Finite Group Databasebeta

← #14417363

Subgroups — #14417363

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756304C211yesmaximal, characteristic, complemented
2C2×#91481C211yesmaximal, characteristic
3#11752729C211yesmaximal, characteristic, complemented
4C5×#5014C211yesmaximal, characteristic, complemented
5C3×C4×#686C211yesmaximal, characteristic, complemented
6#11748996C211yesmaximal, characteristic, complemented
7#11748993C211yesmaximal, characteristic, complemented
8#11748972C211yesmaximal, characteristic, complemented
9#11747479C211yesmaximal, characteristic, complemented
10#11747439C211yesmaximal, characteristic, complemented
11#11747233C211yesmaximal, characteristic, complemented
12#11747229C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14#11747023C211yesmaximal, characteristic, complemented
15#11746981C211yesmaximal, characteristic, complemented
16#10611598—31nomaximal, Hall
17C2×D4×D15C2211yescharacteristic
18C2×#6777C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic, complemented
20D4×Dic15C2211yescharacteristic, complemented
21C4×#1220—21no—
22C2×#6714—21no—
23#91782C2211yescharacteristic, complemented
24#91781C2211yescharacteristic
25#91770—21no—
26C22⋊C4×D15—21no—
27C4×D60C2211yescharacteristic, complemented
28#91761C2211yescharacteristic
29C2×C5×#213C2211yescharacteristic
30C4×C5×D12C2211yescharacteristic, complemented
31C2×C3×#686C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic, complemented
33#91481C418yescomplemented
34D3×#685—21no—
35D5×(C2×D3)⋊C4—21no—
36#91441—21no—
37#91440—21no—
38#91435C2211yescharacteristic, complemented
39#91434C2211yescharacteristic, complemented
40#91347C2211yescharacteristic
41C2×#6654C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6651C2211yescharacteristic
44C2×#6648C2211yescharacteristic
45C5×#832C2211yescharacteristic, complemented
46C5×#809C2211yescharacteristic, complemented
47C5×#808C2211yescharacteristic, complemented
48C5×#803C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52C3×C4×#168C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90969C2211yescharacteristic, complemented
56#90968C2211yescharacteristic, complemented
57#90967C2211yescharacteristic, complemented
58#90965C2211yescharacteristic, complemented
59#90954C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#79588—51nomaximal, Hall
62C2×D5×D8—31no—
63#65879—31no—
64#65879—31no—
65C5×#442—31no—
66#65441—31no—
67C4×#686—31no—
68C4×#686D311yescharacteristic, complemented
69#65158—31no—
70#65149—31no—
71#65059—31no—
72#65059—31no—
73#65045—31no—
74#65045—31no—
75#65000—31no—
76#64997—31no—
77C23×D15—21no—
78C22×D3×D5—21no—
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C2×#1220—21no—
82C22×Dic15—21no—
83D4×D15—22no—
84D4×D15C2×C414yescomplemented
85C2×D60C2311yescharacteristic
86C2×C4×D15—21no—
87C2×C4×D15—21no—
88C2×C4×D15C2311yescharacteristic
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3—21no—
91C2×C3×D20C2311yescharacteristic
92C2×C3×C4×D5—21no—
93C2×#1201—21no—
94C2×D3×Dic5—21no—
95C2×D5×Dic3—21no—
