Finite Group Databasebeta

← #14458988

Subgroups — #14458988

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#11754608C211yesmaximal, characteristic, complemented
2#11754540C211yesmaximal, characteristic, complemented
3#11750823C211yesmaximal, characteristic, complemented
4C5×#4732C211yesmaximal, characteristic, complemented
5C3×#65014C211yesmaximal, characteristic, complemented
6#11748533C211yesmaximal, characteristic, complemented
7C2×#90967C211yesmaximal, characteristic, complemented
8#11748156C211yesmaximal, characteristic, complemented
9#11748135C211yesmaximal, characteristic, complemented
10#11747963C211yesmaximal, characteristic, complemented
11#11747903C211yesmaximal, characteristic, complemented
12#11747898C211yesmaximal, characteristic, complemented
13#11747777C211yesmaximal, characteristic, complemented
14#11747771C211yesmaximal, characteristic, complemented
15Dic5×D24C211yesmaximal, characteristic, complemented
16#10611746—31nomaximal, Hall
17C22×C5×D12C2211yescharacteristic
18C2×#6772C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20#91813C2211yescharacteristic
21C5×#930C2211yescharacteristic
22C2×C5×D24C2211yescharacteristic
23C2×C5×D24C2211yescharacteristic
24C3×C4×C22⋊D5C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26C2×C3×C8×D5C2211yescharacteristic, complemented
27#91571—21no—
28#91568—21no—
29#67⋊Dic5—21no—
30D3×C22⋊Dic5—21no—
31#91457—21no—
32#91453—21no—
33#91449C2211yescharacteristic
34#91449C2211yescharacteristic, complemented
35#91423—21no—
36Dic5×D12C2211yescharacteristic
37Dic5×D12C2211yescharacteristic, complemented
38#91388C2211yescharacteristic, complemented
39#91373C2211yescharacteristic
40#91358C2211yescharacteristic, complemented
41#91342—21no—
42C2×#6659C2211yescharacteristic, complemented
43C3×C5×C22⋊C8C2211yescharacteristic
44#91102C2211yescharacteristic, complemented
45#91102C2211yescharacteristic, complemented
46#91100C2211yescharacteristic, complemented
47#91100C2211yescharacteristic, complemented
48C5×#821C2211yescharacteristic
49C5×#821C2211yescharacteristic
50C3×#3952C2211yescharacteristic, complemented
51C3×#3946C2211yescharacteristic, complemented
52C3×C8×Dic5C2211yescharacteristic, complemented
53#90985C2211yescharacteristic, complemented
54#90975C2211yescharacteristic, complemented
55#90967C2211yescharacteristic
56#90967C2211yescharacteristic
57#90967C2211yescharacteristic
58#90967C2211yescharacteristic
59#90967C2211yescharacteristic, complemented
60#79441—51nomaximal, Hall
61#66140—31no—
62#65952—31no—
63C5×#447—31no—
64C2×#3964—31no—
65#65447—31no—
66#65446—31no—
67#65442—31no—
68D8×Dic5—31no—
69#65330—31no—
70#65073—31no—
71#65061—31no—
72#65057—31no—
73#65055—31no—
74#65014D311yescharacteristic, complemented
75#65011—31no—
76C23×C5×D3—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C22×Dic15—21no—
79C2×Dic30C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×D12—22no—
82C2×C5×D12—21no—
83C2×C5×D12—41no—
84C2×C5×D12C2311yescharacteristic
85C2×C5×D12C2311yescharacteristic
86C2×C5×D12C2311yescharacteristic
87C2×C3×C22⋊D5D411yescharacteristic
88C2×C3×C4×D5C2311yescharacteristic
89C2×#1201—21no—
90C2×#1201—21no—
91C2×#1201—21no—
92C2×D3×Dic5—21no—
93C2×D3×Dic5—21no—
94C2×D3×Dic5—21no—
95#6772—22no—
96#6772—41no—
97C2×C3×C5×C8C2311yescharacteristic
98C2×C3×C5×C8C2311yescharacteristic
99#6719—21no—
100C4⋊Dic15—21no—
101C4⋊Dic15C2311yescharacteristic
102C4⋊Dic15C2311yescharacteristic
103C4⋊Dic15C2311yescharacteristic
104#6712—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C5×D24—22no—
108C5×D24—41no—
109C3×C22⋊Dic5D411yescharacteristic
110C3×#685D411yescharacteristic
111C3×#683D411yescharacteristic
112C3×C4×Dic5C2311yescharacteristic
113C2×C3×#168—41no—
114C2×C3×#168C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116C3×C8×D5—41no—
117Dic3⋊Dic5—21no—
118#6669—21no—
119(C2×D3)⋊Dic5—21no—
120(C2×D3)⋊Dic5—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5—21no—
