Finite Group Databasebeta

← #14458983

Subgroups — #14458983

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×#5630C211yesmaximal, characteristic, complemented
2#11754512C211yesmaximal, characteristic, complemented
3#11751145C211yesmaximal, characteristic, complemented
4C3×#65337C211yesmaximal, characteristic, complemented
5#11749281C211yesmaximal, characteristic, complemented
6#11749228C211yesmaximal, characteristic, complemented
7#11749211C211yesmaximal, characteristic, complemented
8#11749188C211yesmaximal, characteristic, complemented
9#11748516C211yesmaximal, characteristic, complemented
10#67×#168C211yesmaximal, characteristic, complemented
11C2×#90967C211yesmaximal, characteristic, complemented
12#11747394C211yesmaximal, characteristic, complemented
13#11747319C211yesmaximal, characteristic, complemented
14#11747219C211yesmaximal, characteristic, complemented
15#11747209C211yesmaximal, characteristic, complemented
16#10615226—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic
20C2×C4⋊Dic15C2211yescharacteristic
21C5×#947C2211yescharacteristic
22C4×C5×#67C2211yescharacteristic
23C5×#895—21no—
24C5×#895C2211yescharacteristic
25C5×#894—21no—
26C5×#893C2211yescharacteristic
27C5×#882—21no—
28C5×D3×C22⋊C4—21no—
29C2×C3×#688C2211yescharacteristic, complemented
30C3×#4076C2211yescharacteristic
31C22×C3×#168C2211yescharacteristic
32#91571—21no—
33#91559—21no—
34#91456C2211yescharacteristic, complemented
35Dic3×D20C2211yescharacteristic, complemented
36#91414—21no—
37#91381C2211yescharacteristic, complemented
38#91362—21no—
39#91338C2211yescharacteristic, complemented
40C2×#6652C2211yescharacteristic
41C2×#6652C2211yescharacteristic
42C2×D3×#168C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91119C2211yescharacteristic, complemented
45#91114C2211yescharacteristic
46#91091C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C3×#3967C2211yescharacteristic, complemented
49C3×#3941C2211yescharacteristic, complemented
50C3×#3940C2211yescharacteristic, complemented
51Dic3⋊#168C2211yescharacteristic, complemented
52#90967C2211yescharacteristic
53#90967C2211yescharacteristic
54#90967C2211yescharacteristic
55#90967C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60#80681—51nomaximal, Hall
61C5×#546—31no—
62#65899—31no—
63#65527—31no—
64#65522—31no—
65#65506—31no—
66C2×#3964—31no—
67#65346—31no—
68#65345—31no—
69#65337D311yescharacteristic, complemented
70#65333—31no—
71#65327—31no—
72#65324—31no—
73C4×#686—31no—
74D4×#168—31no—
75#65298—31no—
76C23×C5×D3—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×Dic15—21no—
80C2×C5×#67D411yescharacteristic
81C5×#239—22no—
82C5×#239—41no—
83C2×C5×D12—22no—
84C2×C5×D12—21no—
85C2×C5×D12—21no—
86C2×C5×D12—21no—
87C2×C5×D12—41no—
88C2×C5×D12C2311yescharacteristic
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3—21no—
91C2×C4×C5×D3—21no—
92C2×C4×C5×D3C2311yescharacteristic
93C2×C3×C22⋊D5—21no—
94C2×C3×D20C2311yescharacteristic
95C2×#1201—21no—
96C2×D5×Dic3—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×#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×Dic3⋊C4D411yescharacteristic
112C4×C5×Dic3C2311yescharacteristic
113C3×#688—41no—
114C3×#685—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C2×C3×#168—41no—
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119#6669—21no—
120#6668—21no—
121(C2×D3)⋊Dic5—21no—
122#6665—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125#6652—22no—
126#6652—41no—
127D3×#168—41no—
128#5630D511yescharacteristic, complemented
129#5618—51no—
130C3×#465—51no—
131#5172—51no—
132#5165—51no—
133C2×#821—51no—
134C8×#67—51no—
135#5044—51no—
136#5036—51no—
137#4871—51no—
