Finite Group Databasebeta

← #14458950

Subgroups — #14458950

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
1C5×#5514C211yesmaximal, characteristic, complemented
2#11754305C211yesmaximal, characteristic, complemented
3#11751071C211yesmaximal, characteristic, complemented
4C2×C3×#3941C211yesmaximal, characteristic, complemented
5#11748533C211yesmaximal, characteristic, complemented
6#11748510C211yesmaximal, characteristic, complemented
7#67×#168C211yesmaximal, characteristic, complemented
8#11747515C211yesmaximal, characteristic, complemented
9#11747502C211yesmaximal, characteristic, complemented
10#11747375C211yesmaximal, characteristic, complemented
11#11747374C211yesmaximal, characteristic, complemented
12#11747322C211yesmaximal, characteristic, complemented
13#11747319C211yesmaximal, characteristic, complemented
14#11747249C211yesmaximal, characteristic, complemented
15#11747219C211yesmaximal, characteristic, complemented
16#10615345—31nomaximal, Hall
17C22×C3×D20C2211yescharacteristic
18C2×#6765C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20#91813C2211yescharacteristic
21C5×#930—21no—
22C5×#930C2211yescharacteristic
23C4×C5×#67—21no—
24C4×C5×#67C2211yescharacteristic
25C5×#898—21no—
26C5×#895C2211yescharacteristic, complemented
27C5×#894—21no—
28C5×#893C2211yescharacteristic, complemented
29C5×#892C2211yescharacteristic, complemented
30C5×#890C2211yescharacteristic, complemented
31C22×C3×#168C2211yescharacteristic
32#91563—21no—
33D5×#217—21no—
34#91456C2211yescharacteristic
35Dic3×D20C2211yescharacteristic
36#91408—21no—
37#91407—21no—
38#91364C2211yescharacteristic
39C2×#6659C2211yescharacteristic, complemented
40C2×#6652C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91114C2211yescharacteristic
44#91094C2211yescharacteristic, complemented
45#91094C2211yescharacteristic, complemented
46#91091C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C3×#3941C2211yescharacteristic
49C3×#3941C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52#90985C2211yescharacteristic, complemented
53Dic3⋊#168C2211yescharacteristic, complemented
54#90975C2211yescharacteristic, complemented
55#90967C2211yescharacteristic, complemented
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#78760—51nomaximal, Hall
61C5×#553—31no—
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65330—31no—
66#65327—31no—
67#65326—31no—
68#65325—31no—
69#65305—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65259—31no—
75C2×#3941D311yescharacteristic, complemented
76C23×C3×D5—21no—
77C22×C3×C4×C5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×#67D411yescharacteristic
82C2×C5×D12—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3C2311yescharacteristic
86C2×C3×D20—22no—
87C2×C3×D20—21no—
88C2×C3×D20—41no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×D20C2311yescharacteristic
91C2×#1201—21no—
92C2×#1201—21no—
93C2×D5×Dic3—21no—
94C2×D5×Dic3—21no—
95#6765—22no—
96#6765—41no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100#6719—21no—
101C4⋊Dic15C2311yescharacteristic
102#6712—21no—
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×#217D411yescharacteristic
106C5×(C2×D3)⋊C4—21no—
107C5×(C2×D3)⋊C4—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4D411yescharacteristic
111C5×C4⋊Dic3—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C5×Dic3⋊C4D411yescharacteristic
115C4×C5×Dic3—21no—
116C4×C5×Dic3C2311yescharacteristic
117C2×C3×#168—41no—
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120#6665—21no—
121#6665—21no—
122#6665—21no—
123#6665—21no—
124#6659—41no—
125#6652—22no—
126#6652—41no—
127D3×#168—41no—
128#5806—51no—
