Finite Group Databasebeta

← #14416759

Subgroups — #14416759

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
1C2×#91250C211yesmaximal, characteristic
2D5×#893C211yesmaximal, characteristic, complemented
3#11753402C211yesmaximal, characteristic, complemented
4#11750990C211yesmaximal, characteristic, complemented
5C5×#4872C211yesmaximal, characteristic, complemented
6C3×#65170C211yesmaximal, characteristic, complemented
7#11747813C211yesmaximal, characteristic, complemented
8#11747789C211yesmaximal, characteristic, complemented
9Dic3×#676C211yesmaximal, characteristic, complemented
10#11747498C211yesmaximal, characteristic, complemented
11#11747475C211yesmaximal, characteristic, complemented
12#11747277C211yesmaximal, characteristic, complemented
13#11747236C211yesmaximal, characteristic, complemented
14#11747235C211yesmaximal, characteristic, complemented
15#11747230C211yesmaximal, characteristic, complemented
16C4×#4057—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18C2×C4×D3×D5—21no—
19C2×#6772C2211yescharacteristic
20C2×#6706C2211yescharacteristic
21#91782C2211yescharacteristic
22#91776C2211yescharacteristic, complemented
23C2×C5×D24C2211yescharacteristic
24C5×#893C2211yescharacteristic
25C5×#893C2211yescharacteristic, complemented
26C2×C3×#676C2211yescharacteristic
27C3×#4038C2211yescharacteristic
28C3×D5×C4⋊C4C2211yescharacteristic
29D5×(C2×D3)⋊C4—21no—
30#91446—21no—
31#91442—21no—
32#91441—21no—
33#91435C2211yescharacteristic
34#91435C2211yescharacteristic, complemented
35#91428C2211yescharacteristic
36#91406—21no—
37#91398—21no—
38C4×D3×Dic5—21no—
39C4×D5×Dic3C2211yescharacteristic
40#91340C2211yescharacteristic, complemented
41C2×#6659C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44#91250C418yescomplemented
45C3×C5×#107C2211yescharacteristic, complemented
46#91099C2211yescharacteristic, complemented
47#91094C2211yescharacteristic, complemented
48#91093C2211yescharacteristic
49C5×C8×Dic3C2211yescharacteristic, complemented
50C5×#809C2211yescharacteristic
51C5×#809C2211yescharacteristic, complemented
52C3×#3949C2211yescharacteristic, complemented
53C3×#3940C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90974C2211yescharacteristic, complemented
56#90968C2211yescharacteristic
57#90966C2211yescharacteristic
58#90966C2211yescharacteristic, complemented
59#90954C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#79199—51nomaximal, Hall
62C2×#4057—31no—
63C4×D4×D5—31no—
64C4×#711—31no—
65C4×C5×D8—31no—
66#65441—31no—
67C4×#687—31no—
68C4×#686—31no—
69#65178—31no—
70#65170D311yescharacteristic, complemented
71#65074—31no—
72#65060—31no—
73#65059—31no—
74#65046—31no—
75C4×#677—31no—
76C4×#676—31no—
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30C2311yescharacteristic
81C2×C5×D12C2311yescharacteristic
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1203—21no—
88C2×#1201—21no—
89C2×#1200—21no—
90C2×D3×Dic5—21no—
91C2×D3×Dic5—21no—
92C2×D3×Dic5—21no—
93C2×D5×Dic3D411yescharacteristic
94C2×D5×Dic3D411yescharacteristic
95D5×D12—22no—
96D5×D12C2×C414yescomplemented
97C4×D3×D5—44no—
98#6772—22no—
99#6772C2×C414yescomplemented
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103#6714—21no—
104#6712—21no—
105C4×Dic15—21no—
