Finite Group Databasebeta

← #14458961

Subgroups — #14458961

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#11756324C211yesmaximal, characteristic, complemented
2C3×#65884C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748541C211yesmaximal, characteristic, complemented
5#11748518C211yesmaximal, characteristic, complemented
6#11748513C211yesmaximal, characteristic, complemented
7#11748512C211yesmaximal, characteristic, complemented
8#11748403C211yesmaximal, characteristic, complemented
9#11748376C211yesmaximal, characteristic, complemented
10#11748365C211yesmaximal, characteristic, complemented
11C2×#90965C211yesmaximal, characteristic, complemented
12#11747044C211yesmaximal, characteristic, complemented
13C4×#6653C211yesmaximal, characteristic, complemented
14#11746891C211yesmaximal, characteristic, complemented
15#11746888C211yesmaximal, characteristic, complemented
16#10611172—31nomaximal, Hall
17C2×C3×#709C2211yescharacteristic
18C22×C3×D20C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20#91828—21no—
21#91819C2211yescharacteristic
22#91819C2211yescharacteristic, complemented
23#91815C2211yescharacteristic, complemented
24C2×C4⋊Dic15C2211yescharacteristic
25#91787—21no—
26#91772—21no—
27#91770—21no—
28C4×D60C2211yescharacteristic, complemented
29#91759C2211yescharacteristic, complemented
30C22×C5×C3⋊C8C2211yescharacteristic
31C22×C5×C3⋊C8C2211yescharacteristic, complemented
32C3×#4083—21no—
33C3×#4076C2211yescharacteristic
34C3×#4070C2211yescharacteristic
35C3×#4040—21no—
36C3×#4030—21no—
37C3×D5×C22⋊C4—21no—
38C3×#4021C2211yescharacteristic
39C3×C4×D20C2211yescharacteristic
40C2×#6658C2211yescharacteristic, complemented
41C2×#6653C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C5×#830C2211yescharacteristic
44C5×#830C2211yescharacteristic, complemented
45C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
46C4×C5×C3⋊C8C2211yescharacteristic, complemented
47#90990C2211yescharacteristic, complemented
48#90990C2211yescharacteristic, complemented
49#90987C2211yescharacteristic, complemented
50#90971C2211yescharacteristic, complemented
51#90971C2211yescharacteristic, complemented
52#90971C2211yescharacteristic, complemented
53#90968C2211yescharacteristic, complemented
54#90965C2211yescharacteristic
55#90965C2211yescharacteristic
56#90965C2211yescharacteristic
57#90965C2211yescharacteristic
58#90965C2211yescharacteristic
59#90965C2211yescharacteristic
60#83495—51nomaximal, Hall
61#65899—31no—
62#65884D311yescharacteristic, complemented
63C5×C8×D4—31no—
64#65404—31no—
65#65403—31no—
66#65402—31no—
67C2×#3953—31no—
68#65136—31no—
69#65133—31no—
70#65026—31no—
71#65023—31no—
72#65021—31no—
73#65011—31no—
74#64986—31no—
75C4×D40—31no—
76C23×C3×D5—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×#1220—21no—
82C22×Dic15—21no—
83C2×D60C2311yescharacteristic
84C2×C4×D15—21no—
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C3×#709—22no—
88C3×#709—41no—
89C2×C3×D20—22no—
90C2×C3×D20—21no—
91C2×C3×D20—41no—
92C2×C3×D20C2311yescharacteristic
93C2×C3×D20C2311yescharacteristic
94C2×C3×C4×D5—21no—
95C2×C3×C4×D5—21no—
96C2×C3×Dic10C2311yescharacteristic
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C22⋊C4D411yescharacteristic