138#4866—51no—
139#4804—51no—
140#4800—51no—
141#4775—51no—
142#4756—51no—
143C2×C5×#41—31no—
144C22×C5×D4—31no—
145C5×#124—31no—
146C5×#123—61no—
147C5×C22⋊Q8C2×D311yescharacteristic
148C5×#121—31no—
149C5×#121—61no—
150C5×#120—61no—
151C4×C5×D4—31no—
152C4×C5×D4—31no—
153C2×C5×C22⋊C4—61no—
154C2×#688C2×D311yescharacteristic, complemented
155#4085—61no—
156C2×#686—31no—
157C2×#686—31no—
158#4076—31no—
159#4076C2×D311yescharacteristic
160#4072—31no—
161C2×C4⋊Dic5—31no—
162C22×#168—31no—
163C22×#168C2×D311yescharacteristic
164#4044—61no—
165#4029—61no—
166#4027—61no—
167C4×D20—31no—
168#4016—31no—
169#3967—31no—
170#3967—31no—
171#3967C2×D311yescharacteristic, complemented
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3941C2×D311yescharacteristic, complemented
181#3940C2×D311yescharacteristic, complemented
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×D3—21no—
190C22×C5×D3—42no—
191C22×C5×D3—42no—
192C22×C5×D3—81no—
193C22×C5×D3C2×D411yescharacteristic
194C22×C3×D5—21no—
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—22no—
207C2×C5×Dic3C2×D411yescharacteristic
208C2×C5×Dic3C2×D411yescharacteristic
209C2×C5×Dic3C2×D411yescharacteristic
210C5×D12—21no—
211C5×D12—21no—
212C5×D12—21no—
213C5×D12—42no—
214C5×D12—42no—
215C5×D12—81no—
216C5×D12#4112yes—
217C4×C5×D3—21no—
218C4×C5×D3—21no—
219C4×C5×D3—42no—
220C4×C5×D3—81no—
221C3×C22⋊D5—42no—
222C2×C3×Dic5—21no—
223C3×D20—21no—
224C3×D20—21no—
225#1201—81no—
226D5×Dic3—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#239C2×D511yescharacteristic
232C22×D12C2×D511yescharacteristic
233C2×C3×SD16—51no—
234C22×C3×C8—51no—
235C3×C22⋊Q8C2×D511yescharacteristic
236C3×#121—51no—
237#947C2×D511yescharacteristic
238#939—101no—
239#938—51no—
240D4×Dic3—51no—
241D4×Dic3—101no—
242C2×#213—51no—
243C2×#213—51no—
244C4×#67C2×D511yescharacteristic
245C2×C4⋊Dic3—51no—
246C2×D3×C8—51no—
247#895—21no—
248#895C2×D511yescharacteristic
249#894—21no—
250#893C2×D511yescharacteristic
251#892—51no—
252#890—51no—
253#886—101no—
254#882—21no—
255D3×C22⋊C4—21no—
256#879—101no—
257C3×#106—51no—
258C3×#103—51no—
259C3×#102—51no—
260#835—51no—
261#835—51no—
262#830—51no—
263#821—51no—
264#821—51no—
265#821—51no—
266#821—51no—
267(C2×D3)⋊C8—51no—
268Dic3⋊C8—51no—
269C8×Dic3—51no—
270#809—51no—
271#809—51no—
272#807—51no—
273#807—51no—
274C24×C5—61no—
275C5×#41—62no—
276C5×#41—121no—
277C2×C5×Q8C22×D311yescharacteristic
278C2×C5×D4—31no—
279C2×C5×D4—31no—
280C2×C5×D4—31no—
281C2×C5×D4—62no—
282C2×C5×D4—61no—
283C2×C5×D4—61no—
284C2×C5×D4—61no—
285C2×C5×D4—121no—
286C22×C4×C5—31no—
287C22×C4×C5—61no—
288C22×C4×C5—61no—
289C22×C4×C5C22×D311yescharacteristic
290C2×C22⋊D5—21no—
291C2×C22⋊D5—61no—
292C22×Dic5—61no—
293C2×D20C22×D311yescharacteristic
294C2×C4×D5—61no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4C22×D311yescharacteristic
298C5×C22⋊C4—21no—
299C5×C22⋊C4—31no—
300C5×C22⋊C4—31no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C5×C22⋊C4—61no—
305C42×C5—31no—
306C22⋊Dic5—61no—
307#688—41no—
308#686—62no—
309#686—121no—
310#685—21no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5—31no—
315C4⋊Dic5—61no—
316C4⋊Dic5C22×D311yescharacteristic
317#683—61no—
318#683—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—41no—
323C2×#168—121no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—151no—
327#546—31no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—51no—
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—21no—
346C2×C5×D3—22no—
347C2×C5×D3—21no—
348C2×C5×D3—21no—
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—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
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—41no—