106C4×Dic15C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108#6706C2×C414yescomplemented
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4—21no—
111C4×C5×Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C5×D24C2×C414yescomplemented
114C3×#685—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×C4×Dic5—21no—
119C2×C3×#168C2311yescharacteristic
120C3×#676C2×C414yescomplemented
121#6669—21no—
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124(C2×D3)⋊Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6659C2×C414yescomplemented
129#6654C2×C414yescomplemented
130#6649—22no—
131C2×#908—51no—
132#5522—51no—
133C2×#893—51no—
134C3×#428—51no—
135Dic3×M16—51no—
136#5001—51no—
137#4966—51no—
138#4889—51no—
139#4889—51no—
140#4872—51no—
141#4872D511yescharacteristic, complemented
142#4869—51no—
143#4869—51no—
144#4852—51no—
145#4852—51no—
146C2×#711—31no—
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×D8—31no—
150C4×C5×D4—31no—
151C4×C5×D4—31no—
152D4×Dic5—31no—
153D4×Dic5—31no—
154C2×#687—31no—
155C2×#686—31no—
156C4×C22⋊D5—61no—
157C4×C22⋊D5—61no—
158C2×C4×Dic5—61no—
159#4057—38no—
160C2×#677—31no—
161C2×#676—31no—
162C2×#676C2×D311yescharacteristic
163#4039—31no—
164#4038C2×D311yescharacteristic
165D5×C4⋊C4C2×D311yescharacteristic
166#4033—31no—
167#4027—61no—
168#4027—61no—
169D5×C22⋊C4—61no—
170#4023—61no—
171C4×D20—31no—
172C42×D5—31no—
173C4×Dic10—31no—
174C5×#107C2×D311yescharacteristic, complemented
175C5×#102—31no—
176C5×#102—31no—
177C4×C5×C8—31no—
178#3964—31no—
179#3964—31no—
180#3953—31no—
181#3949C2×D311yescharacteristic, complemented
182#3948—31no—
183#3947—31no—
184#3947—31no—
185#3942—31no—
186#3941—31no—
187#3940C2×D311yescharacteristic, complemented
188#3939C2×D311yescharacteristic, complemented
189C4×#168—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C3×D5C2×D411yescharacteristic
195C2×D3×D5—24no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2411yescharacteristic
201C2×Dic15—21no—
202C2×Dic15C2×D411yescharacteristic
203C2×Dic15C2×D411yescharacteristic
204D60—21no—
205D60C22×C412yes—
206C4×D15—42no—
207Dic30—21no—
208Dic30C22×C412yescomplemented
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C5×D12—21no—
212C5×D12—21no—
213C5×D12C22×C412yes—
214C5×D12C22×C412yescomplemented
215C4×C5×D3—42no—
216C4×C5×D3—42no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5C2×D411yescharacteristic
220C3×C4×D5—42no—
221C3×C4×D5C22×C412yes—
222C3×C4×D5#4112yes—
223#1203—24no—
224#1201—24no—
225#1200—42no—
226D3×Dic5—24no—
227D3×Dic5—42no—
228D3×Dic5—42no—
229D5×Dic3—22no—
230D5×Dic3—41no—
231C3×C5×C8C22×C412yescomplemented
232C3⋊#168—21no—
233C3×#168C22×C412yescomplemented
234C5×C3⋊C8—21no—
235C2×#235—51no—
236C22×D12—51no—
237C22×C4×D3—101no—
238C2×C3×M16—51no—
239C3×#117—51no—
240C2×C3×C4⋊C4—51no—
241C2×(C2×D3)⋊C4—101no—
242C2×C4×Dic3—51no—
243C2×#208—51no—
244#908—58no—
245C2×D24—51no—
246C2×D24C2×D511yescharacteristic
247C2×#204—51no—
248C2×#204—51no—
249#893—51no—
250#893—51no—
251#893—51no—
252#893—51no—
253#893—101no—
254#893—101no—
255#893C2×D511yescharacteristic
256#893C2×D511yescharacteristic, complemented
257#887—51no—
258#887—51no—
259#67⋊C4—101no—
260#67⋊C4—101no—
261#872—101no—
262C42×D3—101no—
263C3×#107—51no—
