Finite Group Databasebeta

← #14458960

Subgroups — #14458960

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#11756309C211yesmaximal, characteristic, complemented
2C3×#65899C211yesmaximal, characteristic, complemented
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748550C211yesmaximal, characteristic, complemented
5#11748539C211yesmaximal, characteristic, complemented
6#11748524C211yesmaximal, characteristic, complemented
7#11748518C211yesmaximal, characteristic, complemented
8#11748452C211yesmaximal, characteristic, complemented
9#11748414C211yesmaximal, characteristic, complemented
10#11748411C211yesmaximal, characteristic, complemented
11C2×#90968C211yesmaximal, characteristic, complemented
12#11747063C211yesmaximal, characteristic, complemented
13C4×#6653C211yesmaximal, characteristic, complemented
14#11746951C211yesmaximal, characteristic, complemented
15#11746933C211yesmaximal, characteristic, complemented
16#10611172—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20#91826—21no—
21#91819C2211yescharacteristic
22#91813C2211yescharacteristic
23#91783—21no—
24#91773—21no—
25C22⋊C4×D15—21no—
26#91764C2211yescharacteristic
27C4×D60C2211yescharacteristic
28C22×C5×C3⋊C8C2211yescharacteristic
29C22×C5×C3⋊C8C2211yescharacteristic, complemented
30C3×#4085—21no—
31C3×#4076C2211yescharacteristic
32C3×#4076C2211yescharacteristic, complemented
33C3×#4072C2211yescharacteristic, complemented
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C3×#4044—21no—
36C3×#4029—21no—
37C3×#4027—21no—
38C3×C4×D20C2211yescharacteristic, complemented
39C3×#4016C2211yescharacteristic, complemented
40C2×#6657C2211yescharacteristic, 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#90974C2211yescharacteristic, complemented
51#90974C2211yescharacteristic, complemented
52#90974C2211yescharacteristic, complemented
53#90968C2211yescharacteristic
54#90968C2211yescharacteristic
55#90968C2211yescharacteristic
56#90968C2211yescharacteristic
57#90968C2211yescharacteristic
58#90968C2211yescharacteristic
59#90965C2211yescharacteristic, complemented
60#83614—51nomaximal, Hall
61#65899D311yescharacteristic, complemented
62#65884—31no—
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×D15—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×#1220—21no—
82#6817—22no—
83#6817—41no—
84C2×D60—22no—
85C2×D60—21no—
86C2×D60—41no—
87C2×D60C2311yescharacteristic
88C2×D60C2311yescharacteristic
89C2×C4×D15—21no—
90C2×C4×D15—21no—
91C2×Dic30C2311yescharacteristic
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C22×C3×Dic5—21no—
95C2×C3×D20C2311yescharacteristic
96C2×C3×C4×D5—21no—
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—
105#6714—21no—
106C4⋊Dic15C2311yescharacteristic
107#6712—21no—
108C2×C5×C3⋊C8—41no—
109C2×C5×C3⋊C8—41no—
110C2×C5×C3⋊C8C2311yescharacteristic
111C2×C5×C3⋊C8C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C3×C22⋊Dic5—21no—
115C3×#685—21no—
116C3×#685—21no—
117C3×#685—21no—
118C3×C4⋊Dic5—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C3×C4⋊Dic5C2311yescharacteristic
121C3×C4⋊Dic5C2311yescharacteristic
122C3×#683—21no—
123C3×#683—21no—
124C3×C4×Dic5—21no—
125#6657—41no—
126#6653—22no—
127#6653—41no—
128C3×#553—51no—
129#5550—51no—
130#5068—51no—
131#5066—51no—
132#5041—51no—
133#5038—51no—
134#5037—51no—
135#5036—51no—
136#5016—51no—
137C4×#213—51no—
138D4×C3⋊C8D511yescharacteristic, complemented
139#5003—51no—
140#5002—51no—
141#4970—51no—
142C2×#809—51no—
143C2×#709—31no—
144C22×D20—31no—
145C22×C5×C8—31no—
146C22×C5×C8—31no—
147C4×C5×D4C2×D311yescharacteristic
148#4085—21no—
149#4083—61no—
150#4076—31no—
151#4076C2×D311yescharacteristic
152#4076C2×D311yescharacteristic, complemented
153#4072C2×D311yescharacteristic, complemented
154C2×C4⋊Dic5C2×D311yescharacteristic
155#4070—31no—
156C2×D40—31no—
157C2×D40—31no—
158C2×#677—31no—
159#4044—21no—
160#4040—61no—
161#4030—61no—
162#4029—21no—
163#4027—21no—
164D5×C22⋊C4—61no—
165#4021—31no—
166C4×D20—31no—
167C4×D20C2×D311yescharacteristic, complemented
168#4016C2×D311yescharacteristic, complemented
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×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—81no—
194C22×C3×D5—21no—
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—
209D60—21no—
210D60—21no—
211D60—21no—
212D60—42no—
213D60#4112yes—
214C4×D15—42no—