96#6777—22no—
97#6777C2×C414yescomplemented
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C42×C5C2311yescharacteristic
101#6719—21no—
102#6714—21no—
103#6714—21no—
104#6714—21no—
105#6714D411yescharacteristic
106#6714D411yescharacteristic
107C4⋊Dic15C2311yescharacteristic
108#6712D411yescharacteristic
109#6712D411yescharacteristic
110C4×Dic15—21no—
111C4×Dic15C2311yescharacteristic
112C5×#213C2×C414yescomplemented
113C5×(C2×D3)⋊C4—21no—
114C5×C4⋊Dic3C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C2×C5×C3⋊C8C2311yescharacteristic
117C3×#686C2×C414yescomplemented
118C3×#685—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6654C2×C414yescomplemented
127#6653C2×C414yescomplemented
128#6651—22no—
129#6648C2×C414yescomplemented
130C2×D3×D8—51no—
131#5545—51no—
132#5545—51no—
133C3×C4×D8—51no—
134Dic3×D8—51no—
135#5014—51no—
136#5014D511yescharacteristic, complemented
137#4880—51no—
138#4872—51no—
139#4785—51no—
140#4785—51no—
141#4770—51no—
142#4770—51no—
143C4×D24—51no—
144#4689—51no—
145C2×D4×D5—31no—
146C2×D4×D5—31no—
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4C2×D311yescharacteristic, complemented
150D4×Dic5—31no—
151D4×Dic5—31no—
152C2×#686—31no—
153C2×#686C2×D311yescharacteristic
154C4×C22⋊D5—61no—
155C4×C22⋊D5—61no—
156C2×#685—61no—
157C2×#685—61no—
158D5×D8—38no—
159C2×D40—31no—
160C2×#676—31no—
161C2×C8×D5—31no—
162#4039—31no—
163#4039—31no—
164#4038—31no—
165#4038—31no—
166#4027—61no—
167#4027—61no—
168D5×C22⋊C4—61no—
169D5×C22⋊C4—61no—
170C4×D20—31no—
171C4×D20C2×D311yescharacteristic, complemented
172#4018—31no—
173C5×#106—31no—
174C5×#102—31no—
175C5×#102—31no—
176C5×#97—31no—
177#3964—31no—
178#3964C2×D311yescharacteristic, complemented
179#3953—31no—
180#3953—31no—
181#3949—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941C2×D311yescharacteristic, complemented
186#3939—31no—
187#3939C2×D311yescharacteristic, complemented
188C4×#168C2×D311yescharacteristic, complemented
189#2948—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×D15—24no—
193C22×D15—81no—
194C22×D15—81no—
195C22×D15C2×D411yescharacteristic
196C22×C5×D3—21no—
197C22×C3×D5—21no—
198C2×D3×D5—24no—
199C2×D3×D5—81no—
200C2×D3×D5—81no—
201C3×C5×D4—21no—
202C3×C5×D4C22×C412yes—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—81no—
205C2×C3×C4×C5C2×D411yescharacteristic
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2411yescharacteristic
208#1220—24no—
209C2×Dic15—21no—
210C2×Dic15—81no—
211C2×Dic15C2×D411yescharacteristic
212C2×Dic15C2×D411yescharacteristic
213C2×Dic15C2×D411yescharacteristic
214D60—21no—
215D60C22×C412yes—
216C4×D15—81no—
217C4×D15—81no—
218C4×D15C22×C412yes—
219C4×D15#4112yes—
220C2×C5×Dic3—21no—
221C5×D12—21no—
222C5×D12C22×C412yes—
223C4×C5×D3—81no—
224C2×C3×Dic5—21no—
225C3×D20—21no—
226C3×D20C22×C412yes—
227C3×C4×D5—81no—
228#1201—24no—
229D3×Dic5—81no—
230D5×Dic3—81no—
231C3×#168—21no—
232C3×#168C22×C412yes—
233C5×C3⋊C8—21no—
234C5×C3⋊C8C22×C412yes—
235C2×D3×D4—51no—
236C2×D3×D4—51no—
237C2×C3×D8—51no—
238C3×C4×D4—51no—
