Finite Group Databasebeta

← #14458985

Subgroups — #14458985

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
1C3×#65964C211yesmaximal, characteristic, complemented
2#11754608C211yesmaximal, characteristic, complemented
3#11751145C211yesmaximal, characteristic, complemented
4C5×#5048C211yesmaximal, characteristic, complemented
5#11749331C211yesmaximal, characteristic, complemented
6#11749270C211yesmaximal, characteristic, complemented
7#11749224C211yesmaximal, characteristic, complemented
8#11749207C211yesmaximal, characteristic, complemented
9#11748510C211yesmaximal, characteristic, complemented
10C3⋊C8×C22⋊D5C211yesmaximal, characteristic, complemented
11C2×#90965C211yesmaximal, characteristic, complemented
12#11747392C211yesmaximal, characteristic, complemented
13#11747307C211yesmaximal, characteristic, complemented
14#11747216C211yesmaximal, characteristic, complemented
15#11747207C211yesmaximal, characteristic, complemented
16#10612412—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C2×C5×#215C2211yescharacteristic, complemented
22C5×#930C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C3×#4093C2211yescharacteristic
25C3×C4×C22⋊D5C2211yescharacteristic
26C3×#4041—21no—
27C3×#4041C2211yescharacteristic
28C3×#4040—21no—
29C3×#4039C2211yescharacteristic
30C3×#4028—21no—
31C3×D5×C22⋊C4—21no—
32#91571—21no—
33#67⋊Dic5—21no—
34#91457—21no—
35#91449C2211yescharacteristic, complemented
36Dic5×D12C2211yescharacteristic, complemented
37#91388C2211yescharacteristic, complemented
38#91358C2211yescharacteristic, complemented
39#91342—21no—
40C2×#6652C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91119C2211yescharacteristic, complemented
45#91114C2211yescharacteristic
46#91091C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C5×#835C2211yescharacteristic, complemented
49C5×#809C2211yescharacteristic, complemented
50C5×#808C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90965C2211yescharacteristic
53#90965C2211yescharacteristic
54#90965C2211yescharacteristic
55#90965C2211yescharacteristic
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58#90955C2211yescharacteristic, complemented
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83495—51nomaximal, Hall
61#65964D311yescharacteristic, complemented
62#65952—31no—
63C5×#465—31no—
64#65461—31no—
65#65454—31no—
66C2×#3953—31no—
67C8×C22⋊D5—31no—
68#65333—31no—
69#65325—31no—
70#65160—31no—
71#65155—31no—
72#65093—31no—
73#65089—31no—
74#65064—31no—
75#65045—31no—
76C23×C3×D5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15—21no—
80C2×C5×#67—21no—
81C2×C5×D12C2311yescharacteristic
82C2×C3×C22⋊D5D411yescharacteristic
83C3×#713—22no—
84C3×#713—41no—
85C2×C3×D20—22no—
86C2×C3×D20—21no—
87C2×C3×D20—21no—
88C2×C3×D20—21no—
89C2×C3×D20—41no—
90C2×C3×D20C2311yescharacteristic
91C2×C3×D20C2311yescharacteristic
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5C2311yescharacteristic
95C2×#1201—21no—
96C2×D3×Dic5—21no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C4⋊Dic15—21no—
101C4⋊Dic15C2311yescharacteristic
102C4⋊Dic15C2311yescharacteristic
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×#215—41no—
106C5×(C2×D3)⋊C4—21no—
107C5×C4⋊Dic3C2311yescharacteristic
108C2×C5×C3⋊C8—41no—
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5D411yescharacteristic
112C3×#685—21no—
113C3×#685—21no—
114C3×#685—21no—
115C3×#685—21no—
116C3×#685D411yescharacteristic
117C3×#683D411yescharacteristic
118C3×C4×Dic5C2311yescharacteristic
119Dic3⋊Dic5—21no—
120#6669—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125#6652—22no—
126#6652—41no—
127D5×C3⋊C8—41no—
128C3×#546—51no—
129#5565—51no—
130#5238—51no—
131#5233—51no—
132#5217—51no—
133C2×#832—51no—
134#5057—51no—
135#5056—51no—
136#5048D511yescharacteristic, complemented
137#5044—51no—
138#5038—51no—
139#5035—51no—
140C4×#213—51no—
141D4×C3⋊C8—51no—
142#5009—51no—
143C2×#713C2×D311yescharacteristic
144C22×D20C2×D311yescharacteristic
