Finite Group Databasebeta

← #14458874

Subgroups — #14458874

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#11756324C211yesmaximal, characteristic, complemented
2#11756309C211yesmaximal, characteristic, complemented
3C3×C5×C8×D4C211yesmaximal, characteristic, complemented
4#11751216C211yesmaximal, characteristic, complemented
5#11751215C211yesmaximal, characteristic, complemented
6#11751214C211yesmaximal, characteristic, complemented
7C2×#91105C211yesmaximal, characteristic, complemented
8#11750948C211yesmaximal, characteristic, complemented
9#11750945C211yesmaximal, characteristic, complemented
10#11750838C211yesmaximal, characteristic, complemented
11#11750835C211yesmaximal, characteristic, complemented
12#11750833C211yesmaximal, characteristic, complemented
13#11750823C211yesmaximal, characteristic, complemented
14#11750798C211yesmaximal, characteristic, complemented
15C4×D120C211yesmaximal, characteristic, complemented
16#10611172—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×C3×C5×C8C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic, complemented
21C3×C4×C5×D4C2211yescharacteristic
22#91828—21no—
23#91826—21no—
24#91819C2211yescharacteristic
25#91819C2211yescharacteristic
26#91819C2211yescharacteristic, complemented
27#91815C2211yescharacteristic, complemented
28C2×C4⋊Dic15C2211yescharacteristic
29#91813C2211yescharacteristic
30C2×D120C2211yescharacteristic
31C2×D120C2211yescharacteristic
32C2×#6706C2211yescharacteristic, complemented
33#91787—21no—
34#91783—21no—
35#91773—21no—
36#91772—21no—
37#91770—21no—
38C22⋊C4×D15—21no—
39#91764C2211yescharacteristic
40C4×D60C2211yescharacteristic
41C4×D60C2211yescharacteristic, complemented
42#91759C2211yescharacteristic, complemented
43C3×C5×C4⋊C8C2211yescharacteristic, complemented
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×C5×C22⋊C8C2211yescharacteristic, complemented
46C3×C4×C5×C8C2211yescharacteristic, complemented
47#91105C2211yescharacteristic
48#91105C2211yescharacteristic
49#91105C2211yescharacteristic
50#91105C2211yescharacteristic
51#91105C2211yescharacteristic
52#91105C2211yescharacteristic
53#91105C2211yescharacteristic, complemented
54#91102C2211yescharacteristic, complemented
55#91102C2211yescharacteristic, complemented
56#91101C2211yescharacteristic, complemented
57#91100C2211yescharacteristic, complemented
58#91100C2211yescharacteristic, complemented
59#91100C2211yescharacteristic, complemented
60#79441—51nomaximal, Hall
61#65899—31no—
62#65884—31no—
63C5×C8×D4D311yescharacteristic, complemented
64#65404—31no—
65#65403—31no—
66#65402—31no—
67C2×#3953—31no—
68#65136—31no—
69#65133—31no—
70#65026—31no—
71#65023—31no—
72#65021—31no—
73#65011—31no—
74#64986—31no—
75C4×D40—31no—
76C23×D15—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×#1220—21no—
82C2×#1220—21no—
83C2×#1220—21no—
84C22×Dic15—21no—
85#6817—22no—
86#6817—41no—
87C2×D60—22no—
88C2×D60—21no—
89C2×D60—41no—
90C2×D60C2311yescharacteristic
91C2×D60C2311yescharacteristic
92C2×D60C2311yescharacteristic
93C2×C4×D15—21no—
94C2×C4×D15—21no—
95C2×C4×D15—21no—
96C2×Dic30C2311yescharacteristic
97C2×C3×C5×C8—41no—
98C2×C3×C5×C8—41no—
99C2×C3×C5×C8C2311yescharacteristic
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103C3×C5×C4⋊C4D411yescharacteristic
104C3×C5×C22⋊C4D411yescharacteristic
105C3×C5×C22⋊C4D411yescharacteristic
106C3×C42×C5C2311yescharacteristic
107#6719—21no—
108#6719—21no—
109#6714—21no—
110#6714—21no—
111#6714—21no—
112#6714—21no—
113#6714—21no—
114#6714—21no—
115#6714—21no—
116C4⋊Dic15—21no—
117C4⋊Dic15C2311yescharacteristic
118C4⋊Dic15C2311yescharacteristic
119C4⋊Dic15C2311yescharacteristic
120C4⋊Dic15C2311yescharacteristic
121#6712—21no—
122#6712—21no—
123#6712—21no—
124C4×Dic15—21no—
125D120—22no—
126D120—41no—
127#6706—41no—
128#5565—51no—
129#5550—51no—
130C3×C8×D4D511yescharacteristic, complemented
131#5115—51no—
132#5114—51no—
133#5113—51no—
134C2×#821—51no—
135#4847—51no—
136#4844—51no—
137#4737—51no—
138#4734—51no—
139#4732—51no—
140#4722—51no—