129#5514D511yescharacteristic, complemented
130C2×C3×#102—51no—
131#5217—51no—
132#5114—51no—
133C8×#67—51no—
134#4970—51no—
135#4787—51no—
136#4781—51no—
137#4779—51no—
138#4775—51no—
139#4772—51no—
140#4768—51no—
141#4763—51no—
142#4756—51no—
143C2×#709—31no—
144C22×D20C2×D311yescharacteristic
145C5×#126—61no—
146C5×#125—31no—
147C5×#123—61no—
148C5×#121—31no—
149C5×#121—31no—
150C5×#121—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C4×C5×D4—61no—
154C5×#117—31no—
155C2×C5×C4⋊C4C2×D311yescharacteristic
156#4083—61no—
157C2×#687—31no—
158C2×#686—31no—
159C2×#686—31no—
160#4076—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168C2×D311yescharacteristic
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021—31no—
168C4×D20—31no—
169#3964—31no—
170C22⋊#168—31no—
171C22⋊#168—31no—
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941C2×D311yescharacteristic
178#3941C2×D311yescharacteristic
179#3941C2×D311yescharacteristic
180#3941C2×D311yescharacteristic
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C5×D3—21no—
189C22×C5×D3C2×D411yescharacteristic
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—42no—
193C22×C3×D5—42no—
194C22×C3×D5—81no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—81no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15—21no—
204Dic30—21no—
205Dic30—21no—
206C5×#67—22no—
207C5×#67—42no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C5×D12—21no—
213C5×D12—21no—
214C5×D12—81no—
215C4×C5×D3—21no—
216C4×C5×D3—21no—
217C4×C5×D3—81no—
218C3×D20—21no—
219C3×D20—21no—
220C3×D20—21no—
221C3×D20—42no—
222C3×D20#4112yes—
223#1201—42no—
224#1201—81no—
225D5×Dic3—42no—
226D5×Dic3—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C22×C3×D4—51no—
232C2×#237—51no—
233C22×C3×C8—51no—
234C2×C3×C4⋊C4C2×D511yescharacteristic
235#953—101no—
236C2×#217—101no—
237#939—101no—
238#938—51no—
239#936—51no—
240#935—101no—
241D4×Dic3—51no—
242C2×#213—51no—
243C2×#213—51no—
244#930—21no—
245#930C2×D511yescharacteristic
246C4×#67—21no—
247C4×#67C2×D511yescharacteristic
248#924—51no—
249C2×#204—51no—
250C2×D3×C8—51no—
251#898—21no—
252#895C2×D511yescharacteristic, complemented
253#894—21no—
254#893C2×D511yescharacteristic, complemented
255#892C2×D511yescharacteristic, complemented
256#890C2×D511yescharacteristic, complemented
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261#832—51no—
262#832—51no—
263#830—51no—
264#821—51no—
265(C2×D3)⋊C8—51no—
266#817—51no—
267#816—51no—
268Dic3⋊C8—51no—
269C8×Dic3—51no—
270#810—51no—
271#810—51no—
272#807—51no—
273#807—51no—
274C23×D5—21no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
279C22×C4×C5—21no—
280C22×C4×C5—31no—
281C22×C4×C5—61no—
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—61no—
284C2×C22⋊D5—61no—
285#709—62no—
286#709—121no—
287C2×D20—22no—
288C2×D20—21no—
289C2×D20—41no—
290C2×D20C22×D311yescharacteristic
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×Dic10—31no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—31no—
303C5×C22⋊C4—31no—
304C5×C22⋊C4—61no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4—61no—
307C5×C22⋊C4—61no—
308C42×C5—31no—
309C42×C5—61no—
310C22⋊Dic5—61no—
311#687—121no—
312#686—62no—
313#686—121no—
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—31no—
319#683—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—41no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—31no—
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×D4—151no—
339#416—151no—
340C2×#102—51no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5#13512yes—
344C22×C3×C5C22×D411yescharacteristic
345C2×C5×D3—21no—
346C2×C5×D3—21no—
