Finite Group Databasebeta

← #14458913

Subgroups — #14458913

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#11754665C211yesmaximal, characteristic, complemented
2#11754406C211yesmaximal, characteristic, complemented
3#11751214C211yesmaximal, characteristic, complemented
4C5×#5115C211yesmaximal, characteristic, complemented
5C3×C8×C22⋊D5C211yesmaximal, characteristic, complemented
6#11748526C211yesmaximal, characteristic, complemented
7#11748378C211yesmaximal, characteristic, complemented
8#11748116C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic, complemented
10#11747963C211yesmaximal, characteristic, complemented
11#11747892C211yesmaximal, characteristic, complemented
12#11747780C211yesmaximal, characteristic, complemented
13#11747777C211yesmaximal, characteristic, complemented
14#11747745C211yesmaximal, characteristic, complemented
15#11747620C211yesmaximal, characteristic, complemented
16#10612456—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C22×C3×C5×C8C2211yescharacteristic, complemented
20#91815C2211yescharacteristic, complemented
21C5×#930C2211yescharacteristic
22C5×#930C2211yescharacteristic, complemented
23C2×C5×D24C2211yescharacteristic
24C3×C4×C22⋊D5C2211yescharacteristic
25C2×C3×C8×D5C2211yescharacteristic
26#91577—21no—
27#91557—21no—
28#91555—21no—
29#91549—21no—
30#91473—21no—
31#91449C2211yescharacteristic
32#91442—21no—
33#91418C2211yescharacteristic
34Dic5×D12C2211yescharacteristic, complemented
35D5×C4⋊Dic3C2211yescharacteristic
36#91388C2211yescharacteristic, complemented
37#91373C2211yescharacteristic
38#91367—21no—
39#91360C2211yescharacteristic
40#91355—21no—
41C2×#6659C2211yescharacteristic, complemented
42C2×#6654C2211yescharacteristic
43#91105C2211yescharacteristic
44#91105C2211yescharacteristic
45#91100C2211yescharacteristic, complemented
46#91100C2211yescharacteristic, complemented
47C5×#821C2211yescharacteristic
48C5×#821C2211yescharacteristic, complemented
49C5×#818C2211yescharacteristic, complemented
50C3×C22⋊#168C2211yescharacteristic, complemented
51C3×#3952C2211yescharacteristic
52C3×#3946C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55#90985C2211yescharacteristic, complemented
56#90975C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90967C2211yescharacteristic
59#90967C2211yescharacteristic
60#79441—51nomaximal, Hall
61#65948—31no—
62#65946—31no—
63C5×#466—31no—
64#65445—31no—
65#65442—31no—
66#65402—31no—
67C8×C22⋊D5D311yescharacteristic, complemented
68#65326—31no—
69#65324—31no—
70#65180—31no—
71#65173—31no—
72#65067—31no—
73D5×#102—31no—
74#65057—31no—
75#65045—31no—
76C22×D3×D5—21no—
77C22×C3×C4×C5C2311yescharacteristic
78C2×#1220—21no—
79#6817—22no—
80#6817—41no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×Dic30C2311yescharacteristic
84C2×C5×#67—21no—
85C2×C5×#67—21no—
86C2×C5×D12C2311yescharacteristic
87C2×C5×D12C2311yescharacteristic
88C2×C3×C22⋊D5D411yescharacteristic
89C2×C3×C4×D5C2311yescharacteristic
90C2×#1203—21no—
91C2×#1201—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95D5×D12—22no—
96D5×D12—41no—
97C2×C3×C5×C8—41no—
98C2×C3×C5×C8C2311yescharacteristic
99C2×C3×C5×C8C2311yescharacteristic
100#6719—21no—
101C4⋊Dic15C2311yescharacteristic
102C4⋊Dic15C2311yescharacteristic
103C4×Dic15—21no—
104C5×(C2×D3)⋊C4—21no—
105C5×(C2×D3)⋊C4—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C5×C4⋊Dic3C2311yescharacteristic
108C5×D24—41no—
109C3×C22⋊Dic5D411yescharacteristic
110C3×#685D411yescharacteristic
111C3×#683D411yescharacteristic
112C3×C4×Dic5C2311yescharacteristic
113C2×C3×#168C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115C3×C8×D5—41no—
116Dic3⋊Dic5—21no—
117Dic3⋊Dic5—21no—
118#6669—21no—
119#6668—21no—
120#6667—21no—
121(C2×D3)⋊Dic5—21no—
