Finite Group Databasebeta

← #14416781

Subgroups — #14416781

Order 1920.

1096 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#11755200C211yesmaximal, characteristic, complemented
2C2×#91506C211yesmaximal, characteristic
3#11753840C211yesmaximal, characteristic, complemented
4#11750904C211yesmaximal, characteristic, complemented
5C5×#4817C211yesmaximal, characteristic, complemented
6C3×#65077C211yesmaximal, characteristic, complemented
7#11749234C211yesmaximal, characteristic, complemented
8Dic5×#215C211yesmaximal, characteristic, complemented
9#11748109C211yesmaximal, characteristic, complemented
10#11747745C211yesmaximal, characteristic, complemented
11#11747741C211yesmaximal, characteristic, complemented
12#11747592C211yesmaximal, characteristic, complemented
13#11747470C211yesmaximal, characteristic, complemented
14#11747458C211yesmaximal, characteristic, complemented
15#11747223C211yesmaximal, characteristic, complemented
16#10611504—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×#6777C2211yescharacteristic
19C2×C4×D3×D5—21no—
20C2×#6705C2211yescharacteristic
21C4⋊C4×D15C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic, complemented
23C2×C5×#215C2211yescharacteristic
24C5×#893C2211yescharacteristic
25C3×Q8×Dic5C2211yescharacteristic, complemented
26C2×C3×#688C2211yescharacteristic
27C3×#4039C2211yescharacteristic
28#91506C418yescomplemented
29#91473—21no—
30#91441—21no—
31#91440—21no—
32#91428—21no—
33#91428C2211yescharacteristic, complemented
34Dic3×D20C2211yescharacteristic
35#91418—21no—
36#91418C2211yescharacteristic, complemented
37Dic5×D12C2211yescharacteristic
38C4×#1200—21no—
39C4×#1200C2211yescharacteristic
40#91347—21no—
41#91347C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×#6653C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic, complemented
46#91119C2211yescharacteristic, complemented
47#91105C2211yescharacteristic, complemented
48#91093C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×#815C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3940C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90987C2211yescharacteristic, complemented
57#90966C2211yescharacteristic
58#90964C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61C4×#914—51nomaximal, Hall
62C2×#4060—31no—
63C4×#713—31no—
64C4×D4×D5—31no—
65C5×#440—31no—
66SD16×Dic5—31no—
67#65315—31no—
68#65303—31no—
69#65170—31no—
70#65161—31no—
71#65092—31no—
72#65077D311yescharacteristic, complemented
73#65059—31no—
74#65045—31no—
75#65000—31no—
76#64996—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79#6821—22no—
80#6821C2×C414yescomplemented
81C2×D60—21no—
82C2×D60C2311yescharacteristic
83C2×C4×D15—21no—
84C2×C4×D15—21no—
85C2×C4×D15C2311yescharacteristic
86C2×C5×D12C2311yescharacteristic
87C2×C4×C5×D3—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×#1201—21no—
91C2×#1200—21no—
92C2×#1200—21no—
93C2×#1200D411yescharacteristic
94C2×#1200D411yescharacteristic
95C2×D3×Dic5—21no—
96C2×D5×Dic3—21no—
97#6777—22no—
98#6777C2×C414yescomplemented
99C4×D3×D5—44no—
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C4⋊Dic15C2311yescharacteristic
103#6712—21no—
104C2×C3⋊#168C2311yescharacteristic
105#6705—22no—
106C5×#215C2×C414yescomplemented
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C4×C5×Dic3—21no—
111C4×C5×Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C3×#688C2×C414yescomplemented
114C3×#685—21no—