124(C2×D3)⋊Dic5—21no—
125#6665—21no—
126Dic3×Dic5—21no—
127#6659—41no—
128#5565—51no—
129#5550—51no—
130C3×C8×D4—51no—
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#4732D511yescharacteristic, complemented
140#4722—51no—
141#4697—51no—
142C4×D24—51no—
143C22×C5×D4—31no—
144C2×#711—31no—
145C2×C5×D8—31no—
146C2×C5×D8—31no—
147C5×#121—31no—
148#4099—61no—
149C2×C22⋊Dic5—61no—
150#4085—61no—
151#4085—61no—
152#4084—31no—
153#4084—31no—
154#4082—31no—
155#4081—61no—
156D4×Dic5—31no—
157D4×Dic5—31no—
158D4×Dic5—61no—
159C2×#687—31no—
160C4×C22⋊D5C2×D311yescharacteristic
161C2×C4⋊Dic5—31no—
162#4070—31no—
163C22×#168C2×D311yescharacteristic
164C2×C8×D5C2×D311yescharacteristic, complemented
165#4038—31no—
166#4036—31no—
167#4032—61no—
168#4025—61no—
169C5×#102—31no—
170C5×#102—31no—
171C5×C22⋊C8C2×D311yescharacteristic
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3952C2×D311yescharacteristic, complemented
178#3950—31no—
179#3950—31no—
180#3948—31no—
181#3948—31no—
182#3946C2×D311yescharacteristic, complemented
183C8×Dic5C2×D311yescharacteristic, complemented
184#3942—31no—
185#3940—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C5×D3—21no—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—42no—
192C22×C5×D3—42no—
193C22×C5×D3—81no—
194C22×C3×D5C2×D411yescharacteristic
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—81no—
204Dic30—21no—
205Dic30—21no—
206C5×#67—42no—
207C2×C5×Dic3—21no—
208C5×D12—21no—
209C5×D12—21no—
210C5×D12—21no—
211C5×D12—21no—
212C5×D12—21no—
213C5×D12—42no—
214C5×D12#4112yes—
215C3×C22⋊D5—22no—
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C3×C4×D5—21no—
220C3×C4×D5—21no—
221#1201—42no—
222#1201—81no—
223#1201—81no—
224D3×Dic5—42no—
225D3×Dic5—81no—
226D3×Dic5—81no—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#235—51no—
232C22×D12C2×D511yescharacteristic
233C22×C3×C8—51no—
234C22×C3×C8—51no—
235C3×C4×D4—51no—
236#939—101no—
237#937—101no—
238#930—51no—
239#930—51no—
240#930C2×D511yescharacteristic
241#926—51no—
242C2×C4⋊Dic3—51no—
243#924—51no—
244C2×D24C2×D511yescharacteristic
245C2×D24C2×D511yescharacteristic
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⋊C8—51no—
258C3×C22⋊C8—51no—
259C3×C22⋊C8C2×D511yescharacteristic
260C3×C4×C8—51no—
261#821—51no—
262#821—51no—
263#821—51no—
264#821—51no—
265#821—51no—
266#821C2×D511yescharacteristic
267#821C2×D511yescharacteristic
268#818—51no—
269#818—51no—
270#817—51no—
271#816—51no—
272#816—51no—
273#816—51no—
274C24×C5—61no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—31no—
278C2×C5×D4—62no—
279C2×C5×D4—61no—
280C2×C5×D4—61no—
281C2×C5×D4—121no—
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—61no—
284C2×C22⋊D5—61no—
285C2×C22⋊D5—61no—
286C2×C22⋊D5D1211yescharacteristic
287C22×Dic5—61no—
288C22×Dic5—61no—
289C22×Dic5—61no—
290C22×Dic5—61no—
291#711—62no—
292#711—121no—
293C2×C4×D5C22×D311yescharacteristic
294C2×Dic10—31no—
295C5×D8—62no—
296C5×D8—121no—
297C2×C5×C8C22×D311yescharacteristic
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C22⋊C4—61no—
301C22⋊Dic5—61no—
302C22⋊Dic5—61no—
303C22⋊Dic5—61no—
304C22⋊Dic5—61no—
305C22⋊Dic5—61no—
306C22⋊Dic5—61no—
307C22⋊Dic5—61no—
308C22⋊Dic5D1211yescharacteristic
309#687—121no—
310#685—61no—
311#685D1211yescharacteristic
312C4⋊Dic5—31no—
313C4⋊Dic5—31no—
314C4⋊Dic5—31no—
315C4⋊Dic5—61no—
316C4⋊Dic5—61no—
317#683—61no—
318#683—61no—
319#683D1211yescharacteristic
320C4×Dic5—61no—
321C4×Dic5C22×D311yescharacteristic
322C2×#168—41no—
323C2×#168C22×D311yescharacteristic
324C2×#168C22×D311yescharacteristic
325C8×D5—41no—
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—31no—
337C4×D8—151no—
338C8×D4—51no—
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—22no—
346C2×C5×D3—41no—
347C2×C5×D3—41no—
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C5×D3—41no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C5×D3—84no—
355C2×C3×D5—21no—
356C2×C3×D5—21no—
357C2×C3×D5—21no—