239C3×C4×D4C2×D511yescharacteristic, complemented
240D4×Dic3—51no—
241D4×Dic3—51no—
242C2×#213—51no—
243C2×#213C2×D511yescharacteristic
244C4×#67—101no—
245C4×#67—101no—
246C2×(C2×D3)⋊C4—101no—
247C2×(C2×D3)⋊C4—101no—
248D3×D8—58no—
249C2×D24—51no—
250C2×ΓL(1,𝔽25)—51no—
251C2×D3×C8—51no—
252#893—51no—
253#893—51no—
254#892—51no—
255#892—51no—
256#67⋊C4—101no—
257#67⋊C4—101no—
258D3×C22⋊C4—101no—
259D3×C22⋊C4—101no—
260C4×D12—51no—
261C4×D12C2×D511yescharacteristic, complemented
262#872—51no—
263C3×#107—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×C4×C8—51no—
267#832—51no—
268#832C2×D511yescharacteristic, complemented
269#821—51no—
270#821—51no—
271#818—51no—
272#815—51no—
273C8×Dic3—51no—
274#809—51no—
275#809C2×D511yescharacteristic, complemented
276#808—51no—
277#808C2×D511yescharacteristic, complemented
278#803C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C23×D5—61no—
281C2×C5×D4—31no—
282C2×C5×D4C22×D311yescharacteristic
283C22×C4×C5—21no—
284C22×C4×C5—61no—
285C2×C22⋊D5—61no—
286C2×C22⋊D5—61no—
287C22×Dic5—61no—
288C22×Dic5—61no—
289D4×D5—34no—
290D4×D5—34no—
291D4×D5—62no—
292D4×D5—62no—
293C2×D20—31no—
294C2×D20C22×D311yescharacteristic
295C2×C4×D5—21no—
296C2×C4×D5—31no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C5×D8—34no—
301C2×C5×C8—31no—
302C2×C5×C8—31no—
303C5×C4⋊C4—31no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C22⋊C4—21no—
306C5×C22⋊C4—61no—
307C42×C5C22×D311yescharacteristic
308C22⋊Dic5—61no—
309C22⋊Dic5—61no—
310#686—34no—
311#686C4×D314yescomplemented
312#685—21no—
313#685—31no—
314#685—31no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319#685—61no—
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—31no—
323#683—31no—
324C4×Dic5—31no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327C2×#168C22×D311yescharacteristic
328C2×#168C22×D311yescharacteristic
329D40—34no—
330#676—62no—
331C8×D5—34no—
332C22×D8—151no—
333#518—151no—
334#518—151no—
335#442—31no—
336#442—151no—
337#442—151no—
338#442—151no—
339C4×D8—51no—
340C4×D8—151no—
341C4×D8—151no—
342C4×D8—151no—
343#427—151no—
344#418—151no—
345#418—151no—
346#405—151no—
347C22×C3×C5—22no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—21no—
352C2×D15—21no—
353C2×D15—22no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—84no—
357C2×D15C4×D412yes—
358C2×C5×D3—22no—
359C2×C5×D3—41no—
360C2×C5×D3—41no—
361C2×C3×D5—22no—
362C2×C3×D5—41no—
363C2×C3×D5—41no—
364D3×D5—84no—
365C3×C4×C5—21no—
366C3×C4×C5—21no—
367C3×C4×C5—41no—
368C3×C4×C5C23×C411yescharacteristic
369C3×C4×C5C2×#4111yescharacteristic
370Dic15—21no—
371Dic15—21no—
372Dic15—41no—
373Dic15C4×D412yes—
374C3×Dic5—41no—
375C5×Dic3—41no—
376C23×D3—101no—
377C23×D3—101no—
378C2×C3×D4—51no—
379C2×C3×D4C22×D511yescharacteristic
380C22×C3×C4—21no—
381C22×C3×C4—101no—
382C2×#67—101no—
383C2×#67—101no—
384C22×Dic3—101no—
385C22×Dic3—101no—
386D3×D4—54no—
387D3×D4—54no—
388D3×D4—102no—
389D3×D4—102no—
390C2×D12—51no—
391C2×D12C22×D511yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—51no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—101no—
