Finite Group Databasebeta

← #14459028

Subgroups — #14459028

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×#65892C211yesmaximal, characteristic, complemented
2#11752740C211yesmaximal, characteristic, complemented
3#11751117C211yesmaximal, characteristic, complemented
4C4×C5×#213C211yesmaximal, characteristic, complemented
5#11749159C211yesmaximal, characteristic, complemented
6#11749151C211yesmaximal, characteristic, complemented
7#11749046C211yesmaximal, characteristic, complemented
8#11749023C211yesmaximal, characteristic, complemented
9#11747499C211yesmaximal, characteristic, complemented
10D5×#809C211yesmaximal, characteristic, complemented
11#11747169C211yesmaximal, characteristic, complemented
12#11747166C211yesmaximal, characteristic, complemented
13C3⋊C8×D20C211yesmaximal, characteristic, complemented
14#11746933C211yesmaximal, characteristic, complemented
15#11746902C211yesmaximal, characteristic, complemented
16#10611340—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18C2×#6772C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic, complemented
20C2×#6716C2211yescharacteristic, complemented
21C2×#6715C2211yescharacteristic
22#91764C2211yescharacteristic
23C2×C5×#213C2211yescharacteristic
24C4×C5×D12C2211yescharacteristic
25C3×#4084C2211yescharacteristic
26C3×#4084C2211yescharacteristic, complemented
27C3×#4075—21no—
28C3×C4×C22⋊D5—21no—
29C3×#4038C2211yescharacteristic, complemented
30C3×D5×C4⋊C4C2211yescharacteristic
31C3×#4030—21no—
32C3×#4025—21no—
33C3×C4×D20C2211yescharacteristic
34C3×#4016C2211yescharacteristic, complemented
35#91474—21no—
36D3×#685—21no—
37#91454—21no—
38#91450C2211yescharacteristic
39#91427—21no—
40#91360C2211yescharacteristic
41C2×D5×C3⋊C8C2211yescharacteristic
42C2×D5×C3⋊C8C2211yescharacteristic, complemented
43#91094C2211yescharacteristic, complemented
44#91093C2211yescharacteristic
45C4⋊(C3⋊#168)C2211yescharacteristic, complemented
46C5×#832C2211yescharacteristic, complemented
47C5×#809C2211yescharacteristic
48C5×#807C2211yescharacteristic, complemented
49C4×C5×C3⋊C8C2211yescharacteristic, complemented
50#90989C2211yescharacteristic, complemented
51#90986C2211yescharacteristic, complemented
52#90974C2211yescharacteristic, complemented
53#90974C2211yescharacteristic, complemented
54#90968C2211yescharacteristic
55#90968C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58#90955C2211yescharacteristic
59#90955C2211yescharacteristic, complemented
60#83614—51nomaximal, Hall
61#65892D311yescharacteristic, complemented
62#65888—31no—
63C4×C5×D8—31no—
64#65447—31no—
65#65445—31no—
66#65305—31no—
67#65298—31no—
68#65174—31no—
69#65173—31no—
70#65067—31no—
71#65064—31no—
72#65061—31no—
73D5×#102—31no—
74#64986—31no—
75C8×D20—31no—
76C22×D3×D5—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×C3×C4×C5—21no—
79C2×D60C2311yescharacteristic
80C2×Dic30C2311yescharacteristic
81C2×C5×D12C2311yescharacteristic
82C2×C4×C5×D3—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5—21no—
85C2×C3×D20D411yescharacteristic
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5C2311yescharacteristic
88C2×C3×C4×D5C2311yescharacteristic
89C2×#1203—21no—
90C2×#1202—21no—
91C2×#1201—21no—
92C2×D3×Dic5—21no—
93D5×D12—22no—