358C3×C4×C5—21no—
359C3×C4×C5C2×#4111yescharacteristic
360C3×C4×C5H(5,𝔽2)11yescharacteristic
361Dic15—41no—
362Dic15—41no—
363Dic15—41no—
364Dic15—41no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—21no—
368C5×Dic3—41no—
369C23×D3—21no—
370C2×C3×D4—51no—
371C22×C3×C4—51no—
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—21no—
374C2×#67—101no—
375C2×#67—101no—
376C2×#67—101no—
377C22×Dic3—101no—
378#235—102no—
379#235—201no—
380C2×D12—22no—
381C2×D12—21no—
382C2×D12—41no—
383C2×D12C22×D511yescharacteristic
384C2×D12C22×D511yescharacteristic
385C2×D12C22×D511yescharacteristic
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C2×C3×C8—51no—
391C2×C3×C8—51no—
392C2×C3×C8—201no—
393C2×C3×C8—201no—
394C2×C3×C8C22×D511yescharacteristic
395C2×C3×C8C22×D511yescharacteristic
396C3×C4⋊C4—51no—
397C3×C22⋊C4—51no—
398C3×C22⋊C4—51no—
399C3×C42—51no—
400#217—101no—
401#217—101no—
402(C2×D3)⋊C4—21no—
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—101no—
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—101no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—101no—
418D24—22no—
419D24—41no—
420#204—201no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—61no—
424C23×C5—122no—
425C23×C5—122no—
426C23×C5—241no—
427C23×C5C2×D1211yescharacteristic
428C22×D5C2×D1211yescharacteristic
429C5×D4—32no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—61no—
433C5×D4—61no—
434C5×D4—61no—
435C5×D4—122no—
436C5×D4—122no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—61no—
440C2×C4×C5C2×D1211yescharacteristic
441C2×C4×C5C23×D311yescharacteristic
442C22⋊D5—22no—
443C22⋊D5—122no—
444C22⋊D5—241no—
445C22⋊D5—241no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—122no—
451C2×Dic5—241no—
452C2×Dic5—241no—
453C2×Dic5—241no—
454C2×Dic5C2×D1211yescharacteristic
455C2×Dic5C2×D1211yescharacteristic
456C2×Dic5C2×D1211yescharacteristic
457C4×D5—21no—
458C4×D5—21no—
459Dic10—61no—
460Dic10—61no—
461C5×C8—21no—
462C5×C8—21no—
463#168—21no—
464#168—21no—
465C2×#41—151no—
466C22×D4—31no—
467C2×SD16—151no—
468C2×D8—31no—
469C2×D8—31no—
470C22×C8—51no—
471C22×C8—51no—
472#126—301no—
473#125—151no—
474#124—151no—
475#123—301no—
476#123—301no—
477C22⋊Q8—151no—
478#121—31no—
479#121—151no—
480#121—151no—
481#121—301no—
482#121—301no—
483#120—301no—
484C4×D4—51no—
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—51no—
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—51no—
506C22⋊C8D3×D511yescharacteristic
507C4×C8—51no—
508C2×C3×C5—22no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C3×D5—41no—
513C5×D3—42no—
514C5×D3—81no—
515C5×D3—81no—
516C23×C3—51no—
517C23×C3D4×D511yescharacteristic
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—42no—
522C22×D3—42no—
523C22×D3—81no—
524C3×D4—102no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—51no—
528C2×C3×C4—51no—
529C2×C3×C4—51no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4D4×D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—42no—
535#67—202no—
536#67—401no—
537#67—401no—
538C2×Dic3—21no—
539C2×Dic3—101no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—401no—
544D12—21no—
545D12—21no—
546D12—21no—
547D12—21no—
548D12—21no—
549D12—42no—
550D12#71112yes—
551C4×D3—202no—
552C4×D3—401no—
553C4×D3—401no—
554Dic6—101no—
555Dic6—101no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—101no—
559C3×C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—62no—
563C22×C5—121no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5—121no—
571C22×C5—244no—
572C22×C5#90412yes—
573C22×C5C22×D1211yescharacteristic
574C2×D5—21no—
575C2×D5—21no—
576C2×D5—21no—
577C4×C5—21no—
578C4×C5—121no—
579C4×C5#100411yescharacteristic
580C4×C5D3×#4111yescharacteristic
581Dic5—21no—
582Dic5—21no—
583Dic5—21no—
584Dic5—121no—
585Dic5—121no—
586Dic5—121no—
587Dic5—121no—
588C24—61no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—51no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—121no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4—301no—