141#4697—51no—
142C4×D24—51no—
143C2×#709—31no—
144C22×D20—31no—
145C22×C5×C8C2×D311yescharacteristic
146C22×C5×C8C2×D311yescharacteristic, complemented
147C4×C5×D4C2×D311yescharacteristic
148#4085—61no—
149#4083—61no—
150#4076—31no—
151#4076—31no—
152#4076—31no—
153#4072—31no—
154C2×C4⋊Dic5—31no—
155#4070—31no—
156C2×D40—31no—
157C2×D40—31no—
158C2×#677—31no—
159#4044—61no—
160#4040—61no—
161#4030—61no—
162#4029—61no—
163#4027—61no—
164D5×C22⋊C4—61no—
165#4021—31no—
166C4×D20—31no—
167C4×D20—31no—
168#4016—31no—
169C5×C4⋊C8C2×D311yescharacteristic, complemented
170C5×C22⋊C8C2×D311yescharacteristic
171C5×C22⋊C8C2×D311yescharacteristic, complemented
172C4×C5×C8C2×D311yescharacteristic, complemented
173#3953—31no—
174#3953—31no—
175#3953—31no—
176#3953—31no—
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3950—31no—
181#3950—31no—
182#3949—31no—
183#3948—31no—
184#3948—31no—
185#3948—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—42no—
193C22×D15—42no—
194C22×D15—81no—
195C3×C5×D4—22no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205#1220—42no—
206#1220—42no—
207#1220—81no—
208#1220—81no—
209C2×Dic15—21no—
210C2×Dic15—21no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214C2×Dic15—81no—
215D60—21no—
216D60—21no—
217D60—21no—
218D60—21no—
219D60—21no—
220D60—42no—
221D60#4112yes—
222C4×D15—42no—
223C4×D15—81no—
224C4×D15—81no—
225Dic30—21no—
226Dic30—21no—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3×C5×C8—21no—
230C3×C5×C8—21no—
231C2×#235—51no—
232C22×D12—51no—
233C22×C3×C8C2×D511yescharacteristic
234C22×C3×C8C2×D511yescharacteristic, complemented
235C3×C4×D4C2×D511yescharacteristic
236#939—101no—
237#937—101no—
238#930—51no—
239#930—51no—
240#930—51no—
241#926—51no—
242C2×C4⋊Dic3—51no—
243#924—51no—
244C2×D24—51no—
245C2×D24—51no—
246C2×#204—51no—
247#898—101no—
248#894—101no—
249#884—101no—
250#883—101no—
251#67⋊C4—101no—
252D3×C22⋊C4—101no—
253#875—51no—
254C4×D12—51no—
255C4×D12—51no—
256#870—51no—
257C3×C4⋊C8C2×D511yescharacteristic, complemented
258C3×C22⋊C8C2×D511yescharacteristic
259C3×C22⋊C8C2×D511yescharacteristic, complemented
260C3×C4×C8C2×D511yescharacteristic, complemented
261#821—51no—
262#821—51no—
263#821—51no—
264#821—51no—
265#821—51no—
266#821—51no—
267#821—51no—
268#818—51no—
269#818—51no—
270#817—51no—
271#816—51no—
272#816—51no—
273#816—51no—
274C23×D5—61no—
275C2×C5×D4D1211yescharacteristic
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C2×C22⋊D5—61no—
279C2×C22⋊D5—61no—
280C2×C22⋊D5—61no—
281C2×C22⋊D5—61no—
282C22×Dic5—61no—
283#709—62no—
284#709—121no—
285C2×D20—31no—
286C2×D20—31no—
287C2×D20—31no—
288C2×D20—62no—
289C2×D20—61no—
290C2×D20—121no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×Dic10—31no—
295C2×C5×C8—41no—
296C2×C5×C8—41no—
297C2×C5×C8C22×D311yescharacteristic
298C2×C5×C8C22×D311yescharacteristic
299C2×C5×C8C22×D311yescharacteristic
300C2×C5×C8C22×D311yescharacteristic
301C5×C4⋊C4D1211yescharacteristic
302C5×C22⋊C4D1211yescharacteristic
303C5×C22⋊C4D1211yescharacteristic
304C42×C5C22×D311yescharacteristic
305C22⋊Dic5—61no—
306C22⋊Dic5—61no—
307#685—61no—
308#685—61no—
309#685—61no—
310#685—61no—
311#685—61no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—31no—
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—31no—
318C4⋊Dic5—61no—
319#683—61no—
320#683—61no—
321#683—61no—
322C4×Dic5—61no—
323D40—62no—
324D40—121no—
325#677—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#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4D1511yescharacteristic, complemented
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—21no—
346C22×C3×C5#13512yes—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×D15—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5C2×#4111yescharacteristic
363C3×C4×C5H(5,𝔽2)11yescharacteristic
364Dic15—41no—
365Dic15—41no—
366Dic15—41no—
367Dic15—41no—
368Dic15—41no—
369C23×D3—101no—
370C2×C3×D4D2011yescharacteristic
371C22×C3×C4C22×D511yescharacteristic
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—101no—