264C3×#107C2×D511yescharacteristic, complemented
265C3×#106—51no—
266C3×#106—51no—
267#815—51no—
268#815—51no—
269C8×Dic3—51no—
270C8×Dic3C2×D511yescharacteristic, complemented
271#810—51no—
272#810—51no—
273#809—51no—
274#809—51no—
275#809—51no—
276#809—51no—
277#809C2×D511yescharacteristic
278#809C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C2×C5×D4—31no—
281C2×C5×D4—31no—
282C22×C4×C5—61no—
283C22×C4×C5—61no—
284C2×C22⋊D5—61no—
285C2×C22⋊D5—61no—
286C22×Dic5—61no—
287C22×Dic5—61no—
288C22×Dic5—61no—
289#711—34no—
290#711—62no—
291D4×D5—34no—
292D4×D5—62no—
293C2×D20—31no—
294C2×C4×D5—21no—
295C2×C4×D5—31no—
296C2×C4×D5—31no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—124no—
300C2×C4×D5C22×D311yescharacteristic
301C2×Dic10—31no—
302C5×D8—34no—
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4C22×D311yescharacteristic
306C5×C4⋊C4C22×D311yescharacteristic
307C5×C22⋊C4—61no—
308C5×C22⋊C4—61no—
309C42×C5—31no—
310C22⋊Dic5—61no—
311C22⋊Dic5—61no—
312#687—34no—
313#686—34no—
314#685—21no—
315#685—61no—
316#685—61no—
317C4⋊Dic5C22×D311yescharacteristic
318C4⋊Dic5C22×D311yescharacteristic
319#683—21no—
320#683—61no—
321#683—61no—
322C4×Dic5—21no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C4×Dic5—61no—
327C4×Dic5—61no—
328C2×#168—31no—
329C2×#168C22×D311yescharacteristic
330#677—34no—
331#676—62no—
332#676C4×D314yescomplemented
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—151no—
337#442—151no—
338#440—151no—
339#440—151no—
340C4×SD16—151no—
341C4×SD16—151no—
342C4×D8—31no—
343C4×D8—151no—
344#428—51no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—22no—
350C2×D15—41no—
351C2×D15—41no—
352C2×C5×D3—22no—
353C2×C5×D3—22no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C3×D5—21no—
359C2×C3×D5—21no—
360C2×C3×D5C4×D412yes—
361D3×D5—48no—
362C3×C4×C5—41no—
363C3×C4×C5—41no—
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—22no—
367Dic15—21no—
368Dic15—21no—
369C3×Dic5—41no—
370C3×Dic5—41no—
371C3×Dic5C4×D412yes—
372C5×Dic3—21no—
373C5×Dic3AGL(1,ℤ/8)12yescomplemented
374C23×D3—101no—
375C22×C3×C4—51no—
376C22×C3×C4—101no—
377C2×#67—101no—
378C22×Dic3—51no—
379C22×Dic3—51no—
380#235—54no—
381#235—102no—
382C2×D12—51no—
383C2×D12—54no—
384C2×D12—102no—
385C2×D12—101no—
386C2×D12C22×D511yescharacteristic
387C2×D12C22×D511yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3—21no—
390C2×C4×D3—101no—
391C2×C4×D3—101no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—204no—
396C2×Dic6—51no—
397C3×M16—54no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—101no—
403C3×C4⋊C4C22×D511yescharacteristic
404C3×C4⋊C4C22×D511yescharacteristic
405C3×C22⋊C4—101no—
406C3×C42—101no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413Dic3⋊C4—101no—
414Dic3⋊C4—101no—
415C4×Dic3—51no—
416C4×Dic3—51no—
417C4×Dic3—51no—
418C4×Dic3—101no—
419C4×Dic3—101no—
420C4×Dic3C22×D511yescharacteristic
421#208—102no—
422C2×C3⋊C8—51no—
423C2×C3⋊C8C22×D511yescharacteristic
424D24—54no—
425D24C4×D514yescomplemented
426#204—54no—
427#204—54no—
428C23×C5—61no—
429C23×C5—61no—
430C22×D5—61no—
431C22×D5—64no—
432C22×D5—122no—
433C22×D5—122no—
434C22×D5D3×D411yescharacteristic
435C5×D4—32no—
436C5×D4—32no—
437C5×D4—61no—
438C5×D4—61no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—31no—