94D5×D12—41no—
95#6772—22no—
96#6772—41no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C22⋊C4—21no—
99C3×C42×C5C2311yescharacteristic
100#6716—41no—
101#6715—41no—
102#6714—21no—
103#6714—21no—
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C5×#213—22no—
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×C22⋊Dic5—21no—
113C3×#685—21no—
114C3×#685D411yescharacteristic
115C3×#685D411yescharacteristic
116C3×C4⋊Dic5D411yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×C4⋊Dic5C2311yescharacteristic
119C3×#683—21no—
120C3×#683—21no—
121C3×#683—21no—
122C3×C4×Dic5—21no—
123Dic3⋊Dic5—21no—
124#6667—21no—
125#6665—21no—
126D5×C3⋊C8—41no—
127D5×C3⋊C8—41no—
128C3×#553—51no—
129#5550—51no—
130#5068—51no—
131#5066—51no—
132#5041—51no—
133#5038—51no—
134#5037—51no—
135#5036—51no—
136#5016—51no—
137C4×#213D511yescharacteristic, complemented
138D4×C3⋊C8—51no—
139#5003—51no—
140#5002—51no—
141#4970—51no—
142C2×#809—51no—
143C2×#711—31no—
144C2×D4×D5—31no—
145C2×C5×D8—31no—
146C4×C5×D4—31no—
147C4×C5×D4C2×D311yescharacteristic, complemented
148#4084C2×D311yescharacteristic
149#4084C2×D311yescharacteristic, complemented
150C2×#687—31no—
151C2×#686—31no—
152#4076—61no—
153#4075—21no—
154C4×C22⋊D5—21no—
155C2×#685—61no—
156C2×C8×D5—31no—
157C2×C8×D5—31no—
158#4043—31no—
159#4041—31no—
160#4038C2×D311yescharacteristic, complemented
161D5×C4⋊C4C2×D311yescharacteristic
162#4032—61no—
163#4030—21no—
164#4028—61no—
165#4025—21no—
166#4021—31no—
167C4×D20C2×D311yescharacteristic
168#4016C2×D311yescharacteristic, complemented
169C5×#107—31no—
170C5×#102—31no—
171C5×#102—31no—
172C4×C5×C8—31no—
173#3964—31no—
174#3964—31no—
175#3953—31no—
176#3953—31no—
177#3952—31no—
178#3952—31no—
179#3948—31no—
180#3948—31no—
181#3942—31no—
182#3941—31no—
183#3940—31no—
184#3939—31no—
185C4⋊#168—31no—
186#3297—151noSylow
187C23×C3×C5—21no—
188C22×D15—21no—
189C22×C5×D3—21no—
190C22×C3×D5C2×D411yescharacteristic
191C22×C3×D5C2×D411yescharacteristic
192C2×D3×D5—42no—
193C2×D3×D5—42no—
194C2×D3×D5—81no—
195C3×C5×D4—21no—
196C3×C5×D4—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—81no—
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203D60—21no—
204D60—21no—
205Dic30—21no—
206Dic30—21no—
207C2×C5×Dic3—21no—
208C5×D12—21no—
209C5×D12#4112yes—
210C4×C5×D3—81no—
211C3×C22⋊D5—42no—
212C3×C22⋊D5—81no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×D20—22no—
218C3×C4×D5—21no—
219C3×C4×D5—21no—
220C3×C4×D5—21no—
221C3×C4×D5—21no—
222C3×C4×D5—81no—
223#1203—42no—
224#1202—81no—
225#1201—42no—
226D3×Dic5—42no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C5×C3⋊C8—21no—
230C5×C3⋊C8—21no—
231C2×#235—51no—
232C22×D12—51no—
233C3×#126—101no—
234C3×#125—51no—
235C3×#123—101no—
236C3×#121—51no—
237C3×#121—51no—
238C3×#121—101no—
239C3×C4×D4—51no—
240C3×C4×D4—101no—
241C3×C4×D4C2×D511yescharacteristic, complemented
242C3×#117—51no—
243C2×C3×C4⋊C4—51no—
244#937—101no—
245C2×#214—51no—
246C2×#213—51no—
247C2×#213C2×D511yescharacteristic
248#930—51no—
249#924—51no—
250C22×C3⋊C8—51no—
251C22×C3⋊C8—51no—
252#894—101no—
253#884—101no—
254D3×C22⋊C4—101no—
255#875—51no—
256C4×D12C2×D511yescharacteristic
257#832C2×D511yescharacteristic, complemented
258#830—51no—