115C3×C4⋊Dic5—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4×Dic5—21no—
118C3×C4×Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120#6667—21no—
121#6667—21no—
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6654C2×C414yescomplemented
129#6653C2×C414yescomplemented
130#6651C2×C414yescomplemented
131C2×#914—51no—
132C4×#239—51no—
133C4×D3×D4—51no—
134C3×C4×SD16—51no—
135#5164—51no—
136C4×#215—51no—
137C4×#213—51no—
138#4869—51no—
139#4861—51no—
140#4817D511yescharacteristic, complemented
141#4803—51no—
142#4785—51no—
143#4770—51no—
144C4×D24—51no—
145C4×ΓL(1,𝔽25)—51no—
146C2×#713—31no—
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×SD16—31no—
150C4×C5×Q8—31no—
151C4×C5×D4—31no—
152Q8×Dic5C2×D311yescharacteristic, complemented
153C2×#688C2×D311yescharacteristic
154D4×Dic5—31no—
155C2×#686—31no—
156C4×C22⋊D5—61no—
157#4060—38no—
158C2×D40—31no—
159C2×#676—31no—
160C2×#676—31no—
161#4039—31no—
162#4039—61no—
163#4039C2×D311yescharacteristic
164#4038—31no—
165#4038—61no—
166D5×C4⋊C4—31no—
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C4×D20—31no—
171C4×D20—61no—
172C42×D5—31no—
173C42×D5—61no—
174C5×#107—31no—
175C5×#103C2×D311yescharacteristic, complemented
176C5×#102—31no—
177C5×#97—31no—
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3953C2×D311yescharacteristic
182#3949—31no—
183C8×Dic5—31no—
184C8×Dic5C2×D311yescharacteristic, complemented
185#3941—31no—
186#3941—31no—
187#3940C2×D311yescharacteristic, complemented
188#3939—31no—
189#3935—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×D15C2×D411yescharacteristic
193C22×C5×D3—21no—
194C22×C3×D5—21no—
195C2×D3×D5—24no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C3×C5×Q8—21no—
199C3×C5×Q8C22×C412yescomplemented
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15C2×D411yescharacteristic
205D60—24no—
206D60—21no—
207D60C22×C412yescomplemented
208C4×D15—24no—
209C4×D15—42no—
210C4×D15C22×C412yes—
211C4×D15#4112yes—
212C2×C5×Dic3—21no—
213C2×C5×Dic3C2×D411yescharacteristic
214C2×C5×Dic3C2×D411yescharacteristic
215C5×D12—21no—
216C5×D12C22×C412yes—
217C4×C5×D3—42no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×D20—21no—
222C3×D20C22×C412yes—
223C3×C4×D5—42no—
224#1201—24no—
225#1200—22no—
226#1200—41no—
227#1200—42no—
228#1200—42no—
229D3×Dic5—42no—
230D5×Dic3—42no—
231C3×C5×C8—21no—
232C3⋊#168—21no—
233C3×#168C22×C412yescomplemented
234C5×C3⋊C8C22×C412yescomplemented
235C2×#239—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×SD16—51no—
239C3×C4×Q8—51no—
240C3×C4×D4—51no—
241Q8×Dic3C2×D511yescharacteristic, complemented
242C2×#215C2×D511yescharacteristic
243D4×Dic3—51no—
244C2×#213—51no—
245C4×#67—101no—
246#914—58no—
247C2×D24—51no—
248C2×ΓL(1,𝔽25)—51no—
249C2×ΓL(1,𝔽25)—51no—
250#893—51no—
251#893—101no—
252#893C2×D511yescharacteristic
253#892—51no—
254#892—101no—
255D3×C4⋊C4—51no—
256#67⋊C4—101no—
257D3×C22⋊C4—101no—
258C4×D12—51no—
259C4×D12—51no—
260C4×D12—101no—
261C42×D3—51no—
262C42×D3—101no—
263C3×#106—51no—
264C3×#103C2×D511yescharacteristic, complemented
265C3×#102—51no—
266C3×C4×C8—51no—
267#835—51no—
268#832—51no—
269#821—51no—
270#821C2×D511yescharacteristic
271#818—51no—
272#815—51no—
273#815C2×D511yescharacteristic, complemented
274#809—51no—
275#809—51no—
276#808—51no—
277#807C2×D511yescharacteristic, complemented
278C4×C3⋊C8—51no—
279C23×D5—61no—
280C2×C5×Q8C22×D311yescharacteristic
281C2×C5×D4—31no—
282C22×C4×C5—61no—
283C2×C22⋊D5—61no—
284C22×Dic5—61no—