374C2×#67—101no—
375C2×#67—101no—
376C2×#67—101no—
377C22×Dic3—101no—
378#235—102no—
379#235—201no—
380C2×D12—51no—
381C2×D12—51no—
382C2×D12—51no—
383C2×D12—102no—
384C2×D12—101no—
385C2×D12—201no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C2×C3×C8—41no—
391C2×C3×C8—41no—
392C2×C3×C8C22×D511yescharacteristic
393C2×C3×C8C22×D511yescharacteristic
394C2×C3×C8C22×D511yescharacteristic
395C2×C3×C8C22×D511yescharacteristic
396C3×C4⋊C4D2011yescharacteristic
397C3×C22⋊C4D2011yescharacteristic
398C3×C22⋊C4D2011yescharacteristic
399C3×C42C22×D511yescharacteristic
400#217—101no—
401#217—101no—
402(C2×D3)⋊C4—101no—
403(C2×D3)⋊C4—101no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—51no—
410C4⋊Dic3—51no—
411C4⋊Dic3—51no—
412C4⋊Dic3—51no—
413C4⋊Dic3—101no—
414Dic3⋊C4—101no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—101no—
418D24—102no—
419D24—201no—
420#204—201no—
421C23×C5C2×D1211yescharacteristic
422C23×C5C2×D1211yescharacteristic
423C22×D5—61no—
424C22×D5—61no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
429C5×D4—22no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5C2×D1211yescharacteristic
435C2×C4×C5C2×D1211yescharacteristic
436C2×C4×C5C2×D1211yescharacteristic
437C2×C4×C5C2×D1211yescharacteristic
438C2×C4×C5C23×D311yescharacteristic
439C22⋊D5—122no—
440C22⋊D5—122no—
441C22⋊D5—241no—
442C22⋊D5—241no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—241no—
449D20—32no—
450D20—61no—
451D20—61no—
452D20—61no—
453D20—61no—
454D20—61no—
455D20—122no—
456C4×D5—122no—
457C4×D5—241no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461C5×C8—21no—
462C5×C8—21no—
463C5×C8—21no—
464C5×C8—21no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8C2×D1511yescharacteristic
471C22×C8C2×D1511yescharacteristic, complemented
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—151no—
481#121—301no—
482#121—301no—
483#120—301no—
484C4×D4—151no—
485C4×D4—151no—
486C4×D4—301no—
487C4×D4C2×D1511yescharacteristic
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—301no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8C2×D1511yescharacteristic, complemented
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8C2×D1511yescharacteristic
506C22⋊C8C2×D1511yescharacteristic, complemented
507C4×C8C2×D1511yescharacteristic, complemented
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513D15—42no—
514D15—81no—
515D15—81no—
516C23×C3C2×D2011yescharacteristic
517C23×C3C2×D2011yescharacteristic
518C22×D3—101no—
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
524C3×D4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4C2×D2011yescharacteristic
530C2×C3×C4C2×D2011yescharacteristic
531C2×C3×C4C2×D2011yescharacteristic
532C2×C3×C4C2×D2011yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—202no—
535#67—202no—
536#67—401no—
537#67—401no—
538C2×Dic3—101no—
539C2×Dic3—101no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—401no—
544D12—52no—
545D12—101no—
546D12—101no—
547D12—101no—
548D12—101no—
549D12—101no—
550D12—202no—
551C4×D3—202no—
552C4×D3—401no—
553C4×D3—401no—
554Dic6—101no—
555Dic6—101no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5#90412yes—
566C22×C5C22×D1211yescharacteristic
567C2×D5—62no—
568C2×D5—121no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—121no—
572C2×D5—121no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5#100411yescharacteristic
582C4×C5D3×#4111yescharacteristic
583Dic5—121no—
584Dic5—121no—
585Dic5—121no—
586Dic5—121no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—151no—
593C2×D4—151no—
594C2×D4—151no—
595C2×D4—302no—
596C2×D4—301no—
597C2×D4—301no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—301no—
601C2×D4—601no—
602C2×D4D6011yescharacteristic
603C22×C4—301no—
604C22×C4—301no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4C22×D1511yescharacteristic
608C22×C4C22×D1511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8C22×D1511yescharacteristic
615C2×C8C22×D1511yescharacteristic