347C2×C5×D3—21no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C3×D5—22no—
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—
365C5×Dic3—21no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—41no—
369C24×C3—101no—
370C2×C3×D4—51no—
371C2×C3×D4—51no—
372C2×C3×D4—102no—
373C2×C3×D4—101no—
374C2×C3×D4—201no—
375C22×C3×C4—21no—
376C22×C3×C4C22×D511yescharacteristic
377C2×#67—21no—
378C2×#67—101no—
379C2×#67—101no—
380C2×#67C22⋊D511yescharacteristic
381C22×Dic3—101no—
382C22×Dic3—101no—
383#237—102no—
384#237—201no—
385C2×D12—21no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3C22×D511yescharacteristic
389C2×Dic6—51no—
390C2×C3×C8—51no—
391C2×C3×C8—51no—
392C2×C3×C8—201no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C4⋊C4C22×D511yescharacteristic
396#217—101no—
397#217—101no—
398#217—101no—
399#217—101no—
400#217—101no—
401#217C22⋊D511yescharacteristic
402#213—102no—
403#213—201no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4C22⋊D511yescharacteristic
409C4⋊Dic3—21no—
410C4⋊Dic3—51no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—21no—
413Dic3⋊C4—101no—
414Dic3⋊C4C22⋊D511yescharacteristic
415C4×Dic3—21no—
416C4×Dic3C22×D511yescharacteristic
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
419#204—201no—
420D3×C8—201no—
421C23×C5—31no—
422C23×C5—61no—
423C23×C5D3×D411yescharacteristic
424C22×D5—21no—
425C22×D5—21no—
426C22×D5—42no—
427C22×D5—42no—
428C22×D5—81no—
429C5×D4—62no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—122no—
433C5×D4—241no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—31no—
439C2×C4×C5—31no—
440C2×C4×C5—31no—
441C2×C4×C5—61no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—81no—
445C2×C4×C5—241no—
446C2×C4×C5D3×D411yescharacteristic
447C2×C4×C5C23×D311yescharacteristic
448C22⋊D5—122no—
449C22⋊D5—241no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452D20—21no—
453D20—21no—
454D20—21no—
455D20—42no—
456D20#23512yes—
457C4×D5—122no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—151no—
466C22×D4—51no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—51no—
471C22×C8—151no—
472#126—61no—
473#125—31no—
474#124—151no—
475#123—61no—
476#123—301no—
477C22⋊Q8—151no—
478#121—31no—
479#121—31no—
480#121—61no—
481#121—151no—
482#121—301no—
483#120—301no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—61no—
487C4×D4—151no—
488#117—31no—
489C2×C4⋊C4D3×D511yescharacteristic
490C2×C22⋊C4—301no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—51no—
499#102—51no—
500#102—51no—
501#102—51no—
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—42no—
513C3×D5—81no—
514C5×D3—41no—
515C5×D3—81no—
516C23×C3—101no—
517C23×C3—101no—
518C23×C3—202no—
519C23×C3—202no—
520C23×C3—401no—
521C23×C3C2×C22⋊D511yescharacteristic
522C22×D3—21no—
523C22×D3C2×C22⋊D511yescharacteristic
524C3×D4—52no—
525C3×D4—101no—
526C3×D4—101no—
527C3×D4—101no—
528C3×D4—202no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—81no—
534C2×C3×C4C2×C22⋊D511yescharacteristic
535C2×C3×C4C23×D511yescharacteristic
536#67—22no—
537#67—42no—
538#67—202no—
539#67—401no—
540C2×Dic3—21no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—202no—
544C2×Dic3—401no—
545C2×Dic3C2×C22⋊D511yescharacteristic
546C2×Dic3C2×C22⋊D511yescharacteristic
547C2×Dic3C2×C22⋊D511yescharacteristic
548D12—21no—
549D12—21no—
550D12—81no—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—81no—
554Dic6—101no—
555Dic6—101no—
556C3×C8—101no—
557C3×C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—61no—
563C22×C5—61no—
564C22×C5—61no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5#91612yes—
569C22×C5C2×D3×D411yescharacteristic
570C2×D5—22no—