442C2×C4×C5—31no—
443C2×C4×C5—122no—
444C2×C4×C5—122no—
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C22⋊D5—64no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—31no—
451C2×Dic5—31no—
452C2×Dic5—61no—
453C2×Dic5—64no—
454C2×Dic5—122no—
455C2×Dic5—122no—
456C2×Dic5D3×D411yescharacteristic
457D20—32no—
458D20—61no—
459C4×D5—42no—
460C4×D5—62no—
461C4×D5—122no—
462C4×D5—122no—
463C4×D5—121no—
464C4×D5C2×C4×D312yes—
465C4×D5#23912yes—
466Dic10—32no—
467Dic10—61no—
468C5×C8—61no—
469C5×C8C2×C4×D312yescomplemented
470#168—61no—
471#168C2×C4×D312yescomplemented
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—151no—
477C2×SD16—151no—
478C2×D8—31no—
479C2×D8—151no—
480C2×M16—51no—
481C2×M16—151no—
482C4×Q8—151no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—31no—
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—51no—
495#117—301no—
496C2×C4⋊C4—51no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—51no—
501#107D3×D511yescharacteristic, complemented
502#106—51no—
503#106—51no—
504#103—151no—
505#103—151no—
506#102—31no—
507#102—31no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—151no—
513#97—151no—
514C4×C8—31no—
515C4×C8—151no—
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—42no—
520C3×D5—22no—
521C5×D3—42no—
522C5×D3—42no—
523C23×C3—51no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—104no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—51no—
533C2×C3×C4—52no—
534C2×C3×C4—52no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—202no—
538C2×C3×C4C23×D511yescharacteristic
539#67—104no—
540C2×Dic3—51no—
541C2×Dic3—51no—
542C2×Dic3—101no—
543C2×Dic3—102no—
544C2×Dic3—201no—
545C2×Dic3D4×D511yescharacteristic
546C2×Dic3D4×D511yescharacteristic
547D12—21no—
548D12—21no—
549D12—52no—
550D12—104no—
551D12—101no—
552D12C2×C4×D512yes—
553D12C2×C4×D512yescomplemented
554C4×D3—42no—
555C4×D3—42no—
556C4×D3—104no—
557C4×D3—202no—
558C4×D3—202no—
559C4×D3—202no—
560C4×D3—202no—
561Dic6—52no—
562Dic6—101no—
563C3×C8—52no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—21no—
566C3⋊C8—101no—
567C22×C5—62no—
568C22×C5—62no—
569C22×C5—121no—
570C22×C5—121no—
571C22×C5—121no—
572C22×C5—121no—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—21no—
575C2×D5—21no—
576C2×D5—62no—
577C2×D5—128no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5#89312yes—
581C4×C5—32no—
582C4×C5—41no—
583C4×C5—41no—
584C4×C5—61no—
585C4×C5C22×C4×D311yescharacteristic
586C4×C5C2×#23911yescharacteristic
587Dic5—41no—
588Dic5—41no—
589Dic5—62no—
590Dic5—61no—
591Dic5—61no—
592Dic5#89312yes—
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—151no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—154no—
600C2×D4—151no—
601C2×D4—302no—
602C2×D4—301no—
603C2×D4—301no—
604C22×C4—51no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—101no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—154no—
617SD16—154no—
618D8—34no—
619D8—154no—
620M16—54no—
621M16—302no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—51no—
627C4⋊C4—51no—
628C4⋊C4—101no—
629C4⋊C4—301no—
630C4⋊C4—301no—
631C4⋊C4C2×D3×D511yescharacteristic
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—101no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—101no—