122(C2×D3)⋊Dic5—21no—
123(C2×D3)⋊Dic5—21no—
124(C2×D3)⋊Dic5—21no—
125#6665—21no—
126#6659—41no—
127#6654—22no—
128#5565—51no—
129#5550—51no—
130C3×C8×D4—51no—
131#5115D511yescharacteristic, complemented
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×D4×D5—31no—
144C2×#709—31no—
145C2×C5×D8—31no—
146C22×C5×C8C2×D311yescharacteristic, complemented
147C5×#121—31no—
148C5×#121—31no—
149#4084—31no—
150#4084—61no—
151#4084—61no—
152#4083—61no—
153#4082—31no—
154#4081—61no—
155D4×Dic5—31no—
156C2×#687—31no—
157C2×#686—31no—
158C4×C22⋊D5C2×D311yescharacteristic
159#4072—31no—
160C2×C8×D5C2×D311yescharacteristic
161#4043—31no—
162#4039—31no—
163D5×C4⋊C4—31no—
164#4036—31no—
165#4029—61no—
166#4027—61no—
167D5×C22⋊C4—61no—
168#4025—61no—
169C5×#107—31no—
170C5×#102—31no—
171C5×#102—31no—
172#3964—31no—
173#3964—31no—
174C22⋊#168C2×D311yescharacteristic, complemented
175#3953—31no—
176#3953—31no—
177#3952C2×D311yescharacteristic
178#3948—31no—
179#3948—31no—
180#3946C2×D311yescharacteristic, complemented
181C8×Dic5C2×D311yescharacteristic, complemented
182#3942—31no—
183#3941—31no—
184#3940—31no—
185#3939—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×D15—21no—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C3×D5C2×D411yescharacteristic
192C2×D3×D5—42no—
193C2×D3×D5—42no—
194C2×D3×D5—81no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2411yescharacteristic
199#1220—42no—
200C2×Dic15—21no—
201C2×Dic15—21no—
202C2×Dic15—21no—
203D60—21no—
204D60#4112yes—
205C4×D15—42no—
206Dic30—21no—
207Dic30—21no—
208C5×#67—81no—
209C5×#67—81no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C5×D12—21no—
213C5×D12—21no—
214C5×D12—21no—
215C5×D12—21no—
216C3×C22⋊D5—22no—
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C2×C3×Dic5C2×D411yescharacteristic
220C3×C4×D5—21no—
221C3×C4×D5—21no—
222#1203—42no—
223#1201—42no—
224#1200—81no—
225D3×Dic5—81no—
226D5×Dic3—81no—
227C3×C5×C8—21no—
228C3×C5×C8—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#235—51no—
232C22×D12—51no—
233C22×C3×C8—51no—
234C22×C3×C8C2×D511yescharacteristic, complemented
235C3×C4×D4—51no—
236#939—101no—
237#937—101no—
238#930—51no—
239#930C2×D511yescharacteristic
240#930C2×D511yescharacteristic, complemented
241#926—51no—
242C2×C4⋊Dic3—51no—
243#924—51no—
244C2×D24—51no—
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⋊C8—51no—
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, complemented
268#818—51no—
269#818C2×D511yescharacteristic, complemented
270#817—51no—
271#816—51no—
272#816—51no—
273#816—51no—
274C23×D5—61no—
275C2×C5×D4—31no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4—61no—
279C22×C4×C5C22×D311yescharacteristic
280C2×C22⋊D5—61no—
281C2×C22⋊D5—61no—
282C2×C22⋊D5—61no—
283C2×C22⋊D5D1211yescharacteristic
284C22×Dic5—61no—
285D4×D5—62no—
286D4×D5—121no—
287#709—62no—
288#709—121no—
289C2×D20—31no—
290C2×C4×D5—61no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5C22×D311yescharacteristic
294C2×Dic10—31no—
295C5×D8—121no—
296C2×C5×C8—41no—
297C2×C5×C8C22×D311yescharacteristic
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4—31no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C22⋊Dic5—61no—
304C22⋊Dic5—61no—
305C22⋊Dic5—61no—
306C22⋊Dic5—61no—
307C22⋊Dic5—61no—
308C22⋊Dic5D1211yescharacteristic
309#687—121no—
310#686—62no—
311#685—61no—
312#685—61no—
313#685D1211yescharacteristic
314C4⋊Dic5—31no—
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317C4⋊Dic5—61no—
318#683—61no—
319#683—61no—
320#683D1211yescharacteristic
321C4×Dic5—61no—
322C4×Dic5C22×D311yescharacteristic
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—31no—
333#465—151no—
334#463—151no—