285#713—34no—
286#713—62no—
287D4×D5—34no—
288D4×D5—62no—
289C2×D20—31no—
290C2×D20—61no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—31no—
294C2×C4×D5—31no—
295C2×C4×D5—31no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—61no—
301C2×C4×D5—124no—
302C5×SD16—34no—
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—61no—
307C5×C4⋊C4C22×D311yescharacteristic
308C5×C22⋊C4—61no—
309C42×C5—31no—
310C42×C5—61no—
311C22⋊Dic5—61no—
312#688C4×D314yescomplemented
313#686—34no—
314#685—21no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—21no—
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—61no—
323C4×Dic5—21no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C4×Dic5—61no—
327C4×Dic5C22×D311yescharacteristic
328C2×#168—31no—
329C2×#168C22×D311yescharacteristic
330D40—34no—
331#676—34no—
332#676—62no—
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—151no—
337#442—151no—
338#440—31no—
339#440—151no—
340C4×SD16—51no—
341C4×SD16—151no—
342C4×D8—151no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—21no—
350C2×D15—21no—
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15C4×D412yes—
355C2×C5×D3—22no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C3×D5—22no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361D3×D5—48no—
362C3×C4×C5—22no—
363C3×C4×C5—41no—
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—41no—
367Dic15C4×D412yes—
368C3×Dic5—21no—
369C3×Dic5—41no—
370C3×Dic5AGL(1,ℤ/8)12yescomplemented
371C5×Dic3—21no—
372C5×Dic3—21no—
373C5×Dic3—41no—
374C23×D3—101no—
375C2×C3×Q8C22×D511yescharacteristic
376C2×C3×D4—51no—
377C22×C3×C4—101no—
378C2×#67—101no—
379C22×Dic3—101no—
380#239—54no—
381#239—102no—
382D3×D4—54no—
383D3×D4—102no—
384C2×D12—51no—
385C2×D12—101no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—51no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—101no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—204no—
397C3×SD16—54no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—101no—
404C3×C42—51no—
405C3×C42—101no—
406#217—101no—
407#215C4×D514yescomplemented
408#213—54no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414C4⋊Dic3—21no—
415C4⋊Dic3—51no—
416C4⋊Dic3C22×D511yescharacteristic
417Dic3⋊C4—101no—
418C4×Dic3—21no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—101no—
422C4×Dic3C22×D511yescharacteristic
423C2×C3⋊C8—51no—
424C2×C3⋊C8C22×D511yescharacteristic
425D24—54no—
426ΓL(1,𝔽25)—54no—
427ΓL(1,𝔽25)—102no—
428C23×C5—61no—
429C22×D5—21no—
430C22×D5—31no—
431C22×D5—64no—
432C22×D5—61no—
433C22×D5—122no—
434C22×D5—122no—
435C5×Q8—21no—
436C5×Q8C2×C4×D312yescomplemented
437C5×D4—32no—
438C5×D4—61no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—31no—
442C2×C4×C5—31no—
443C2×C4×C5—61no—
444C2×C4×C5—122no—
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C2×Dic5—21no—
448C2×Dic5—31no—
449C2×Dic5—61no—
450C2×Dic5—122no—
451C2×Dic5D3×D411yescharacteristic
452C2×Dic5D3×D411yescharacteristic
453D20—21no—
454D20—32no—
455D20—64no—
456D20—61no—
457D20C2×C4×D312yes—
458C4×D5—32no—
459C4×D5—32no—
460C4×D5—42no—
461C4×D5—64no—
462C4×D5—62no—
463C4×D5—121no—
464C4×D5—122no—
465C4×D5—122no—
466C4×D5—122no—
467C4×D5—122no—
468C5×C8—21no—
469C5×C8—32no—
470#168—61no—
471#168C2×C4×D312yescomplemented
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—31no—
477C2×SD16—51no—
478C2×D8—151no—
479C2×D8—151no—
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—31no—