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—61no—
581C4×C5—61no—
582C4×C5—61no—
583C4×C5—121no—
584C4×C5C2×#23511yescharacteristic
585C4×C5#100411yescharacteristic
586Dic5—121no—
587Dic5—121no—
588C24—101no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—51no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—102no—
599C2×D4—101no—
600C2×D4—201no—
601C2×D4—301no—
602C2×D4—301no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—201no—
617C2×C8—601no—
618C4⋊C4—21no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—151no—
624C4⋊C4—301no—
625C4⋊C4C2×D3×D511yescharacteristic
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—31no—
639C42—61no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—102no—
644C22×C3—201no—
645C22×C3—201no—
646C22×C3—201no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—404no—
650C22×C3#409612yes—
651C22×C3C22×C22⋊D511yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4D5×#4111yescharacteristic
662C3×C4#414911yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—121no—
671C2×C5—241no—
672C2×C5#549011yescharacteristic
673C2×C5#575711yescharacteristic
674C2×C5C2×#91611yescharacteristic
675D5—42no—
676D5—81no—
677C23—31no—
678C23—61no—
679C23—101no—
680C23—101no—
681C23—202no—
682C23—202no—
683C23—401no—
684C23D3×C22⋊D511yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—52no—
688D4—62no—
689D4—61no—
690D4—61no—
691D4—101no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—202no—
696D4—241no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—81no—
710C2×C4—241no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—602no—
714C2×C4—1201no—
715C2×C4D3×C22⋊D511yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—202no—
723C2×C3—401no—
724C2×C3C2×#409611yescharacteristic
725C2×C3#6616311yescharacteristic
726C2×C3#6616911yescharacteristic
727D3—41no—
728D3—81no—
729C5#7876011yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—102no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—404no—
745C22#9151712yes—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4—601no—
755C4—601no—
756C4D5×#23511yescharacteristic
757C4#9201711yescharacteristic
758C3#1061534511yescharacteristic, complemented, Sylow
759C2—22no—
760C2—121no—
761C2—202no—
762C2—241no—
763C2—401no—
764C2#1175465011yescharacteristic
765C2#1175469711yescharacteristic
766C2C2×#9151711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#5514C2semidirect
2. #11754305C2semidirect
3. #11751071C2semidirect
4. C2×C3×#3941C2semidirect
5. #11748533C2semidirect
6. #11748510C2semidirect
7. #67×#168C2semidirect
8. #11747515C2semidirect
9. #11747502C2semidirect
10. #11747375C2semidirect
11. #11747374C2semidirect
12. #11747322C2semidirect
13. #11747319C2semidirect
14. #11747249C2semidirect
15. #11747219C2semidirect
26. C5×#895C22semidirect
28. C5×#893C22semidirect
29. C5×#892C22semidirect
30. C5×#890C22semidirect
39. C2×#6659C22semidirect
42. C2×D3×#168C22semidirect
44. #91094C22semidirect
45. #91094C22semidirect
46. #91091C22semidirect
47. #91091C22semidirect
52. #90985C22semidirect
53. Dic3⋊#168C22semidirect
54. #90975C22semidirect
55. #90967C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
75. C2×#3941D3semidirect
129. #5514D5semidirect
252. #895C2×D5semidirect
254. #893C2×D5semidirect
255. #892C2×D5semidirect
256. #890C2×D5semidirect
640. C3×C5#3297semidirect
729. C5#78760semidirect
758. C3#10615345semidirect

Maximal subgroups

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

subgroupindex
C5×#55142
#117543052
#117510712
C2×C3×#39412
#117485332
#117485102
#67×#1682
#117475152
#117475022
#117473752
#117473742
#117473222
#117473192
#117472492
#117472192
#106153453
#787605