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⋊C4D6011yescharacteristic
627C22⋊C4—301no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4D6011yescharacteristic
637C22⋊C4D6011yescharacteristic
638C42—301no—
639C42C22×D1511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3#405012yes—
647C22×C3C22×D2011yescharacteristic
648C2×D3—102no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—201no—
652C2×D3—201no—
653C2×D3—201no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4#414411yescharacteristic
663C3×C4D5×#4111yescharacteristic
664Dic3—201no—
665Dic3—201no—
666Dic3—201no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5#555411yescharacteristic
672C2×C5C2×#90411yescharacteristic
673C2×C5#575211yescharacteristic
674D5—122no—
675D5—241no—
676D5—241no—
677C23—301no—
678C23—301no—
679C23—301no—
680C23—602no—
681C23—602no—
682C23—1201no—
683C23C2×D6011yescharacteristic
684C23C2×D6011yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—22no—
688D4—152no—
689D4—301no—
690D4—301no—
691D4—301no—
692D4—301no—
693D4—301no—
694D4—602no—
695D4—602no—
696D4—602no—
697D4—1201no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—301no—
704C2×C4—301no—
705C2×C4—301no—
706C2×C4—301no—
707C2×C4—301no—
708C2×C4—602no—
709C2×C4—1201no—
710C2×C4—1201no—
711C2×C4—1201no—
712C2×C4C2×D6011yescharacteristic
713C2×C4C2×D6011yescharacteristic
714C2×C4C2×D6011yescharacteristic
715C2×C4C2×D6011yescharacteristic
716C2×C4C23×D1511yescharacteristic
717C8—21no—
718C8—21no—
719C8—21no—
720C8—21no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3#6588811yescharacteristic
724C2×C3C2×#405011yescharacteristic
725C2×C3#6608611yescharacteristic
726D3—202no—
727D3—401no—
728D3—401no—
729C5#7944111yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—302no—
736C22—601no—
737C22—601no—
738C22—601no—
739C22—601no—
740C22—601no—
741C22—601no—
742C22—601no—
743C22—601no—
744C22—1204no—
745C22#9179312yes—
746C22C22×D6011yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—601no—
752C4—601no—
753C4—601no—
754C4—601no—
755C4—601no—
756C4#9209511yescharacteristic
757C4#41×D1511yescharacteristic
758C3#1061117211yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—602no—
762C2—1201no—
763C2—1201no—
764C2#1175631311yescharacteristic
765C2C2×#9179311yescharacteristic
766C2#1175651111yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×C8×D4C2
socleC22×C3×C5C22×D4
hypercenterC8×D4D15
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #11756324C2semidirect
2. #11756309C2semidirect
3. C3×C5×C8×D4C2semidirect
4. #11751216C2semidirect
5. #11751215C2semidirect
6. #11751214C2semidirect
7. C2×#91105C2semidirect
8. #11750948C2semidirect
9. #11750945C2semidirect
10. #11750838C2semidirect
11. #11750835C2semidirect
12. #11750833C2semidirect
13. #11750823C2semidirect
14. #11750798C2semidirect
15. C4×D120C2semidirect
20. C22×C3×C5×C8C22semidirect
26. #91819C22semidirect
27. #91815C22semidirect
32. C2×#6706C22semidirect
41. C4×D60C22semidirect
42. #91759C22semidirect
43. C3×C5×C4⋊C8C22semidirect
45. C3×C5×C22⋊C8C22semidirect
46. C3×C4×C5×C8C22semidirect
53. #91105C22semidirect
54. #91102C22semidirect
55. #91102C22semidirect
56. #91101C22semidirect
57. #91100C22semidirect
58. #91100C22semidirect
59. #91100C22semidirect
63. C5×C8×D4D3semidirect
130. C3×C8×D4D5semidirect
146. C22×C5×C8C2×D3semidirect
169. C5×C4⋊C8C2×D3semidirect
171. C5×C22⋊C8C2×D3semidirect
172. C4×C5×C8C2×D3semidirect
234. C22×C3×C8C2×D5semidirect
257. C3×C4⋊C8C2×D5semidirect
259. C3×C22⋊C8C2×D5semidirect
260. C3×C4×C8C2×D5semidirect
338. C8×D4D15semidirect
471. C22×C8C2×D15semidirect
494. C4⋊C8C2×D15semidirect
506. C22⋊C8C2×D15semidirect
507. C4×C8C2×D15semidirect
640. C3×C5#3297semidirect
729. C5#79441semidirect
758. C3#10611172semidirect

Maximal subgroups

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

subgroupindex
#117563242
#117563092
C3×C5×C8×D42
#117512162
#117512152
#117512142
C2×#911052
#117509482
#117509452
#117508382
#117508352
#117508332
#117508232
#117507982
C4×D1202
#106111723
#794415