2×D511yescharacteristic
259C3×C22⋊C8C2×D511yescharacteristic, complemented
260#835—51no—
261#835—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265#821—51no—
266#821—51no—
267(C2×D3)⋊C8—51no—
268#818—51no—
269#817—51no—
270Dic3⋊C8—51no—
271C8×Dic3—51no—
272#809—51no—
273#807—51no—
274C23×D5—61no—
275C5×#41—22no—
276C5×#41—41no—
277C2×C5×Q8C22×D311yescharacteristic
278C2×C5×D4—21no—
279C2×C5×D4—21no—
280C2×C5×D4C22×D311yescharacteristic
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—21no—
283C22×C4×C5C22×D311yescharacteristic
284C2×C22⋊D5—31no—
285C2×C22⋊D5—61no—
286C2×C22⋊D5—61no—
287C2×C22⋊D5—61no—
288C22×Dic5—61no—
289C22×Dic5—61no—
290D4×D5—62no—
291D4×D5—121no—
292C2×D20—31no—
293C2×C4×D5—31no—
294C2×C4×D5—61no—
295C5×SD16—41no—
296C5×D8—22no—
297C2×C5×C8C22×D311yescharacteristic
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C22⋊C4—21no—
301C22⋊Dic5—31no—
302C22⋊Dic5—61no—
303C22⋊Dic5—61no—
304C22⋊Dic5—61no—
305C22⋊Dic5—61no—
306#686—121no—
307#685—31no—
308#685—61no—
309#685—61no—
310#685—61no—
311#685—61no—
312C4⋊Dic5—31no—
313C4⋊Dic5—31no—
314C4⋊Dic5—31no—
315C4⋊Dic5—61no—
316#683—31no—
317#683—61no—
318#683—61no—
319#683—61no—
320C4×Dic5—31no—
321C4×Dic5—61no—
322C2×#168—31no—
323C2×#168—31no—
324C2×#168—121no—
325C8×D5—121no—
326#553—151no—
327#546—151no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—151no—
335#449D1511yescharacteristic, complemented
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—22no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—21no—
352C2×D15—21no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—84no—
357C2×D15#13512yes—
358C3×C4×C5—21no—
359C3×C4×C5—41no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5H(5,𝔽2)11yescharacteristic
363Dic15—21no—
364Dic15—21no—
365Dic15—21no—
366Dic15—41no—
367Dic15—41no—
368Dic15—41no—
369C23×D3—101no—
370C3×#41—22no—
371C3×#41—41no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4C22×D511yescharacteristic
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—21no—
378C22×C3×C4C22×D511yescharacteristic
379C2×#67—51no—
380C2×#67—101no—
381C2×#67—101no—
382C2×#67—101no—
383C22×Dic3—101no—
384C22×Dic3—101no—
385D3×D4—102no—
386D3×D4—201no—
387C2×D12—51no—
388C2×C4×D3—51no—
389C2×C4×D3—101no—
390C3×SD16—41no—
391C3×D8—22no—
392C2×C3×C8C22×D511yescharacteristic
393C2×C3×C8C22×D511yescharacteristic
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C22⋊C4—21no—
396#217—51no—
397#217—101no—
398#217—101no—
399#217—101no—
400#217—101no—
401#213—201no—
402(C2×D3)⋊C4—51no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407C4⋊Dic3—51no—
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410C4⋊Dic3—101no—
411Dic3⋊C4—51no—
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414Dic3⋊C4—101no—
415C4×Dic3—51no—
416C4×Dic3—101no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8—201no—
420D3×C8—201no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5D3×D411yescharacteristic
424C22×D5—31no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—21no—
432C5×D4—21no—
433C5×D4—21no—
434C5×D4—42no—
435C5×D4—81no—
436C5×D4#23712yes—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—42no—
442C2×C4×C5D3×D411yescharacteristic
443C2×C4×C5C23×D311yescharacteristic
444C22⋊D5—62no—
445C22⋊D5—122no—
446C22⋊D5—122no—
447C22⋊D5—241no—
448C2×Dic5—31no—
449C2×Dic5—31no—
450C2×Dic5—31no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—241no—