483C4×Q8—51no—
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—151no—
489C4×D4—151no—
490C4×D4—301no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4—301no—
494#117—151no—
495#117—301no—
496C2×C4⋊C4—151no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—31no—
501#107—151no—
502#106—51no—
503#106—151no—
504#103—151no—
505#103D3×D511yescharacteristic, complemented
506#102—31no—
507#102—51no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—31no—
513#97—151no—
514C4×C8—51no—
515C4×C8—151no—
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—22no—
520D15—42no—
521C3×D5—42no—
522C5×D3—42no—
523C23×C3—101no—
524C22×D3—21no—
525C22×D3—51no—
526C22×D3—104no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C3×Q8—21no—
531C3×Q8C2×C4×D512yescomplemented
532C3×D4—52no—
533C3×D4—101no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—51no—
537C2×C3×C4—51no—
538C2×C3×C4—101no—
539C2×C3×C4—202no—
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542C2×Dic3—21no—
543C2×Dic3—51no—
544C2×Dic3—101no—
545C2×Dic3—202no—
546C2×Dic3D4×D511yescharacteristic
547C2×Dic3D4×D511yescharacteristic
548D12—21no—
549D12—52no—
550D12—104no—
551D12—101no—
552D12C2×C4×D512yes—
553C4×D3—42no—
554C4×D3—52no—
555C4×D3—52no—
556C4×D3—102no—
557C4×D3—104no—
558C4×D3—201no—
559C4×D3—202no—
560C4×D3—202no—
561C4×D3—202no—
562C4×D3—202no—
563C3×C8—21no—
564C3×C8—52no—
565C3⋊C8—101no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—62no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5C2×D3×D411yescharacteristic
571C2×D5—22no—
572C2×D5—32no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—61no—
576C2×D5—61no—
577C2×D5—62no—
578C2×D5—128no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—22no—
582C4×C5—41no—
583C4×C5—61no—
584C4×C5—61no—
585C4×C5—121no—
586C4×C5C22×C4×D311yescharacteristic
587C4×C5D3×#4111yescharacteristic
588Dic5—21no—
589Dic5—32no—
590Dic5—41no—
591Dic5—121no—
592Dic5#91412yescomplemented
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8C2×D3×D511yescharacteristic
597C2×D4—31no—
598C2×D4—51no—
599C2×D4—154no—
600C2×D4—151no—
601C2×D4—301no—
602C2×D4—302no—
603C2×D4—301no—
604C22×C4—61no—
605C22×C4—101no—
606C22×C4—151no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—301no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—34no—
617SD16—54no—
618D8—154no—
619D8—154no—
620M16—154no—
621M16—302no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—51no—
628C4⋊C4—61no—
629C4⋊C4—101no—
630C4⋊C4—151no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—61no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—51no—
642C42—61no—
643C42—101no—
644C42—151no—
645C42—151no—
646C42—301no—
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—102no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3C2×D4×D511yescharacteristic
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—52no—
656C2×D3—101no—
657C2×D3—101no—
658C2×D3—102no—
659C2×D3—208no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—22no—
663C3×C4—41no—
664C3×C4—52no—
665C3×C4—101no—
666C3×C4—201no—
667C3×C4C22×C4×D511yescharacteristic
668C3×C4D5×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—52no—
673Dic3—201no—
674C2×C5—122no—
675C2×C5C4×D3×D411yescharacteristic
676C2×C5C2×#91411yescharacteristic
677C2×C5#576811yescharacteristic
678D5—42no—
679D5—62no—
680D5—122no—
681C23—61no—
682C23—101no—
683C23—151no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—21no—