397C3×D8—54no—
398C2×C3×C8—51no—
399C2×C3×C8—51no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—101no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#217—101no—
407#213—54no—
408#213C4×D514yescomplemented
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—51no—
411(C2×D3)⋊C4—51no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415(C2×D3)⋊C4—101no—
416(C2×D3)⋊C4—101no—
417C4⋊Dic3—51no—
418C4⋊Dic3C22×D511yescharacteristic
419Dic3⋊C4—51no—
420Dic3⋊C4—51no—
421C4×Dic3—51no—
422C4×Dic3—101no—
423C4×Dic3—101no—
424C2×C3⋊C8C22×D511yescharacteristic
425C2×C3⋊C8C22×D511yescharacteristic
426D24—54no—
427ΓL(1,𝔽25)—102no—
428D3×C8—54no—
429C23×C5—21no—
430C23×C5—61no—
431C22×D5—21no—
432C22×D5—31no—
433C22×D5—64no—
434C22×D5—64no—
435C22×D5—61no—
436C22×D5—241no—
437C22×D5—241no—
438C22×D5—241no—
439C22×D5—241no—
440C5×D4—21no—
441C5×D4—32no—
442C5×D4—61no—
443C5×D4C2×C4×D312yes—
444C2×C4×C5—21no—
445C2×C4×C5—61no—
446C2×C4×C5—81no—
447C2×C4×C5—241no—
448C2×C4×C5D3×D411yescharacteristic
449C2×C4×C5D3×D411yescharacteristic
450C2×C4×C5C23×D311yescharacteristic
451C22⋊D5—64no—
452C22⋊D5—64no—
453C2×Dic5—21no—
454C2×Dic5—31no—
455C2×Dic5—31no—
456C2×Dic5—31no—
457C2×Dic5—61no—
458C2×Dic5—241no—
459C2×Dic5—241no—
460D20—21no—
461D20—32no—
462D20—61no—
463D20C2×C4×D312yes—
464C4×D5—32no—
465C4×D5—32no—
466C4×D5—81no—
467C4×D5—241no—
468C4×D5—241no—
469C4×D5—241no—
470C5×C8—32no—
471C5×C8—61no—
472#168—21no—
473#168C2×C4×D312yes—
474C22×D4—151no—
475C22×D4—151no—
476C2×D8—31no—
477C2×D8—51no—
478C2×D8—151no—
479C2×D8—151no—
480C2×D8—158no—
481C2×M16—151no—
482C22×C8—151no—
483C4×D4—31no—
484C4×D4—51no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—151no—
489C4×D4—151no—
490C4×D4—301no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4—301no—
494C4×D4D3×D511yescharacteristic, complemented
495#117—151no—
496#117—151no—
497#117—151no—
498C2×C22⋊C4—301no—
499C2×C22⋊C4—301no—
500C2×C22⋊C4—301no—
501C2×C22⋊C4—301no—
502#107—51no—
503#107—151no—
504#106—31no—
505#106—151no—
506#102—31no—
507#102—31no—
508#102—51no—
509#102—51no—
510#102—151no—
511#102—151no—
512#102—151no—
513#102—151no—
514#97—31no—
515#97—151no—
516C4×C8—51no—
517C4×C8—151no—
518C2×C3×C5—42no—
519C2×C3×C5C2×C4×D411yescharacteristic
520C2×C3×C5#57611yescharacteristic
521C2×C3×C5#57611yescharacteristic
522D15—22no—
523D15—42no—
524C3×D5—42no—
525C5×D3—42no—
526C23×C3—21no—
527C23×C3—101no—
528C22×D3—21no—
529C22×D3—51no—
530C22×D3—104no—
531C22×D3—104no—
532C22×D3—101no—
533C22×D3—401no—
534C22×D3—401no—
535C22×D3—401no—
536C22×D3—401no—
537C3×D4—21no—
538C3×D4—52no—
539C3×D4—101no—
540C3×D4C2×C4×D512yes—
541C2×C3×C4—21no—
542C2×C3×C4—81no—
543C2×C3×C4—101no—
544C2×C3×C4—401no—
545C2×C3×C4D4×D511yescharacteristic
546C2×C3×C4D4×D511yescharacteristic
547C2×C3×C4C23×D511yescharacteristic
548#67—104no—
549#67—104no—
550C2×Dic3—21no—
551C2×Dic3—51no—
552C2×Dic3—51no—
553C2×Dic3—51no—
554C2×Dic3—101no—
555C2×Dic3—401no—
556C2×Dic3—401no—
557D12—21no—
558D12—52no—
559D12—101no—