99C3×C5×C22⋊C4D411yescharacteristic
100C3×C42×C5C2311yescharacteristic
101#6719—21no—
102#6714—21no—
103#6714—21no—
104#6714—21no—
105C4⋊Dic15—21no—
106C4⋊Dic15C2311yescharacteristic
107C4⋊Dic15C2311yescharacteristic
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110#6712—21no—
111C4×Dic15—21no—
112C2×C5×C3⋊C8—41no—
113C2×C5×C3⋊C8—41no—
114C2×C5×C3⋊C8C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C2×C5×C3⋊C8C2311yescharacteristic
117C2×C5×C3⋊C8C2311yescharacteristic
118C3×C22⋊Dic5—21no—
119C3×#685—21no—
120C3×#685—21no—
121C3×#685—21no—
122C3×#685—21no—
123C3×C4⋊Dic5C2311yescharacteristic
124C3×#683—21no—
125#6658—41no—
126#6653—22no—
127#6653—41no—
128C3×#546—51no—
129#5565—51no—
130#5238—51no—
131#5233—51no—
132#5217—51no—
133C2×#832—51no—
134#5057—51no—
135#5056—51no—
136#5048—51no—
137#5044—51no—
138#5038—51no—
139#5035—51no—
140C4×#213—51no—
141D4×C3⋊C8D511yescharacteristic, complemented
142#5009—51no—
143C2×#709C2×D311yescharacteristic
144C22×D20C2×D311yescharacteristic
145C22×C5×C8—31no—
146C22×C5×C8—31no—
147C4×C5×D4C2×D311yescharacteristic
148#4085—61no—
149#4083—21no—
150#4076—31no—
151#4076—31no—
152#4076C2×D311yescharacteristic
153#4072—31no—
154C2×C4⋊Dic5—31no—
155#4070C2×D311yescharacteristic
156C2×D40—31no—
157C2×D40—31no—
158C2×#677—31no—
159#4044—61no—
160#4040—21no—
161#4030—21no—
162#4029—61no—
163#4027—61no—
164D5×C22⋊C4—21no—
165#4021C2×D311yescharacteristic
166C4×D20—31no—
167C4×D20C2×D311yescharacteristic
168#4016—31no—
169C5×C4⋊C8—31no—
170C5×C22⋊C8—31no—
171C5×C22⋊C8—31no—
172C4×C5×C8—31no—
173#3953—31no—
174#3953—31no—
175#3953—31no—
176#3953—31no—
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3950—31no—
181#3950—31no—
182#3949—31no—
183#3948—31no—
184#3948—31no—
185#3948—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—42no—
193C22×C3×D5—42no—
194C22×C3×D5—81no—
195C3×C5×D4—22no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205#1220—42no—
206#1220—81no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—81no—
211D60—21no—
212D60—21no—
213C4×D15—81no—
214C3×C22⋊D5—42no—
215C3×C22⋊D5—81no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C3×D20—21no—
219C3×D20—21no—
220C3×D20—21no—
221C3×D20—42no—
222C3×D20#4112yes—
223C3×C4×D5—42no—
224C3×C4×D5—81no—
225C3×Dic10—21no—
226C3×Dic10—21no—
227C5×C3⋊C8—21no—
228C5×C3⋊C8—21no—
229C5×C3⋊C8—21no—
230C5×C3⋊C8—21no—
231C2×C3×#41—51no—
232C22×C3×D4—51no—
233C3×#124—51no—
234C3×#123—101no—
235C3×C22⋊Q8—51no—
236C3×#121—51no—
237C3×#121—101no—
238C3×#120—101no—
239C3×C4×D4—51no—
240C3×C4×D4C2×D511yescharacteristic
241C2×C3×C22⋊C4—101no—
242C2×#215—51no—
243#939—101no—
244C2×#213—51no—
245C2×#213—51no—
246#930—51no—
247#930—51no—
248#926—51no—
249C2×C4⋊Dic3—51no—
250C22×C3⋊C8C2×D511yescharacteristic
251C22×C3⋊C8C2×D511yescharacteristic, complemented
252#898—101no—
253#883—101no—
254#67⋊C4—101no—
255C4×D12—51no—
256#870—51no—
257#835—51no—
258#835—51no—
259#835—51no—
260#832—51no—
261#832—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265#832—51no—
266#830C2×D511yescharacteristic
267#830C2×D511yescharacteristic, complemented
268#809—51no—
269#808—51no—
270#807—51no—
271#807—51no—
272C4⋊(C3⋊C8)C2×D511yescharacteristic, complemented
273C4×C3⋊C8C2×D511yescharacteristic, complemented