366C5×Dic3—21no—
367C5×Dic3—21no—
368C5×Dic3—21no—
369C23×D3—21no—
370C2×C3×Q8C22×D511yescharacteristic
371C2×C3×D4—51no—
372C2×C3×D4—101no—
373C22×C3×C4C22×D511yescharacteristic
374C2×#67—101no—
375C2×#67C22⋊D511yescharacteristic
376C22×Dic3—101no—
377C22×Dic3—101no—
378#239—22no—
379#239—41no—
380C2×D12—22no—
381C2×D12—21no—
382C2×D12—21no—
383C2×D12—21no—
384C2×D12—41no—
385C2×D12C22×D511yescharacteristic
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×C4×D3C22×D511yescharacteristic
390C3×SD16—201no—
391C2×C3×C8—51no—
392C2×C3×C8—51no—
393C2×C3×C8—201no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—51no—
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—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)⋊C4—101no—
409(C2×D3)⋊C4C22⋊D511yescharacteristic
410C4⋊Dic3—51no—
411C4⋊Dic3—51no—
412C4⋊Dic3—101no—
413C4⋊Dic3—101no—
414Dic3⋊C4—101no—
415Dic3⋊C4C22⋊D511yescharacteristic
416C4×Dic3—101no—
417C4×Dic3C22×D511yescharacteristic
418C2×C3⋊C8—51no—
419C2×C3⋊C8—51no—
420D3×C8—201no—
421C23×C5—31no—
422C23×C5—61no—
423C23×C5—61no—
424C23×C5—122no—
425C23×C5—122no—
426C23×C5—241no—
427C23×C5D3×D411yescharacteristic
428C22×D5—21no—
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—32no—
432C5×D4—62no—
433C5×D4—61no—
434C5×D4—61no—
435C5×D4—61no—
436C5×D4—122no—
437C5×D4—122no—
438C5×D4—241no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—31no—
444C2×C4×C5—31no—
445C2×C4×C5—31no—
446C2×C4×C5—61no—
447C2×C4×C5—61no—
448C2×C4×C5—122no—
449C2×C4×C5—241no—
450C2×C4×C5D3×D411yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—42no—
453C22⋊D5—241no—
454C2×Dic5—21no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458D20—21no—
459D20—21no—
460C4×D5—241no—
461#168—21no—
462#168—21no—
463#168—61no—
464#168—61no—
465C2×#41—31no—
466C22×D4—31no—
467C2×SD16—51no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—51no—
471C22×C8—151no—
472#126—301no—
473#125—151no—
474#124—31no—
475#123—61no—
476#123—301no—
477C22⋊Q8D3×D511yescharacteristic
478#121—31no—
479#121—51no—
480#121—61no—
481#121—151no—
482#121—301no—
483#120—61no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—151no—
487C4×D4—301no—
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—61no—
491#107—151no—
492#107—151no—
493#106—51no—
494C4⋊C8—151no—
495#103—51no—
496#103—151no—
497#103—151no—
498#102—51no—
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—81no—
513C5×D3—41no—
514C5×D3—42no—
515C5×D3—81no—
516C23×C3—101no—
517C23×C3C2×C22⋊D511yescharacteristic
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—81no—
523C22×D3C2×C22⋊D511yescharacteristic
524C3×Q8—21no—
525C3×Q8—21no—
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—101no—
534C2×C3×C4C2×C22⋊D511yescharacteristic
535C2×C3×C4C23×D511yescharacteristic
536#67—22no—
537#67—401no—
538C2×Dic3—101no—
539C2×Dic3—101no—
540C2×Dic3—401no—
541C2×Dic3—401no—
542C2×Dic3C2×C22⋊D511yescharacteristic
543C2×Dic3C2×C22⋊D511yescharacteristic
544C2×Dic3C2×C22⋊D511yescharacteristic
545D12—21no—
546D12—21no—
547D12—21no—
548D12—42no—
549D12—42no—
550D12—81no—
551D12#71112yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—42no—
555C4×D3—81no—
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—62no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5—121no—
571C22×C5—244no—
572C22×C5#91612yes—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—41no—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—41no—
580C4×C5—61no—
581C4×C5—61no—
582C4×C5—61no—
583C4×C5#100411yescharacteristic
584C4×C5D3×#4111yescharacteristic
585Dic5—41no—
586Dic5—121no—
587Dic5—121no—
588C24—61no—
589#41—62no—
590#41—121no—