259#830—51no—
260#810—51no—
261#810—51no—
262#810—51no—
263#809—51no—
264#809—51no—
265#809—51no—
266#809—51no—
267#809—51no—
268#809C2×D511yescharacteristic
269#808—51no—
270#807—51no—
271#807C2×D511yescharacteristic, complemented
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8C2×D511yescharacteristic, complemented
274C23×D5—61no—
275C2×C5×D4—31no—
276C2×C5×D4C22×D311yescharacteristic
277C22×C4×C5—21no—
278C22×C4×C5—61no—
279C2×C22⋊D5—21no—
280C2×C22⋊D5—21no—
281C2×C22⋊D5—61no—
282C2×C22⋊D5—61no—
283C22×Dic5—61no—
284#711—62no—
285#711—121no—
286D4×D5—62no—
287D4×D5—121no—
288C2×D20—31no—
289C2×D20—61no—
290C2×D20#6711yescharacteristic
291C2×C4×D5—21no—
292C2×C4×D5C22×D311yescharacteristic
293C2×C4×D5C22×D311yescharacteristic
294C2×Dic10—31no—
295C5×D8—62no—
296C2×C5×C8—31no—
297C2×C5×C8—31no—
298C5×C4⋊C4—31no—
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C22⋊C4—21no—
301C5×C22⋊C4—61no—
302C42×C5C22×D311yescharacteristic
303C22⋊Dic5—21no—
304C22⋊Dic5—21no—
305#687—121no—
306#686—121no—
307#685—21no—
308#685—61no—
309#685—61no—
310#685—61no—
311#685—61no—
312#685#6711yescharacteristic
313#685#6711yescharacteristic
314C4⋊Dic5—61no—
315C4⋊Dic5#6711yescharacteristic
316C4⋊Dic5C22×D311yescharacteristic
317C4⋊Dic5C22×D311yescharacteristic
318#683—21no—
319#683—21no—
320#683—21no—
321C4×Dic5—21no—
322C2×#168—31no—
323C2×#168—31no—
324C8×D5—121no—
325C8×D5—121no—
326#553—51no—
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—31no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—41no—
346C2×D15—41no—
347C2×D15—41no—
348C2×C5×D3—22no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C3×D5—21no—
352C2×C3×D5—21no—
353C2×C3×D5—21no—
354C2×C3×D5—21no—
355C2×C3×D5—21no—
356C2×C3×D5#13512yes—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—41no—
361C3×C4×C5C2×#4111yescharacteristic
362C3×C4×C5H(5,𝔽2)11yescharacteristic
363Dic15—41no—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—41no—
367C3×Dic5—41no—
368C5×Dic3—41no—
369C23×D3—101no—
370C2×C3×D4—51no—
371C2×C3×D4—101no—
372C2×C3×D4—101no—
373C2×C3×D4C22×D511yescharacteristic
374C22×C3×C4—21no—
375C22×C3×C4—51no—
376C22×C3×C4—51no—
377C22×C3×C4—101no—
378C2×#67—101no—
379C2×#67—101no—
380#235—102no—
381#235—201no—
382C2×D12—51no—
383C2×D12—102no—
384C2×D12—101no—
385C2×D12—201no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C3×C4⋊C4—51no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—51no—
399C3×C22⋊C4—51no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#214—201no—
407#213—22no—
408#213—201no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—101no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—201no—
418C2×C3⋊C8—201no—
419C2×C3⋊C8C22×D511yescharacteristic
420C2×C3⋊C8C22×D511yescharacteristic
421C23×C5—21no—
422C23×C5—61no—
423C22×D5—61no—
424C22×D5—122no—
425C22×D5—122no—
426C22×D5—241no—
427C22×D5C2×#6711yescharacteristic
428C22×D5C2×#6711yescharacteristic
429C5×D4—21no—
430C5×D4—21no—
431C5×D4—32no—
432C5×D4—61no—
433C2×C4×C5—21no—
434C2×C4×C5—61no—
435C2×C4×C5—81no—
436C2×C4×C5—241no—
437C2×C4×C5C2×#6711yescharacteristic
438C2×C4×C5C2×#6711yescharacteristic
439C2×C4×C5C23×D311yescharacteristic
440C22⋊D5—42no—
441C22⋊D5—81no—
442C22⋊D5—122no—