274C23×D5—21no—
275C2×C5×D4#6711yescharacteristic
276C22×C4×C5C22×D311yescharacteristic
277C22×C4×C5C22×D311yescharacteristic
278C2×C22⋊D5—21no—
279C2×C22⋊D5—21no—
280C2×C22⋊D5—61no—
281C2×C22⋊D5—61no—
282C22×Dic5—61no—
283#709—22no—
284#709—41no—
285C2×D20—22no—
286C2×D20—21no—
287C2×D20—31no—
288C2×D20—41no—
289C2×D20C22×D311yescharacteristic
290C2×D20C22×D311yescharacteristic
291C2×C4×D5—21no—
292C2×C4×D5—21no—
293C2×C4×D5—61no—
294C2×Dic10C22×D311yescharacteristic
295C2×C5×C8—31no—
296C2×C5×C8—31no—
297C2×C5×C8—31no—
298C2×C5×C8—31no—
299C2×C5×C8—121no—
300C2×C5×C8—121no—
301C5×C4⋊C4#6711yescharacteristic
302C5×C22⋊C4#6711yescharacteristic
303C5×C22⋊C4#6711yescharacteristic
304C42×C5C22×D311yescharacteristic
305C22⋊Dic5—21no—
306C22⋊Dic5—61no—
307#685—21no—
308#685—21no—
309#685—21no—
310#685—21no—
311#685—61no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—31no—
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—61no—
318C4⋊Dic5C22×D311yescharacteristic
319#683—21no—
320#683—61no—
321#683—61no—
322C4×Dic5—61no—
323D40—62no—
324D40—121no—
325#677—121no—
326#553—151no—
327#546—51no—
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—31no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—21no—
346C22×C3×C5#13512yes—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—41no—
349C2×D15—41no—
350C2×D15—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—21no—
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5C2×#4111yescharacteristic
363C3×C4×C5H(5,𝔽2)11yescharacteristic
364Dic15—41no—
365Dic15—41no—
366Dic15—41no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C24×C3—101no—
370C3×#41—102no—
371C3×#41—201no—
372C2×C3×Q8—51no—
373C2×C3×D4—51no—
374C2×C3×D4—51no—
375C2×C3×D4—102no—
376C2×C3×D4—101no—
377C2×C3×D4—101no—
378C2×C3×D4—101no—
379C2×C3×D4—201no—
380C2×C3×D4D2011yescharacteristic
381C22×C3×C4—101no—
382C22×C3×C4—101no—
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—101no—
386C2×#67—101no—
387C22×Dic3—101no—
388C2×D12—51no—
389C2×C4×D3—101no—
390C3×C4⋊C4—51no—
391C3×C4⋊C4—101no—
392C3×C4⋊C4D2011yescharacteristic
393C3×C22⋊C4—101no—
394C3×C22⋊C4—101no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4D2011yescharacteristic
399C3×C22⋊C4D2011yescharacteristic
400C3×C42C22×D511yescharacteristic
401#217—101no—
402#215—201no—
403#213—102no—
404#213—201no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410C4⋊Dic3—51no—
411C4⋊Dic3—101no—
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—101no—
415C2×C3⋊C8—41no—
416C2×C3⋊C8—41no—
417C2×C3⋊C8C22×D511yescharacteristic
418C2×C3⋊C8C22×D511yescharacteristic
419C2×C3⋊C8C22×D511yescharacteristic
420C2×C3⋊C8C22×D511yescharacteristic
421C23×C5C2×#6711yescharacteristic
422C23×C5C2×#6711yescharacteristic
423C22×D5—21no—
424C22×D5—21no—
425C22×D5—42no—
426C22×D5—42no—
427C22×D5—61no—
428C22×D5—81no—
429C5×D4—22no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5C2×#6711yescharacteristic
435C2×C4×C5C2×#6711yescharacteristic
436C2×C4×C5C2×#6711yescharacteristic
437C2×C4×C5C2×#6711yescharacteristic
438C2×C4×C5C23×D311yescharacteristic
439C22⋊D5—42no—
440C22⋊D5—81no—
441C22⋊D5—122no—
442C22⋊D5—241no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—241no—
449D20—21no—
450D20—21no—