455C2×Dic5—241no—
456D20—61no—
457D20—61no—
458C4×D5—61no—
459C4×D5—61no—
460C4×D5—241no—
461C5×C8—21no—
462C5×C8—21no—
463#168—61no—
464#168—61no—
465C2×#41C2×D1511yescharacteristic
466C22×D4—151no—
467C2×SD16C2×D1511yescharacteristic, complemented
468C2×D8—151no—
469C2×D8C2×D1511yescharacteristic
470C22×C8—151no—
471C22×C8—151no—
472#126—301no—
473#125—151no—
474#124—151no—
475#123—301no—
476#123—301no—
477C22⋊Q8—151no—
478#121—151no—
479#121—151no—
480#121—301no—
481#121—301no—
482#121C2×D1511yescharacteristic, complemented
483#120—301no—
484C4×D4—151no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—301no—
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—301no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103C2×D1511yescharacteristic, complemented
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102C2×D1511yescharacteristic
505C22⋊C8—151no—
506C22⋊C8C2×D1511yescharacteristic, complemented
507C4×C8—151no—
508C2×C3×C5—42no—
509C2×C3×C5—41no—
510C2×C3×C5—81no—
511C2×C3×C5#54611yescharacteristic
512C2×C3×C5C2×#13511yescharacteristic
513C2×C3×C5#57611yescharacteristic
514D15—22no—
515D15—81no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3D4×D511yescharacteristic
519C22×D3—51no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—42no—
530C3×D4—81no—
531C3×D4#71112yes—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—42no—
537C2×C3×C4D4×D511yescharacteristic
538C2×C3×C4C23×D511yescharacteristic
539#67—102no—
540#67—202no—
541#67—202no—
542#67—401no—
543C2×Dic3—51no—
544C2×Dic3—51no—
545C2×Dic3—51no—
546C2×Dic3—101no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—401no—
550C2×Dic3—401no—
551D12—101no—
552D12—101no—
553C4×D3—101no—
554C4×D3—101no—
555C4×D3—401no—
556C3×C8—21no—
557C3×C8—21no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—22no—
563C22×C5—21no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5—41no—
569C22×C5C2×D3×D411yescharacteristic
570C2×D5—32no—
571C2×D5—61no—
572C2×D5—61no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—41no—
580C4×C5C2×#23711yescharacteristic
581C4×C5#100411yescharacteristic
582Dic5—61no—
583Dic5—61no—
584Dic5—61no—
585Dic5—121no—
586Dic5—121no—
587Dic5—121no—
588C24—301no—
589#41—22no—
590#41—41no—
591C2×Q8C22×D1511yescharacteristic
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—151no—
595C2×D4—151no—
596C2×D4—301no—
597C2×D4—302no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—601no—
601C2×D4C22×D1511yescharacteristic
602C2×D4C22×D1511yescharacteristic
603C22×C4—21no—
604C22×C4—151no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C22×D1511yescharacteristic
609SD16—41no—
610D8—22no—
611D8—601no—
612C2×C8—151no—
613C2×C8—151no—
614C2×C8—601no—
615C2×C8—601no—
616C2×C8C22×D1511yescharacteristic
617C2×C8C22×D1511yescharacteristic
618C4⋊C4—151no—
619C4⋊C4—151no—
620C4⋊C4—151no—
621C4⋊C4—151no—
622C4⋊C4—301no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4C22×D1511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—151no—
629C22⋊C4—151no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—151no—
639C42—301no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3C2×D4×D511yescharacteristic
651C2×D3—52no—
652C2×D3—101no—
653C2×D3—101no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4C2×#71111yescharacteristic
662C3×C4#414411yescharacteristic
663Dic3—101no—
664Dic3—101no—
665Dic3—101no—
666Dic3—201no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—42no—