335#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4—51no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—41no—
347C2×D15—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×C3×D5—21no—
355C2×C3×D5—21no—
356C2×C3×D5#13512yes—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5C2×#4111yescharacteristic
360C3×C4×C5H(5,𝔽2)11yescharacteristic
361Dic15—41no—
362Dic15—41no—
363Dic15—41no—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C5×Dic3—41no—
368C5×Dic3—41no—
369C23×D3—101no—
370C2×C3×D4—51no—
371C22×C3×C4—51no—
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—101no—
376C2×#67—101no—
377C22×Dic3—101no—
378#235—102no—
379#235—201no—
380C2×D12—51no—
381C2×D12—102no—
382C2×D12—101no—
383C2×D12—201no—
384C2×D12C22×D511yescharacteristic
385C2×D12C22×D511yescharacteristic
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C2×C3×C8—41no—
391C2×C3×C8—51no—
392C2×C3×C8—51no—
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—21no—
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—101no—
412C4⋊Dic3C22×D511yescharacteristic
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—101no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—101no—
418D24—41no—
419D24—102no—
420#204—201no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5C2×D1211yescharacteristic
424C22×D5—61no—
425C22×D5—122no—
426C22×D5—122no—
427C22×D5—241no—
428C22×D5C2×D1211yescharacteristic
429C5×D4—61no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—61no—
433C5×D4—241no—
434C5×D4—241no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—61no—
438C2×C4×C5—61no—
439C2×C4×C5C2×D1211yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—22no—
442C22⋊D5—122no—
443C22⋊D5—122no—
444C22⋊D5—122no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—241no—
449C2×Dic5C2×D1211yescharacteristic
450C2×Dic5C2×D1211yescharacteristic
451C2×Dic5C2×D1211yescharacteristic
452D20—32no—
453D20—61no—
454C4×D5—21no—
455C4×D5—21no—
456C4×D5—122no—
457C4×D5—241no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461C5×C8—21no—
462C5×C8—21no—
463#168—21no—
464#168—21no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—31no—
469C2×D8—151no—
470C22×C8—51no—
471C22×C8D3×D511yescharacteristic, complemented
472#126—301no—
473#125—151no—
474#124—151no—
475#123—301no—
476#123—301no—
477C22⋊Q8—151no—
478#121—31no—
479#121—31no—
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—31no—
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⋊C8—51no—
507C4×C8—51no—
508C2×C3×C5—41no—
509C2×C3×C5#54611yescharacteristic
510C2×C3×C5C2×#13511yescharacteristic
511C2×C3×C5#57611yescharacteristic
512D15—42no—
513C3×D5—22no—
514C5×D3—81no—
515C5×D3—81no—
516C23×C3—51no—
517C23×C3D4×D511yescharacteristic
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
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—81no—
535#67—81no—
536#67—202no—
537#67—202no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—401no—
544D12—21no—
545D12—21no—
546D12—21no—
547D12—21no—
548D12—52no—
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—101no—
559C3×C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—121no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5C22×D1211yescharacteristic
570C2×D5—21no—
571C2×D5—21no—
572C2×D5—62no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—244no—
576C2×D5#90412yes—
577C4×C5—21no—
578C4×C5—121no—
579C4×C5—121no—
580C4×C5#100411yescharacteristic
581C4×C5D3×#4111yescharacteristic
582Dic5—21no—
583Dic5—21no—
584Dic5—21no—
585Dic5—121no—
586Dic5—121no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—151no—
598C2×D4—301no—
599C2×D4—302no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4—601no—
603C22×C4—51no—
604C22×C4—301no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—121no—
611D8—302no—