451D20—21no—
452D20—42no—
453D20—61no—
454D20—61no—
455D20#23712yes—
456C4×D5—42no—
457C4×D5—81no—
458C4×D5—241no—
459Dic10—21no—
460Dic10—21no—
461C5×C8—61no—
462C5×C8—61no—
463C5×C8—61no—
464C5×C8—61no—
465C2×#41—51no—
466C22×D4—51no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—31no—
471C22×C8—31no—
472#126—301no—
473#125—151no—
474#124—51no—
475#123—101no—
476#123—301no—
477C22⋊Q8—51no—
478#121—51no—
479#121—101no—
480#121—151no—
481#121—151no—
482#121—301no—
483#120—101no—
484C4×D4—51no—
485C4×D4—151no—
486C4×D4—301no—
487C4×D4D3×D511yescharacteristic
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—101no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—31no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—31no—
506C22⋊C8—31no—
507C4×C8—31no—
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513D15—81no—
514C3×D5—42no—
515C3×D5—81no—
516C23×C3—101no—
517C23×C3—101no—
518C23×C3—202no—
519C23×C3—202no—
520C23×C3—401no—
521C23×C3C2×D2011yescharacteristic
522C23×C3C2×D2011yescharacteristic
523C22×D3—101no—
524C3×Q8—101no—
525C3×Q8—101no—
526C3×D4—22no—
527C3×D4—52no—
528C3×D4—101no—
529C3×D4—101no—
530C3×D4—101no—
531C3×D4—202no—
532C3×D4—202no—
533C3×D4—401no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—101no—
539C2×C3×C4—101no—
540C2×C3×C4—202no—
541C2×C3×C4—401no—
542C2×C3×C4C2×D2011yescharacteristic
543C2×C3×C4C2×D2011yescharacteristic
544C2×C3×C4C2×D2011yescharacteristic
545C2×C3×C4C2×D2011yescharacteristic
546C2×C3×C4C23×D511yescharacteristic
547#67—202no—
548#67—401no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—401no—
553D12—101no—
554D12—101no—
555C4×D3—401no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5#95012yes—
566C22×C5C22×#6711yescharacteristic
567C2×D5—22no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5—41no—
571C2×D5—41no—
572C2×D5—41no—
573C2×D5—84no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—121no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5C2×#23711yescharacteristic
582C4×C5#100411yescharacteristic
583Dic5—41no—
584Dic5—41no—
585Dic5—121no—
586Dic5—121no—
587Dic5—121no—
588C24—101no—
589#41—102no—
590#41—201no—
591C2×Q8—51no—
592C2×D4—51no—
593C2×D4—51no—
594C2×D4—102no—
595C2×D4—101no—
596C2×D4—101no—
597C2×D4—101no—
598C2×D4—151no—
599C2×D4—201no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4#120211yescharacteristic
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4C2×D3×D511yescharacteristic
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—121no—
617C2×C8—121no—
618C4⋊C4—51no—
619C4⋊C4—101no—
620C4⋊C4—151no—
621C4⋊C4—151no—
622C4⋊C4—151no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4#120211yescharacteristic
627C22⋊C4—101no—
628C22⋊C4—101no—
629C22⋊C4—101no—
630C22⋊C4—101no—
631C22⋊C4—101no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4#120211yescharacteristic
637C22⋊C4#120211yescharacteristic
638C42—301no—
639C42C2×D3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—102no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—404no—
653C22×C3#405012yes—
654C22×C3C22×D2011yescharacteristic
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—201no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—201no—
663C3×C4—201no—
664C3×C4#414411yescharacteristic