145C2×C5×SD16—31no—
146C22×C5×C8—31no—
147C5×C22⋊Q8C2×D311yescharacteristic
148C5×#121—31no—
149#4093C2×D311yescharacteristic
150#4085—61no—
151#4084—31no—
152D4×Dic5—31no—
153D4×Dic5—61no—
154C2×#686—31no—
155C2×#686—31no—
156C4×C22⋊D5C2×D311yescharacteristic
157C2×C4⋊Dic5—31no—
158C2×C8×D5—31no—
159#4041—21no—
160#4041C2×D311yescharacteristic
161#4040—21no—
162#4039C2×D311yescharacteristic
163#4038—31no—
164#4036—31no—
165#4032—61no—
166#4028—21no—
167D5×C22⋊C4—21no—
168#4025—61no—
169C5×#106—31no—
170C5×#103—31no—
171C5×#102—31no—
172#3967—31no—
173#3967—31no—
174C22⋊#168—31no—
175#3953—31no—
176#3953—31no—
177#3953—31no—
178#3953—31no—
179#3952—31no—
180#3946—31no—
181C8×Dic5—31no—
182#3941—31no—
183#3941—31no—
184#3939—31no—
185#3939—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C5×D3—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—42no—
192C22×C3×D5—42no—
193C22×C3×D5—81no—
194C22×C3×D5C2×D411yescharacteristic
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15—21no—
205C2×Dic15—81no—
206C5×#67—42no—
207C2×C5×Dic3—21no—
208C5×D12—21no—
209C5×D12—21no—
210C3×C22⋊D5—22no—
211C2×C3×Dic5C2×D411yescharacteristic
212C2×C3×Dic5C2×D411yescharacteristic
213C2×C3×Dic5C2×D411yescharacteristic
214C3×D20—21no—
215C3×D20—21no—
216C3×D20—21no—
217C3×D20—42no—
218C3×D20—42no—
219C3×D20—81no—
220C3×D20#4112yes—
221C3×C4×D5—21no—
222C3×C4×D5—21no—
223C3×C4×D5—42no—
224C3×C4×D5—81no—
225#1201—81no—
226D3×Dic5—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C5×C3⋊C8—21no—
230C5×C3⋊C8—21no—
231C2×C3×#41—51no—
232C22×C3×D4—51no—
233C3×#124—51no—
234C3×#123—101no—
235C3×C22⋊Q8C2×D511yescharacteristic
236C3×#121—51no—
237C3×#121—101no—
238C3×#120—101no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C2×C3×C22⋊C4—101no—
242C2×#215C2×D511yescharacteristic, complemented
243#939—101no—
244C2×#213—51no—
245C2×#213—51no—
246#930—51no—
247#930C2×D511yescharacteristic
248#926—51no—
249C2×C4⋊Dic3—51no—
250C22×C3⋊C8—51no—
251C22×C3⋊C8C2×D511yescharacteristic
252#898—101no—
253#883—101no—
254#67⋊C4—101no—
255C4×D12—51no—
256#870—51no—
257#835—51no—
258#835—51no—
259#835C2×D511yescharacteristic, complemented
260#832—51no—
261#832—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265#832—51no—
266#830—51no—
267#830—51no—
268#809C2×D511yescharacteristic, complemented
269#808C2×D511yescharacteristic, complemented
270#807—51no—
271#807—51no—
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C23×D5—21no—
275C2×C5×Q8C22×D311yescharacteristic
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C22×C4×C5C22×D311yescharacteristic
279C2×C22⋊D5—61no—
280C2×C22⋊D5#6711yescharacteristic
281C22×Dic5—61no—
282C22×Dic5—61no—
283#713—22no—
284#713—41no—
285C2×D20—22no—
286C2×D20—21no—
287C2×D20—21no—
288C2×D20—21no—
289C2×D20—41no—
290C2×D20C22×D311yescharacteristic
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×C4×D5C22×D311yescharacteristic
295C5×SD16—121no—
296C2×C5×C8—31no—
297C2×C5×C8—31no—
298C2×C5×C8—121no—
299C5×C4⋊C4—21no—
300C5×C4⋊C4—31no—
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—21no—
303C5×C22⋊C4—61no—
304C22⋊Dic5—61no—
305C22⋊Dic5—61no—
306C22⋊Dic5#6711yescharacteristic
307#686—62no—
308#686—121no—
309#685—21no—
310#685—21no—
311#685—21no—
312#685—21no—
313#685—61no—
314#685#6711yescharacteristic
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—61no—
318C4⋊Dic5—61no—
319#683—61no—
320#683#6711yescharacteristic
321C4×Dic5—61no—
322C4×Dic5C22×D311yescharacteristic
323C2×#168—31no—
324C2×#168—31no—
325C8×D5—121no—
326#553—151no—
327#546—51no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—31no—
334#463—151no—
335#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C5×D3—41no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C3×D5—21no—
349C2×C3×D5—22no—
350C2×C3×D5—21no—
351C2×C3×D5—21no—
352C2×C3×D5—41no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—41no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5H(5,𝔽2)11yescharacteristic