443C22⋊D5—122no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—61no—
447C2×Dic5—122no—
448C2×Dic5C2×#6711yescharacteristic
449C2×Dic5C2×#6711yescharacteristic
450D20—22no—
451D20—61no—
452D20—61no—
453D20—241no—
454C4×D5—21no—
455C4×D5—21no—
456C4×D5—21no—
457C4×D5—21no—
458C4×D5—81no—
459Dic10—61no—
460Dic10—61no—
461C5×C8—61no—
462C5×C8—61no—
463#168—61no—
464#168—61no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—31no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—101no—
473#125—51no—
474#124—151no—
475#123—101no—
476#123—301no—
477C22⋊Q8—151no—
478#121—51no—
479#121—51no—
480#121—101no—
481#121—151no—
482#121—301no—
483#120—301no—
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—101no—
487C4×D4D3×D511yescharacteristic, complemented
488#117—51no—
489C2×C4⋊C4—51no—
490C2×C22⋊C4—301no—
491#107—31no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—31no—
499#102—31no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—31no—
508C2×C3×C5—81no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512D15—81no—
513C3×D5—22no—
514C3×D5—41no—
515C5×D3—42no—
516C23×C3—21no—
517C23×C3—51no—
518C23×C3—51no—
519C22×D3—21no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—102no—
527C3×D4—202no—
528C3×D4—401no—
529C2×C3×C4—21no—
530C2×C3×C4—51no—
531C2×C3×C4—51no—
532C2×C3×C4—81no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4—401no—
540C2×C3×C4D4×D511yescharacteristic
541C2×C3×C4D4×D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543#67—202no—
544#67—401no—
545C2×Dic3—21no—
546C2×Dic3—101no—
547D12—21no—
548D12—101no—
549D12—101no—
550D12—202no—
551D12#70912yes—
552C4×D3—81no—
553C4×D3—202no—
554Dic6—101no—
555Dic6—101no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—41no—
561C22×C5—41no—
562C22×C5—41no—
563C22×C5—62no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5C22×#6711yescharacteristic
567C2×D5—21no—
568C2×D5—21no—
569C2×D5—21no—
570C2×D5—21no—
571C2×D5—21no—
572C2×D5—121no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—244no—
576C2×D5#95012yes—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—41no—
580C4×C5—121no—
581C4×C5D3×#4111yescharacteristic
582C4×C5#100911yescharacteristic
583Dic5—21no—
584Dic5—21no—
585Dic5—41no—
586Dic5—41no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—51no—
594C2×D4—101no—
595C2×D4—101no—
596C2×D4—151no—
597C2×D4—301no—
598C2×D4—301no—
599C2×D4—302no—
600C2×D4—301no—
601C2×D4—601no—
602C2×D4C2×D3×D511yescharacteristic
603C22×C4—21no—
604C22×C4—51no—
605C22×C4—51no—
606C22×C4—61no—
607C22×C4—101no—
608C22×C4—301no—
609SD16—601no—
610D8—62no—
611D8—601no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—31no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—51no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—101no—
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—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—101no—
639C42C2×D3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—52no—
645C22×C3—101no—
646C22×C3—101no—
647C22×C3—101no—
648C22×C3—101no—
649C22×C3—101no—
650C22×C3C2×D4×D511yescharacteristic
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—41no—
661C3×C4—101no—
662C3×C4—101no—
663C3×C4—201no—
664C3×C4—201no—
665C3×C4C2×#70911yescharacteristic