665C3×C4D5×#4111yescharacteristic
666Dic3—201no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5#580611yescharacteristic
672C2×C5C2×#95011yescharacteristic
673C2×C5#583511yescharacteristic
674D5—42no—
675D5—81no—
676D5—241no—
677C23—101no—
678C23—101no—
679C23—202no—
680C23—202no—
681C23—301no—
682C23—401no—
683C23C2×#120211yescharacteristic
684C23C2×#120211yescharacteristic
685Q8—101no—
686Q8—101no—
687D4—22no—
688D4—52no—
689D4—101no—
690D4—101no—
691D4—101no—
692D4—202no—
693D4—202no—
694D4—301no—
695D4—301no—
696D4—401no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—101no—
704C2×C4—101no—
705C2×C4—202no—
706C2×C4—301no—
707C2×C4—301no—
708C2×C4—301no—
709C2×C4—401no—
710C2×C4—1201no—
711C2×C4—1201no—
712C2×C4C2×#120211yescharacteristic
713C2×C4C2×#120211yescharacteristic
714C2×C4C2×#120211yescharacteristic
715C2×C4C2×#120211yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—61no—
718C8—61no—
719C8—61no—
720C8—61no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—202no—
724C2×C3—401no—
725C2×C3#6588811yescharacteristic
726C2×C3C2×#405011yescharacteristic
727C2×C3#6608611yescharacteristic
728D3—401no—
729C5#8349511yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—102no—
736C22—201no—
737C22—201no—
738C22—201no—
739C22—201no—
740C22—201no—
741C22—404no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22#9131112yes—
746C22C22×#120211yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—201no—
752C4—201no—
753C4—601no—
754C4—601no—
755C4—601no—
756C4D5×#23711yescharacteristic
757C4#9202511yescharacteristic
758C3#1061117211yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—202no—
762C2—401no—
763C2—1201no—
764C2C2×#9131111yescharacteristic
765C2#1175496311yescharacteristic
766C2#1175531111yescharacteristic
subgroupG/H
centerC22C22×#1202
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 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756324C2semidirect
2. C3×#65884C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748541C2semidirect
5. #11748518C2semidirect
6. #11748513C2semidirect
7. #11748512C2semidirect
8. #11748403C2semidirect
9. #11748376C2semidirect
10. #11748365C2semidirect
11. C2×#90965C2semidirect
12. #11747044C2semidirect
13. C4×#6653C2semidirect
14. #11746891C2semidirect
15. #11746888C2semidirect
22. #91819C22semidirect
23. #91815C22semidirect
28. C4×D60C22semidirect
29. #91759C22semidirect
31. C22×C5×C3⋊C8C22semidirect
40. C2×#6658C22semidirect
44. C5×#830C22semidirect
45. C5×C4⋊(C3⋊C8)C22semidirect
46. C4×C5×C3⋊C8C22semidirect
47. #90990C22semidirect
48. #90990C22semidirect
49. #90987C22semidirect
50. #90971C22semidirect
51. #90971C22semidirect
52. #90971C22semidirect
53. #90968C22semidirect
62. #65884D3semidirect
141. D4×C3⋊C8D5semidirect
251. C22×C3⋊C8C2×D5semidirect
267. #830C2×D5semidirect
272. C4⋊(C3⋊C8)C2×D5semidirect
273. C4×C3⋊C8C2×D5semidirect
640. C3×C5#3297semidirect
729. C5#83495semidirect
758. C3#10611172semidirect

Maximal subgroups

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

subgroupindex
#117563242
C3×#658842
C5×D4×C3⋊C82
#117485412
#117485182
#117485132
#117485122
#117484032
#117483762
#117483652
C2×#909652
#117470442
C4×#66532
#117468912
#117468882
#106111723
#834955