363Dic15—41no—
364Dic15—41no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—21no—
368C5×Dic3—41no—
369C24×C3—101no—
370C3×#41—102no—
371C3×#41—201no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—51no—
374C2×C3×D4—51no—
375C2×C3×D4—51no—
376C2×C3×D4—102no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C2×C3×D4—101no—
380C2×C3×D4—201no—
381C22×C3×C4—51no—
382C22×C3×C4—101no—
383C22×C3×C4—101no—
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—21no—
386C2×#67—101no—
387C22×Dic3—101no—
388C2×D12C22×D511yescharacteristic
389C2×C4×D3—101no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—51no—
395C3×C22⋊C4—51no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C42—51no—
401#217—101no—
402#215—41no—
403#213—102no—
404#213—201no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410C4⋊Dic3—101no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—101no—
415C2×C3⋊C8—41no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—201no—
419C2×C3⋊C8C22×D511yescharacteristic
420C2×C3⋊C8C22×D511yescharacteristic
421C23×C5—61no—
422C23×C5C2×#6711yescharacteristic
423C22×D5—21no—
424C22×D5—21no—
425C22×D5—42no—
426C22×D5—42no—
427C22×D5—81no—
428C22×D5C2×#6711yescharacteristic
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—61no—
432C5×D4—61no—
433C5×D4—122no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—61no—
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—22no—
442C22⋊D5—241no—
443C2×Dic5—61no—
444C2×Dic5—61no—
445C2×Dic5—241no—
446C2×Dic5—241no—
447C2×Dic5C2×#6711yescharacteristic
448C2×Dic5C2×#6711yescharacteristic
449C2×Dic5C2×#6711yescharacteristic
450D20—21no—
451D20—21no—
452D20—21no—
453D20—42no—
454D20—42no—
455D20—81no—
456D20#23712yes—
457C4×D5—21no—
458C4×D5—21no—
459C4×D5—42no—
460C4×D5—81no—
461C5×C8—61no—
462C5×C8—61no—
463#168—61no—
464#168—61no—
465C2×#41—51no—
466C22×D4—51no—
467C2×SD16—31no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—31no—
471C22×C8—151no—
472#126—301no—
473#125—151no—
474#124—51no—
475#123—101no—
476#123—301no—
477C22⋊Q8D3×D511yescharacteristic
478#121—31no—
479#121—51no—
480#121—101no—
481#121—151no—
482#121—301no—
483#120—101no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—151no—
487C4×D4—301no—
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—101no—
491#107—151no—
492#107—151no—
493#106—31no—
494C4⋊C8—151no—
495#103—31no—
496#103—151no—
497#103—151no—
498#102—31no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—22no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C3×D5—41no—
513C3×D5—42no—
514C3×D5—81no—
515C5×D3—81no—
516C23×C3—51no—
517C23×C3—101no—
518C23×C3—101no—
519C23×C3—202no—
520C23×C3—202no—
521C23×C3—401no—
522C23×C3D4×D511yescharacteristic
523C22×D3—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—52no—
527C3×D4—102no—
528C3×D4—101no—
529C3×D4—101no—
530C3×D4—101no—
531C3×D4—202no—
532C3×D4—202no—
533C3×D4—401no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—51no—
539C2×C3×C4—51no—
540C2×C3×C4—51no—
541C2×C3×C4—101no—
542C2×C3×C4—101no—
543C2×C3×C4—202no—
544C2×C3×C4—401no—
545C2×C3×C4D4×D511yescharacteristic
546C2×C3×C4C23×D511yescharacteristic
547#67—42no—
548#67—401no—
549C2×Dic3—21no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—401no—
553D12—21no—
554D12—21no—
555C4×D3—401no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—121no—
563C22×C5—121no—
564C22×C5—121no—
565C22×C5#95012yes—
566C22×C5C22×#6711yescharacteristic
567C2×D5—21no—
568C2×D5—22no—
569C2×D5—21no—
570C2×D5—21no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—84no—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—41no—
580C4×C5—121no—
581C4×C5C2×#23711yescharacteristic
582C4×C5#100411yescharacteristic
583Dic5—21no—
584Dic5—21no—
585Dic5—21no—
586Dic5—121no—
587Dic5—121no—
588C24—101no—
589#41—102no—
590#41—201no—
591C2×Q8C2×D3×D511yescharacteristic
592C2×D4—31no—
593C2×D4—51no—
594C2×D4—51no—