215C4×D15—81no—
216Dic30—21no—
217Dic30—21no—
218C3×C22⋊D5—42no—
219C3×C22⋊D5—81no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—81no—
224C3×D20—21no—
225C3×D20—21no—
226C3×C4×D5—81no—
227C5×C3⋊C8—21no—
228C5×C3⋊C8—21no—
229C5×C3⋊C8—21no—
230C5×C3⋊C8—21no—
231C2×#235—51no—
232C22×D12—51no—
233C3×#126—101no—
234C3×#125—51no—
235C3×#123—101no—
236C3×#121—51no—
237C3×#121—51no—
238C3×#121—101no—
239C3×C4×D4—51no—
240C3×C4×D4—101no—
241C3×C4×D4C2×D511yescharacteristic
242C3×#117—51no—
243C2×C3×C4⋊C4—51no—
244#937—101no—
245C2×#214—51no—
246C2×#213—51no—
247C2×#213—51no—
248#930—51no—
249#924—51no—
250C22×C3⋊C8C2×D511yescharacteristic
251C22×C3⋊C8C2×D511yescharacteristic, complemented
252#894—101no—
253#884—101no—
254D3×C22⋊C4—101no—
255#875—51no—
256C4×D12—51no—
257#832—51no—
258#830C2×D511yescharacteristic
259#830C2×D511yescharacteristic, complemented
260#810—51no—
261#810—51no—
262#810—51no—
263#809—51no—
264#809—51no—
265#809—51no—
266#809—51no—
267#809—51no—
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—61no—
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—21no—
283#709—62no—
284#709—121no—
285C2×D20—31no—
286C2×D20—31no—
287C2×D20—62no—
288C2×D20—61no—
289C2×D20—121no—
290C2×D20C22×D311yescharacteristic
291C2×C4×D5—21no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×Dic10—31no—
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—61no—
311#685—61no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—21no—
315C4⋊Dic5—31no—
316C4⋊Dic5C22×D311yescharacteristic
317C4⋊Dic5C22×D311yescharacteristic
318C4⋊Dic5C22×D311yescharacteristic
319#683—21no—
320#683—21no—
321#683—61no—
322C4×Dic5—21no—
323D40—62no—
324D40—121no—
325#677—121no—
326#553—51no—
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—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—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—84no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
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—
366C3×Dic5—41no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C23×D3—101no—
370C2×C3×D4—51no—
371C2×C3×D4—101no—
372C2×C3×D4—101no—
373C2×C3×D4D2011yescharacteristic
374C22×C3×C4—101no—
375C22×C3×C4—101no—
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—101no—
379C2×#67—101no—
380#235—102no—
381#235—201no—
382C2×D12—51no—
383C2×D12—51no—
384C2×D12—102no—
385C2×D12—101no—
386C2×D12—201no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C3×C4⋊C4—51no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4D2011yescharacteristic
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4D2011yescharacteristic
402C3×C22⋊C4D2011yescharacteristic
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#214—201no—
407#213—102no—
408#213—201no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413C4⋊Dic3—51no—
414Dic3⋊C4—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—61no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
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—21no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—81no—
449D20—21no—
450D20—21no—
451D20—32no—
452D20—61no—
453D20—61no—
454D20—61no—
455D20—122no—
456C4×D5—81no—
457C4×D5—122no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461C5×C8—61no—
462C5×C8—61no—
463C5×C8—61no—
464C5×C8—61no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—31no—
471C22×C8—31no—
472#126—101no—
473#125—51no—
474#124—151no—
475#123—101no—
476#123—301no—
477C22⋊Q8—151no—
478#121—51no—
479#121—51no—
480#121—101no—
481#121—151no—
482#121—301no—
483#120—301no—
484C4×D4—51no—
485C4×D4—101no—
486C4×D4—151no—
487C4×D4D3×D511yescharacteristic
488#117—51no—
489C2×C4⋊C4—51no—
490C2×C22⋊C4—301no—
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—42no—
514D15—81no—
515C3×D5—81no—
516C23×C3—101no—
517C23×C3C2×D2011yescharacteristic
518C23×C3C2×D2011yescharacteristic
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
524C3×D4—22no—
525C3×D4—101no—
526C3×D4—101no—
527C3×D4—202no—
528C3×D4—401no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—401no—
537C2×C3×C4—401no—
538C2×C3×C4C2×D2011yescharacteristic
539C2×C3×C4C2×D2011yescharacteristic
540C2×C3×C4C2×D2011yescharacteristic
541C2×C3×C4C2×D2011yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543#67—202no—
544#67—401no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547D12—52no—