612C2×C8—41no—
613C2×C8—51no—
614C2×C8—51no—
615C2×C8—201no—
616C2×C8C2×D3×D511yescharacteristic
617C2×C8C2×D3×D511yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—51no—
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—61no—
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—21no—
644C22×C3—52no—
645C22×C3—101no—
646C22×C3—101no—
647C22×C3C2×D4×D511yescharacteristic
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—102no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—101no—
660C3×C4—101no—
661C3×C4—101no—
662C3×C4#414411yescharacteristic
663C3×C4D5×#4111yescharacteristic
664Dic3—41no—
665Dic3—41no—
666Dic3—201no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—41no—
670C2×C5—241no—
671C2×C5—241no—
672C2×C5#555411yescharacteristic
673C2×C5C2×#90411yescharacteristic
674C2×C5#575211yescharacteristic
675D5—22no—
676D5—122no—
677C23—51no—
678C23—61no—
679C23—61no—
680C23—301no—
681C23—602no—
682C23—602no—
683C23—1201no—
684C23D5×D1211yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—61no—
688D4—61no—
689D4—61no—
690D4—61no—
691D4—102no—
692D4—152no—
693D4—241no—
694D4—241no—
695D4—301no—
696D4—602no—
697D4—602no—
698D4—602no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—51no—
702C2×C4—51no—
703C2×C4—51no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—101no—
707C2×C4—101no—
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—41no—
722C2×C3—102no—
723C2×C3#6594411yescharacteristic
724C2×C3#6609111yescharacteristic
725C2×C3D5×#13511yescharacteristic
726D3—81no—
727D3—81no—
728D3—202no—
729C5#7944111yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—52no—
734C22—101no—
735C22—101no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—302no—
743C22—601no—
744C22—601no—
745C22—1204no—
746C22C2×D5×D1211yescharacteristic
747C4—21no—
748C4—101no—
749C4—101no—
750C4—101no—
751C4—121no—
752C4—121no—
753C4—601no—
754C4—601no—
755C4—601no—
756C4#9201611yescharacteristic
757C4#9204911yescharacteristic
758C3#1061245611yescharacteristic, complemented, Sylow
759C2—41no—
760C2—102no—
761C2—241no—
762C2—241no—
763C2—602no—
764C2D5×#90411yescharacteristic
765C2#1175396111yescharacteristic
766C2#1175464811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×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. #11754665C2semidirect
2. #11754406C2semidirect
3. #11751214C2semidirect
4. C5×#5115C2semidirect
5. C3×C8×C22⋊D5C2semidirect
6. #11748526C2semidirect
7. #11748378C2semidirect
8. #11748116C2semidirect
9. D5×#821C2semidirect
10. #11747963C2semidirect
11. #11747892C2semidirect
12. #11747780C2semidirect
13. #11747777C2semidirect
14. #11747745C2semidirect
15. #11747620C2semidirect
19. C22×C3×C5×C8C22semidirect
20. #91815C22semidirect
22. C5×#930C22semidirect
34. Dic5×D12C22semidirect
36. #91388C22semidirect
41. C2×#6659C22semidirect
45. #91100C22semidirect
46. #91100C22semidirect
48. C5×#821C22semidirect
49. C5×#818C22semidirect
50. C3×C22⋊#168C22semidirect
52. C3×#3946C22semidirect
53. C3×C8×Dic5C22semidirect
54. #90988C22semidirect
55. #90985C22semidirect
56. #90975C22semidirect
67. C8×C22⋊D5D3semidirect
131. #5115D5semidirect
146. C22×C5×C8C2×D3semidirect
174. C22⋊#168C2×D3semidirect
180. #3946C2×D3semidirect
181. C8×Dic5C2×D3semidirect
234. C22×C3×C8C2×D5semidirect
240. #930C2×D5semidirect
267. #821C2×D5semidirect
269. #818C2×D5semidirect
471. C22×C8D3×D5semidirect
640. C3×C5#3297semidirect
729. C5#79441semidirect
758. C3#10612456semidirect

Maximal subgroups

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

subgroupindex
#117546652
#117544062
#117512142
C5×#51152
C3×C8×C22⋊D52
#117485262
#117483782
#117481162
D5×#8212
#117479632
#117478922
#117477802
#117477772
#117477452
#117476202
#106124563
#794415