666C3×C4#414911yescharacteristic
667Dic3—41no—
668Dic3—201no—
669C2×C5—81no—
670C2×C5—122no—
671C2×C5C2×#95011yescharacteristic
672C2×C5#582911yescharacteristic
673C2×C5#583511yescharacteristic
674D5—22no—
675D5—41no—
676D5—241no—
677C23—21no—
678C23—51no—
679C23—51no—
680C23—61no—
681C23—301no—
682C23—602no—
683C23—602no—
684C23—1201no—
685Q8—301no—
686Q8—301no—
687D4—21no—
688D4—21no—
689D4—32no—
690D4—61no—
691D4—102no—
692D4—202no—
693D4—301no—
694D4—301no—
695D4—401no—
696D4—602no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—51no—
701C2×C4—51no—
702C2×C4—61no—
703C2×C4—81no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—241no—
711C2×C4—301no—
712C2×C4—401no—
713C2×C4—602no—
714C2×C4D5×#6711yescharacteristic
715C2×C4D5×#6711yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—61no—
718C8—61no—
719C8—301no—
720C8—301no—
721C2×C3—81no—
722C2×C3—102no—
723C2×C3—201no—
724C2×C3#6588411yescharacteristic
725C2×C3#6609111yescharacteristic
726C2×C3D5×#13511yescharacteristic
727D3—42no—
728D3—401no—
729C5#8361411yescharacteristic, complemented, Sylow
730C22—41no—
731C22—41no—
732C22—41no—
733C22—52no—
734C22—62no—
735C22—101no—
736C22—101no—
737C22—101no—
738C22—101no—
739C22—101no—
740C22—121no—
741C22—121no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22—1204no—
746C22C2×D5×#6711yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—101no—
751C4—101no—
752C4—121no—
753C4—201no—
754C4—201no—
755C4—601no—
756C4D3×#70911yescharacteristic
757C4#9201911yescharacteristic
758C3#1061134011yescharacteristic, complemented, Sylow
759C2—81no—
760C2—102no—
761C2—122no—
762C2—201no—
763C2—1201no—
764C2#1175463811yescharacteristic
765C2#1175469111yescharacteristic
766C2D5×#95011yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#65892C2semidirect
2. #11752740C2semidirect
3. #11751117C2semidirect
4. C4×C5×#213C2semidirect
5. #11749159C2semidirect
6. #11749151C2semidirect
7. #11749046C2semidirect
8. #11749023C2semidirect
9. #11747499C2semidirect
10. D5×#809C2semidirect
11. #11747169C2semidirect
12. #11747166C2semidirect
13. C3⋊C8×D20C2semidirect
14. #11746933C2semidirect
15. #11746902C2semidirect
19. C3×C4×C5×D4C22semidirect
20. C2×#6716C22semidirect
26. C3×#4084C22semidirect
29. C3×#4038C22semidirect
34. C3×#4016C22semidirect
42. C2×D5×C3⋊C8C22semidirect
43. #91094C22semidirect
45. C4⋊(C3⋊#168)C22semidirect
46. C5×#832C22semidirect
48. C5×#807C22semidirect
49. C4×C5×C3⋊C8C22semidirect
50. #90989C22semidirect
51. #90986C22semidirect
52. #90974C22semidirect
53. #90974C22semidirect
59. #90955C22semidirect
61. #65892D3semidirect
137. C4×#213D5semidirect
147. C4×C5×D4C2×D3semidirect
149. #4084C2×D3semidirect
160. #4038C2×D3semidirect
168. #4016C2×D3semidirect
241. C3×C4×D4C2×D5semidirect
257. #832C2×D5semidirect
271. #807C2×D5semidirect
273. C4×C3⋊C8C2×D5semidirect
487. C4×D4D3×D5semidirect
640. C3×C5#3297semidirect
729. C5#83614semidirect
758. C3#10611340semidirect

Maximal subgroups

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

subgroupindex
C3×#658922
#117527402
#117511172
C4×C5×#2132
#117491592
#117491512
#117490462
#117490232
#117474992
D5×#8092
#117471692
#117471662
C3⋊C8×D202
#117469332
#117469022
#106113403
#836145