548D12—101no—
549D12—101no—
550D12—101no—
551D12—202no—
552C4×D3—202no—
553C4×D3—401no—
554Dic6—101no—
555Dic6—101no—
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—41no—
568C2×D5—41no—
569C2×D5—41no—
570C2×D5—62no—
571C2×D5—121no—
572C2×D5—121no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5D3×#4111yescharacteristic
582C4×C5#100911yescharacteristic
583Dic5—41no—
584Dic5—41no—
585Dic5—41no—
586Dic5—121no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—51no—
593C2×D4—101no—
594C2×D4—101no—
595C2×D4—151no—
596C2×D4—151no—
597C2×D4—302no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—301no—
601C2×D4—601no—
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—51no—
620C4⋊C4—51no—
621C4⋊C4—101no—
622C4⋊C4—101no—
623C4⋊C4—101no—
624C4⋊C4—151no—
625C4⋊C4—301no—
626C4⋊C4#120211yescharacteristic
627C22⋊C4—101no—
628C22⋊C4—101no—
629C22⋊C4—101no—
630C22⋊C4—101no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4#120211yescharacteristic
637C22⋊C4#120211yescharacteristic
638C42—101no—
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—201no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3#405012yes—
650C22×C3C22×D2011yescharacteristic
651C2×D3—102no—
652C2×D3—201no—
653C2×D3—201no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—201no—
663C3×C4—201no—
664C3×C4—201no—
665C3×C4#414411yescharacteristic
666C3×C4D5×#4111yescharacteristic
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5C2×#95011yescharacteristic
672C2×C5#582911yescharacteristic
673C2×C5#583511yescharacteristic
674D5—81no—
675D5—122no—
676D5—241no—
677C23—101no—
678C23—301no—
679C23—301no—
680C23—602no—
681C23—602no—
682C23—1201no—
683C23C2×#120211yescharacteristic
684C23C2×#120211yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—22no—
688D4—101no—
689D4—101no—
690D4—152no—
691D4—202no—
692D4—301no—
693D4—301no—
694D4—301no—
695D4—401no—
696D4—602no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—101no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—301no—
707C2×C4—301no—
708C2×C4—401no—
709C2×C4—401no—
710C2×C4—602no—
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—401no—
724C2×C3#6588811yescharacteristic
725C2×C3C2×#405011yescharacteristic
726C2×C3#6608611yescharacteristic
727D3—202no—
728D3—401no—
729C5#8361411yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—201no—
736C22—201no—
737C22—201no—
738C22—302no—
739C22—601no—
740C22—601no—
741C22—601no—
742C22—601no—
743C22—601no—
744C22—1204no—
745C22#9131112yes—
746C22C22×#120211yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—201no—
752C4—201no—
753C4—201no—
754C4—601no—
755C4—601no—
756C4#9202411yescharacteristic
757C4#9202711yescharacteristic
758C3#1061117211yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—401no—
762C2—602no—
763C2—1201no—
764C2C2×#9131111yescharacteristic
765C2#1175498011yescharacteristic
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. #11756309C2semidirect
2. C3×#65899C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748550C2semidirect
5. #11748539C2semidirect
6. #11748524C2semidirect
7. #11748518C2semidirect
8. #11748452C2semidirect
9. #11748414C2semidirect
10. #11748411C2semidirect
11. C2×#90968C2semidirect
12. #11747063C2semidirect
13. C4×#6653C2semidirect
14. #11746951C2semidirect
15. #11746933C2semidirect
29. C22×C5×C3⋊C8C22semidirect
32. C3×#4076C22semidirect
33. C3×#4072C22semidirect
38. C3×C4×D20C22semidirect
39. C3×#4016C22semidirect
40. C2×#6657C22semidirect
44. C5×#830C22semidirect
45. C5×C4⋊(C3⋊C8)C22semidirect
46. C4×C5×C3⋊C8C22semidirect
47. #90990C22semidirect
48. #90990C22semidirect
49. #90987C22semidirect
50. #90974C22semidirect
51. #90974C22semidirect
52. #90974C22semidirect
59. #90965C22semidirect
61. #65899D3semidirect
138. D4×C3⋊C8D5semidirect
152. #4076C2×D3semidirect
153. #4072C2×D3semidirect
167. C4×D20C2×D3semidirect
168. #4016C2×D3semidirect
251. C22×C3⋊C8C2×D5semidirect
259. #830C2×D5semidirect
272. C4⋊(C3⋊C8)C2×D5semidirect
273. C4×C3⋊C8C2×D5semidirect
640. C3×C5#3297semidirect
729. C5#83614semidirect
758. C3#10611172semidirect

Maximal subgroups

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

subgroupindex
#117563092
C3×#658992
C5×D4×C3⋊C82
#117485502
#117485392
#117485242
#117485182
#117484522
#117484142
#117484112
C2×#909682
#117470632
C4×#66532
#117469512
#117469332
#106111723
#836145