603C22×C4—51no—
604C22×C4—301no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—62no—
611D8—121no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—201no—
615C2×C8—201no—
616C2×C8C2×D3×D511yescharacteristic
617C2×C8C2×D3×D511yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—51no—
620C4⋊C4—151no—
621C4⋊C4—151no—
622C4⋊C4—151no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4—301no—
627C22⋊C4—51no—
628C22⋊C4—51no—
629C22⋊C4—61no—
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—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#405812yes—
647C22×C3C2×D4×D511yescharacteristic
648C2×D3—22no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C3×C4—21no—
659C3×C4—101no—
660C3×C4—101no—
661C3×C4—101no—
662C3×C4C2×#71111yescharacteristic
663C3×C4#414411yescharacteristic
664Dic3—41no—
665Dic3—201no—
666Dic3—201no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—122no—
671C2×C5—241no—
672C2×C5—241no—
673C2×C5#555411yescharacteristic
674C2×C5C2×#90411yescharacteristic
675C2×C5#575211yescharacteristic
676D5—41no—
677C23—51no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—122no—
682C23—122no—
683C23—241no—
684C23D5×D1211yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—32no—
688D4—61no—
689D4—61no—
690D4—61no—
691D4—61no—
692D4—61no—
693D4—102no—
694D4—122no—
695D4—122no—
696D4—602no—
697D4—1201no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—51no—
702C2×C4—51no—
703C2×C4—51no—
704C2×C4—61no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—301no—
708C2×C4—301no—
709C2×C4—301no—
710C2×C4—301no—
711C2×C4—602no—
712C2×C4—1201no—
713C2×C4—1201no—
714C2×C4—1201no—
715C2×C4D5×D1211yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—21no—
718C8—21no—
719C8—101no—
720C8—101no—
721C2×C3—22no—
722C2×C3—201no—
723C2×C3#6592511yescharacteristic
724C2×C3C2×#405811yescharacteristic
725C2×C3#6610811yescharacteristic
726D3—42no—
727D3—81no—
728D3—81no—
729C5#7944111yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—62no—
733C22—101no—
734C22—101no—
735C22—101no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—244no—
745C22#9127012yes—
746C22C2×D5×D1211yescharacteristic
747C4—21no—
748C4—101no—
749C4—101no—
750C4—101no—
751C4—121no—
752C4—601no—
753C4—601no—
754C4—601no—
755C4—601no—
756C4D3×#71111yescharacteristic
757C4#9202511yescharacteristic
758C3#1061174611yescharacteristic, complemented, Sylow
759C2—22no—
760C2—122no—
761C2—201no—
762C2—241no—
763C2—241no—
764C2#1175326511yescharacteristic
765C2C2×#9127011yescharacteristic
766C2#1175402411yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #11754608C2semidirect
2. #11754540C2semidirect
3. #11750823C2semidirect
4. C5×#4732C2semidirect
5. C3×#65014C2semidirect
6. #11748533C2semidirect
7. C2×#90967C2semidirect
8. #11748156C2semidirect
9. #11748135C2semidirect
10. #11747963C2semidirect
11. #11747903C2semidirect
12. #11747898C2semidirect
13. #11747777C2semidirect
14. #11747771C2semidirect
15. Dic5×D24C2semidirect
26. C2×C3×C8×D5C22semidirect
34. #91449C22semidirect
37. Dic5×D12C22semidirect
38. #91388C22semidirect
40. #91358C22semidirect
42. C2×#6659C22semidirect
44. #91102C22semidirect
45. #91102C22semidirect
46. #91100C22semidirect
47. #91100C22semidirect
50. C3×#3952C22semidirect
51. C3×#3946C22semidirect
52. C3×C8×Dic5C22semidirect
53. #90985C22semidirect
54. #90975C22semidirect
59. #90967C22semidirect
74. #65014D3semidirect
139. #4732D5semidirect
164. C2×C8×D5C2×D3semidirect
177. #3952C2×D3semidirect
182. #3946C2×D3semidirect
183. C8×Dic5C2×D3semidirect
640. C3×C5#3297semidirect
729. C5#79441semidirect
758. C3#10611746semidirect

Maximal subgroups

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

subgroupindex
#117546082
#117545402
#117508232
C5×#47322
C3×#650142
#117485332
C2×#909672
#117481562
#117481352
#117479632
#117479032
#117478982
#117477772
#117477712
Dic5×D242
#106117463
#794415