689Q8C4×D3×D512yescomplemented
690D4—32no—
691D4—52no—
692D4—61no—
693D4—101no—
694D4—152no—
695D4—304no—
696D4—304no—
697D4—301no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—51no—
703C2×C4—51no—
704C2×C4—61no—
705C2×C4—101no—
706C2×C4—122no—
707C2×C4—151no—
708C2×C4—152no—
709C2×C4—152no—
710C2×C4—202no—
711C2×C4—304no—
712C2×C4—302no—
713C2×C4—301no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—601no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—32no—
723C8—52no—
724C8—301no—
725C2×C3—202no—
726C2×C3C4×D4×D511yescharacteristic
727C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
728C2×C3#6611111yescharacteristic
729D3—42no—
730D3—102no—
731D3—202no—
732C5C4×#91411yescharacteristic, complemented, Sylow
733C22—62no—
734C22—102no—
735C22—121no—
736C22—121no—
737C22—152no—
738C22—201no—
739C22—201no—
740C22—301no—
741C22—301no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—22no—
748C4—41no—
749C4—52no—
750C4—61no—
751C4—61no—
752C4—101no—
753C4—121no—
754C4—152no—
755C4—201no—
756C4—601no—
757C4C2×C4×D3×D511yescharacteristic
758C4#9202411yescharacteristic
759C3#1061150411yescharacteristic, complemented, Sylow
760C2—122no—
761C2—202no—
762C2—302no—
763C2—602no—
764C2#1175320311yescharacteristic
765C2D5×#91411yescharacteristic
766C2#1175410411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×#91506C2
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #11755200C2semidirect
3. #11753840C2semidirect
4. #11750904C2semidirect
5. C5×#4817C2semidirect
6. C3×#65077C2semidirect
7. #11749234C2semidirect
8. Dic5×#215C2semidirect
9. #11748109C2semidirect
10. #11747745C2semidirect
11. #11747741C2semidirect
12. #11747592C2semidirect
13. #11747470C2semidirect
14. #11747458C2semidirect
15. #11747223C2semidirect
22. C5×Q8×Dic3C22semidirect
25. C3×Q8×Dic5C22semidirect
28. #91506C4semidirect
33. #91428C22semidirect
36. #91418C22semidirect
45. C3×C5×#103C22semidirect
46. #91119C22semidirect
47. #91105C22semidirect
48. #91093C22semidirect
50. C5×#815C22semidirect
51. C5×#807C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3940C22semidirect
55. #90988C22semidirect
56. #90987C22semidirect
59. #90953C22semidirect
60. Dic5×C3⋊C8C22semidirect
72. #65077D3semidirect
80. #6821C2×C4semidirect
98. #6777C2×C4semidirect
106. C5×#215C2×C4semidirect
113. C3×#688C2×C4semidirect
128. #6654C2×C4semidirect
129. #6653C2×C4semidirect
130. #6651C2×C4semidirect
140. #4817D5semidirect
152. Q8×Dic5C2×D3semidirect
175. C5×#103C2×D3semidirect
184. C8×Dic5C2×D3semidirect
187. #3940C2×D3semidirect
199. C3×C5×Q8C22×C4semidirect
207. D60C22×C4semidirect
233. C3×#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
241. Q8×Dic3C2×D5semidirect
264. C3×#103C2×D5semidirect
273. #815C2×D5semidirect
277. #807C2×D5semidirect
312. #688C4×D3semidirect
370. C3×Dic5AGL(1,ℤ/8)semidirect
407. #215C4×D5semidirect
436. C5×Q8C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
505. #103D3×D5semidirect
531. C3×Q8C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
592. Dic5#914semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
689. Q8C4×D3×D5semidirect
732. C5C4×#914semidirect
759. C3#10611504semidirect

Maximal subgroups

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

subgroupindex
#117552002
C2×#915062
#117538402
#117509042
C5×#48172
C3×#650772
#117492342
Dic5×#2152
#117481092
#117477452
#117477412
#117475922
#117474702
#117474582
#117472232
#106115043
C4×#9145