591C2×Q8C2×D3×D511yescharacteristic
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—51no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—101no—
601C2×D4—121no—
602C2×D4—301no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—201no—
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—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—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—31no—
639C42—301no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—201no—
644C22×C3—201no—
645C22×C3—201no—
646C22×C3#409612yes—
647C22×C3C22×C22⋊D511yescharacteristic
648C2×D3—21no—
649C2×D3—22no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—201no—
662C3×C4C2×#71111yescharacteristic
663C3×C4#414411yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—21no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—121no—
671C2×C5—122no—
672C2×C5—241no—
673C2×C5#561011yescharacteristic
674C2×C5C2×#91611yescharacteristic
675C2×C5#576911yescharacteristic
676D5—81no—
677C23—31no—
678C23—61no—
679C23—61no—
680C23—101no—
681C23—122no—
682C23—122no—
683C23—241no—
684C23D3×C22⋊D511yescharacteristic
685Q8—21no—
686Q8—21no—
687D4—32no—
688D4—62no—
689D4—61no—
690D4—61no—
691D4—61no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—122no—
696D4—202no—
697D4—241no—
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—101no—
709C2×C4—122no—
710C2×C4—241no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—1201no—
714C2×C4—1201no—
715C2×C4D3×C22⋊D511yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—401no—
723C2×C3#6614011yescharacteristic
724C2×C3C2×#409611yescharacteristic
725C2×C3#6616911yescharacteristic
726D3—41no—
727D3—42no—
728D3—81no—
729C5#8068111yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—62no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—244no—
745C22#9151712yes—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—41no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—201no—
754C4—601no—
755C4—601no—
756C4D3×#71111yescharacteristic
757C4#9202511yescharacteristic
758C3#1061522611yescharacteristic, complemented, Sylow
759C2—22no—
760C2—121no—
761C2—122no—
762C2—241no—
763C2—401no—
764C2#1175494211yescharacteristic
765C2C2×#9151711yescharacteristic
766C2#1175532511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
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. C5×#5630C2semidirect
2. #11754512C2semidirect
3. #11751145C2semidirect
4. C3×#65337C2semidirect
5. #11749281C2semidirect
6. #11749228C2semidirect
7. #11749211C2semidirect
8. #11749188C2semidirect
9. #11748516C2semidirect
10. #67×#168C2semidirect
11. C2×#90967C2semidirect
12. #11747394C2semidirect
13. #11747319C2semidirect
14. #11747219C2semidirect
15. #11747209C2semidirect
29. C2×C3×#688C22semidirect
34. #91456C22semidirect
35. Dic3×D20C22semidirect
37. #91381C22semidirect
39. #91338C22semidirect
42. C2×D3×#168C22semidirect
43. #91119C22semidirect
44. #91119C22semidirect
46. #91091C22semidirect
47. #91091C22semidirect
48. C3×#3967C22semidirect
49. C3×#3941C22semidirect
50. C3×#3940C22semidirect
51. Dic3⋊#168C22semidirect
58. (C2×D3)⋊#168C22semidirect
59. Dic3×#168C22semidirect
69. #65337D3semidirect
128. #5630D5semidirect
154. C2×#688C2×D3semidirect
171. #3967C2×D3semidirect
180. #3941C2×D3semidirect
181. #3940C2×D3semidirect
640. C3×C5#3297semidirect
729. C5#80681semidirect
758. C3#10615226semidirect

Maximal subgroups

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

subgroupindex
C5×#56302
#117545122
#117511452
C3×#653372
#117492812
#117492282
#117492112
#117491882
#117485162
#67×#1682
C2×#909672
#117473942
#117473192
#117472192
#117472092
#106152263
#806815