560D12C2×C4×D512yes—
561C4×D3—52no—
562C4×D3—52no—
563C4×D3—81no—
564C4×D3—401no—
565C4×D3—401no—
566C4×D3—401no—
567C3×C8—52no—
568C3×C8—101no—
569C3⋊C8—21no—
570C3⋊C8C2×C4×D512yes—
571C22×C5—22no—
572C22×C5—41no—
573C22×C5—41no—
574C22×C5—62no—
575C22×C5—121no—
576C22×C5—121no—
577C22×C5C2×D3×D411yescharacteristic
578C2×D5—22no—
579C2×D5—32no—
580C2×D5—41no—
581C2×D5—41no—
582C2×D5—61no—
583C2×D5—61no—
584C2×D5—62no—
585C2×D5—121no—
586C2×D5—121no—
587C2×D5—244no—
588C2×D5—244no—
589C4×C5—21no—
590C4×C5—21no—
591C4×C5—41no—
592C4×C5—121no—
593C4×C5C22×C4×D311yescharacteristic
594C4×C5D3×#4111yescharacteristic
595Dic5—32no—
596Dic5—41no—
597Dic5—61no—
598Dic5—61no—
599Dic5—121no—
600C24—301no—
601C24—301no—
602C2×D4—31no—
603C2×D4—51no—
604C2×D4—154no—
605C2×D4—154no—
606C2×D4—151no—
607C2×D4—302no—
608C2×D4—302no—
609C2×D4—301no—
610C2×D4—301no—
611C2×D4C2×D3×D511yescharacteristic
612C22×C4—21no—
613C22×C4—61no—
614C22×C4—101no—
615C22×C4—151no—
616C22×C4—301no—
617C22×C4—301no—
618C22×C4—301no—
619C22×C4—301no—
620C22×C4—301no—
621D8—34no—
622D8—54no—
623D8—154no—
624D8—154no—
625M16—302no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—51no—
629C2×C8—51no—
630C2×C8—154no—
631C4⋊C4—31no—
632C4⋊C4—51no—
633C4⋊C4—151no—
634C4⋊C4—151no—
635C4⋊C4—151no—
636C4⋊C4C2×D3×D511yescharacteristic
637C22⋊C4—21no—
638C22⋊C4—61no—
639C22⋊C4—101no—
640C22⋊C4—151no—
641C22⋊C4—151no—
642C22⋊C4—301no—
643C22⋊C4—301no—
644C22⋊C4—301no—
645C22⋊C4—301no—
646C22⋊C4—301no—
647C22⋊C4—301no—
648C22⋊C4—301no—
649C42—151no—
650C42—301no—
651C42—301no—
652C42C2×D3×D511yescharacteristic
653C3×C5#294811yescharacteristic, complemented, Hall
654C22×C3—22no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—102no—
658C22×C3—201no—
659C22×C3—201no—
660C22×C3C2×D4×D511yescharacteristic
661C2×D3—22no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—52no—
665C2×D3—101no—
666C2×D3—101no—
667C2×D3—102no—
668C2×D3—201no—
669C2×D3—201no—
670C2×D3—404no—
671C2×D3—404no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—201no—
676C3×C4C22×C4×D511yescharacteristic
677C3×C4D5×#4111yescharacteristic
678Dic3—41no—
679Dic3—52no—
680Dic3—101no—
681Dic3—101no—
682Dic3—201no—
683C2×C5—42no—
684C2×C5—122no—
685C2×C5C4×D3×D411yescharacteristic
686C2×C5#575711yescharacteristic
687C2×C5#576911yescharacteristic
688D5—42no—
689D5—62no—
690D5—122no—
691C23—21no—
692C23—61no—
693C23—101no—
694C23—151no—
695C23—304no—
696C23—304no—
697C23—301no—
698C23—1201no—
699C23—1201no—
700C23—1201no—
701C23—1201no—
702D4—21no—
703D4—32no—
704D4—52no—
705D4—61no—
706D4—101no—
707D4—152no—
708D4—304no—
709D4—304no—
710D4—301no—
711D4C4×D3×D512yes—
712C2×C4—21no—
713C2×C4—61no—
714C2×C4—81no—
715C2×C4—101no—
716C2×C4—151no—
717C2×C4—152no—
718C2×C4—152no—
719C2×C4—151no—
720C2×C4—151no—
721C2×C4—241no—
722C2×C4—301no—
723C2×C4—401no—
724C2×C4—1201no—
725C2×C4—1201no—
726C2×C4—1201no—
727C2×C4—1201no—
728C2×C4—1201no—
729C2×C4#679011yescharacteristic
730C2×C4#679011yescharacteristic
731C2×C4C22×D3×D511yescharacteristic
732C8—32no—
733C8—52no—