670C2×C5—41no—
671C2×C5—81no—
672C2×C5#559111yescharacteristic
673C2×C5D3×#13511yescharacteristic
674C2×C5#577411yescharacteristic
675D5—62no—
676D5—241no—
677C23—21no—
678C23—21no—
679C23—151no—
680C23—301no—
681C23—602no—
682C23—602no—
683C23—1201no—
684C23D4×D1511yescharacteristic
685Q8—21no—
686Q8—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—81no—
692D4—302no—
693D4—301no—
694D4—301no—
695D4—602no—
696D4—602no—
697D4—1201no—
698D4#681912yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—42no—
704C2×C4—151no—
705C2×C4—151no—
706C2×C4—151no—
707C2×C4—301no—
708C2×C4—301no—
709C2×C4—301no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—1201no—
713C2×C4—1201no—
714C2×C4—1201no—
715C2×C4D4×D1511yescharacteristic
716C2×C4C23×D1511yescharacteristic
717C8—21no—
718C8—21no—
719C8—301no—
720C8—301no—
721C2×C3—42no—
722C2×C3—41no—
723C2×C3—81no—
724C2×C3#6592511yescharacteristic
725C2×C3D5×#13511yescharacteristic
726C2×C3#6610811yescharacteristic
727D3—102no—
728D3—401no—
729C5#8010211yescharacteristic, complemented, Sylow
730C22—21no—
731C22—22no—
732C22—21no—
733C22—21no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—152no—
740C22—301no—
741C22—301no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22—1204no—
746C22C2×D4×D1511yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—301no—
751C4—301no—
752C4—301no—
753C4—601no—
754C4—601no—
755C4—601no—
756C4C2×#681911yescharacteristic
757C4#9209511yescharacteristic
758C3#1061183311yescharacteristic, complemented, Sylow
759C2—41no—
760C2—42no—
761C2—81no—
762C2—302no—
763C2—1201no—
764C2#1175635011yescharacteristic
765C2D15×#13511yescharacteristic
766C2#1175653311yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#449C2
socleC22×C3×C5C22×D4
hypercenter#449D15
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11756588C2semidirect
2. #11756373C2semidirect
3. C3×C5×#449C2semidirect
4. #11751334C2semidirect
5. #11751272C2semidirect
6. #11751266C2semidirect
7. #11751257C2semidirect
8. D8×Dic15C2semidirect
9. #11751139C2semidirect
10. #11750912C2semidirect
11. #11750901C2semidirect
12. D15×#102C2semidirect
13. #11750864C2semidirect
14. #11750838C2semidirect
15. #11750826C2semidirect
19. C2×C3×C5×SD16C22semidirect
21. C3×C5×#121C22semidirect
30. D4×Dic15C22semidirect
36. #91815C22semidirect
37. C22×C3⋊#168C22semidirect
40. #91779C22semidirect
43. C3×C5×#103C22semidirect
45. C3×C5×C22⋊C8C22semidirect
46. #91119C22semidirect
47. #91119C22semidirect
50. #91116C22semidirect
54. #91102C22semidirect
55. #91101C22semidirect
56. #91098C22semidirect
57. C8×Dic15C22semidirect
59. #91091C22semidirect
63. C5×#449D3semidirect
130. C3×#449D5semidirect
145. C2×C5×SD16C2×D3semidirect
147. C5×#121C2×D3semidirect
169. C5×#103C2×D3semidirect
171. C5×C22⋊C8C2×D3semidirect
233. C2×C3×SD16C2×D5semidirect
235. C3×#121C2×D5semidirect
257. C3×#103C2×D5semidirect
259. C3×C22⋊C8C2×D5semidirect
335. #449D15semidirect
467. C2×SD16C2×D15semidirect
482. #121C2×D15semidirect
497. #103C2×D15semidirect
506. C22⋊C8C2×D15semidirect
640. C3×C5#3297semidirect
729. C5#80102semidirect
758. C3#10611833semidirect

Maximal subgroups

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

subgroupindex
#117565882
#117563732
C3×C5×#4492
#117513342
#117512722
#117512662
#117512572
D8×Dic152
#117511392
#117509122
#117509012
D15×#1022
#117508642
#117508382
#117508262
#106118333
#801025