595C2×D4—51no—
596C2×D4—61no—
597C2×D4—102no—
598C2×D4—101no—
599C2×D4—101no—
600C2×D4—101no—
601C2×D4—201no—
602C2×D4—301no—
603C22×C4—51no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—121no—
610D8—302no—
611D8—601no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—121no—
615C2×C8—151no—
616C2×C8—151no—
617C2×C8—601no—
618C4⋊C4—21no—
619C4⋊C4—31no—
620C4⋊C4—51no—
621C4⋊C4—151no—
622C4⋊C4—151no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—51no—
629C22⋊C4—51no—
630C22⋊C4—61no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—51no—
639C42—301no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—101no—
644C22×C3—101no—
645C22×C3—101no—
646C22×C3—102no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—404no—
653C22×C3#406212yes—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—101no—
662C3×C4—101no—
663C3×C4—101no—
664C3×C4#414411yescharacteristic
665C3×C4D5×#4111yescharacteristic
666Dic3—41no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—241no—
671C2×C5#580611yescharacteristic
672C2×C5C2×#95011yescharacteristic
673C2×C5#583511yescharacteristic
674D5—41no—
675D5—42no—
676D5—81no—
677C23—51no—
678C23—61no—
679C23—101no—
680C23—101no—
681C23—202no—
682C23—202no—
683C23—401no—
684C23D5×#6711yescharacteristic
685Q8—21no—
686Q8—21no—
687D4—52no—
688D4—61no—
689D4—61no—
690D4—102no—
691D4—101no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—202no—
696D4—202no—
697D4—401no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—51no—
704C2×C4—51no—
705C2×C4—51no—
706C2×C4—61no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—202no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—401no—
713C2×C4—1201no—
714C2×C4—1201no—
715C2×C4D5×#6711yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—61no—
718C8—61no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—201no—
723C2×C3—202no—
724C2×C3—401no—
725C2×C3#6594411yescharacteristic
726C2×C3C2×#406211yescharacteristic
727C2×C3#6610311yescharacteristic
728D3—81no—
729C5#8349511yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—101no—
733C22—102no—
734C22—101no—
735C22—101no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—404no—
745C22#9151412yes—
746C22C2×D5×#6711yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—101no—
751C4—101no—
752C4—101no—
753C4—121no—
754C4—601no—
755C4—601no—
756C4D5×#23711yescharacteristic
757C4#9202511yescharacteristic
758C3#1061241211yescharacteristic, complemented, Sylow
759C2—22no—
760C2—201no—
761C2—202no—
762C2—241no—
763C2—401no—
764C2#1175479111yescharacteristic
765C2C2×#9151411yescharacteristic
766C2#1175531811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#65964C2semidirect
2. #11754608C2semidirect
3. #11751145C2semidirect
4. C5×#5048C2semidirect
5. #11749331C2semidirect
6. #11749270C2semidirect
7. #11749224C2semidirect
8. #11749207C2semidirect
9. #11748510C2semidirect
10. C3⋊C8×C22⋊D5C2semidirect
11. C2×#90965C2semidirect
12. #11747392C2semidirect
13. #11747307C2semidirect
14. #11747216C2semidirect
15. #11747207C2semidirect
21. C2×C5×#215C22semidirect
35. #91449C22semidirect
36. Dic5×D12C22semidirect
37. #91388C22semidirect
38. #91358C22semidirect
42. C2×D5×C3⋊C8C22semidirect
43. #91119C22semidirect
44. #91119C22semidirect
46. #91091C22semidirect
47. #91091C22semidirect
48. C5×#835C22semidirect
49. C5×#809C22semidirect
50. C5×#808C22semidirect
51. #90982C22semidirect
58. #90955C22semidirect
59. Dic5×C3⋊C8C22semidirect
61. #65964D3semidirect
136. #5048D5semidirect
242. C2×#215C2×D5semidirect
259. #835C2×D5semidirect
268. #809C2×D5semidirect
269. #808C2×D5semidirect
640. C3×C5#3297semidirect
729. C5#83495semidirect
758. C3#10612412semidirect

Maximal subgroups

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

subgroupindex
C3×#659642
#117546082
#117511452
C5×#50482
#117493312
#117492702
#117492242
#117492072
#117485102
C3⋊C8×C22⋊D52
C2×#909652
#117473922
#117473072
#117472162
#117472072
#106124123
#834955