734C8—61no—
735C8—101no—
736C2×C3—42no—
737C2×C3—202no—
738C2×C3C4×D4×D511yescharacteristic
739C2×C3#6610811yescharacteristic
740C2×C3#6610811yescharacteristic
741D3—42no—
742D3—102no—
743D3—202no—
744C5#7958811yescharacteristic, complemented, Sylow
745C22—22no—
746C22—41no—
747C22—41no—
748C22—62no—
749C22—102no—
750C22—121no—
751C22—121no—
752C22—152no—
753C22—201no—
754C22—201no—
755C22—301no—
756C22—301no—
757C22—302no—
758C22—601no—
759C22—601no—
760C22—1204no—
761C22—1204no—
762C22C2×#679011yescharacteristic
763C4—21no—
764C4—21no—
765C4—41no—
766C4—121no—
767C4—152no—
768C4—201no—
769C4—301no—
770C4—301no—
771C4—601no—
772C4C2×C4×D3×D511yescharacteristic
773C4#9201611yescharacteristic
774C3#1061159811yescharacteristic, complemented, Sylow
775C2—42no—
776C2—122no—
777C2—202no—
778C2—302no—
779C2—602no—
780C2C4×#679011yescharacteristic
781C2#1175470311yescharacteristic
782C2#1175533211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91481C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5#2948
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756304C2semidirect
3. #11752729C2semidirect
4. C5×#5014C2semidirect
5. C3×C4×#686C2semidirect
6. #11748996C2semidirect
7. #11748993C2semidirect
8. #11748972C2semidirect
9. #11747479C2semidirect
10. #11747439C2semidirect
11. #11747233C2semidirect
12. #11747229C2semidirect
13. C4×#6654C2semidirect
14. #11747023C2semidirect
15. #11746981C2semidirect
19. C3×C4×C5×D4C22semidirect
20. D4×Dic15C22semidirect
23. #91782C22semidirect
27. C4×D60C22semidirect
30. C4×C5×D12C22semidirect
32. C3×C4×D20C22semidirect
33. #91481C4semidirect
38. #91435C22semidirect
39. #91434C22semidirect
45. C5×#832C22semidirect
46. C5×#809C22semidirect
47. C5×#808C22semidirect
48. C5×#803C22semidirect
49. C3×#3964C22semidirect
50. C3×#3941C22semidirect
51. C3×#3939C22semidirect
52. C3×C4×#168C22semidirect
53. #90988C22semidirect
54. #90987C22semidirect
55. #90969C22semidirect
56. #90968C22semidirect
57. #90967C22semidirect
58. #90965C22semidirect
59. #90954C22semidirect
60. #90951C22semidirect
68. C4×#686D3semidirect
84. D4×D15C2×C4semidirect
97. #6777C2×C4semidirect
112. C5×#213C2×C4semidirect
117. C3×#686C2×C4semidirect
126. #6654C2×C4semidirect
127. #6653C2×C4semidirect
129. #6648C2×C4semidirect
136. #5014D5semidirect
149. C4×C5×D4C2×D3semidirect
171. C4×D20C2×D3semidirect
178. #3964C2×D3semidirect
185. #3941C2×D3semidirect
187. #3939C2×D3semidirect
188. C4×#168C2×D3semidirect
239. C3×C4×D4C2×D5semidirect
261. C4×D12C2×D5semidirect
268. #832C2×D5semidirect
275. #809C2×D5semidirect
277. #808C2×D5semidirect
278. #803C2×D5semidirect
311. #686C4×D3semidirect
408. #213C4×D5semidirect
494. C4×D4D3×D5semidirect
653. C3×C5#2948semidirect
744. C5#79588semidirect
774. C3#10611598semidirect

Maximal subgroups

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

subgroupindex
#117563042
C2×#914812
#117527292
C5×#50142
C3×C4×#6862
#117489962
#117489932
#117489722
#117474792
#117474392
#117472332
#117472292
C4×#66542
#117470232
#117469812
#106115983
#795885