642C42—151no—
643C42—151no—
644C42—151no—
645C42—301no—
646C42—301no—
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—52no—
649C22×C3—101no—
650C22×C3—101no—
651C22×C3C2×D4×D511yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—102no—
659C2×D3—208no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—52no—
665C3×C4—201no—
666C3×C4—201no—
667C3×C4C22×C4×D511yescharacteristic
668C3×C4D5×#4111yescharacteristic
669Dic3—21no—
670Dic3—101no—
671Dic3—101no—
672Dic3—102no—
673Dic3#405712yescomplemented
674C2×C5—122no—
675C2×C5—122no—
676C2×C5C2×#89311yescharacteristic
677C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
678C2×C5#577711yescharacteristic
679D5—22no—
680D5—122no—
681C23—51no—
682C23—61no—
683C23—61no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—152no—
689Q8—301no—
690D4—32no—
691D4—32no—
692D4—61no—
693D4—61no—
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—52no—
704C2×C4—52no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—151no—
710C2×C4—151no—
711C2×C4—202no—
712C2×C4—302no—
713C2×C4—304no—
714C2×C4—301no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—601no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—52no—
722C8—61no—
723C8—301no—
724C8C4×D3×D512yescomplemented
725C2×C3—102no—
726C2×C3C4×D4×D511yescharacteristic
727C2×C3C2×#405711yescharacteristic
728C2×C3#6610211yescharacteristic
729D3—42no—
730D3—42no—
731D3—202no—
732C5#7919911yescharacteristic, complemented, Sylow
733C22—52no—
734C22—62no—
735C22—62no—
736C22—101no—
737C22—101no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—32no—
748C4—41no—
749C4—41no—
750C4—52no—
751C4—61no—
752C4—201no—
753C4—201no—
754C4—301no—
755C4—302no—
756C4—301no—
757C4C2×C4×D3×D511yescharacteristic
758C4D5×#23911yescharacteristic
759C3C4×#405711yescharacteristic, complemented, Sylow
760C2—102no—
761C2—122no—
762C2—122no—
763C2—602no—
764C2D5×#89311yescharacteristic
765C2D3×#405711yescharacteristic
766C2#1175410211yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#91250C2
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. D5×#893C2semidirect
3. #11753402C2semidirect
4. #11750990C2semidirect
5. C5×#4872C2semidirect
6. C3×#65170C2semidirect
7. #11747813C2semidirect
8. #11747789C2semidirect
9. Dic3×#676C2semidirect
10. #11747498C2semidirect
11. #11747475C2semidirect
12. #11747277C2semidirect
13. #11747236C2semidirect
14. #11747235C2semidirect
15. #11747230C2semidirect
22. #91776C22semidirect
25. C5×#893C22semidirect
34. #91435C22semidirect
40. #91340C22semidirect
44. #91250C4semidirect
45. C3×C5×#107C22semidirect
46. #91099C22semidirect
47. #91094C22semidirect
49. C5×C8×Dic3C22semidirect
51. C5×#809C22semidirect
52. C3×#3949C22semidirect
53. C3×#3940C22semidirect
54. C3×#3939C22semidirect
55. #90974C22semidirect
58. #90966C22semidirect
59. #90954C22semidirect
60. Dic3×#168C22semidirect
70. #65170D3semidirect
96. D5×D12C2×C4semidirect
99. #6772C2×C4semidirect
108. #6706C2×C4semidirect
113. C5×D24C2×C4semidirect
120. C3×#676C2×C4semidirect
128. #6659C2×C4semidirect
129. #6654C2×C4semidirect
141. #4872D5semidirect
174. C5×#107C2×D3semidirect
181. #3949C2×D3semidirect
187. #3940C2×D3semidirect
188. #3939C2×D3semidirect
208. Dic30C22×C4semidirect
214. C5×D12C22×C4semidirect
231. C3×C5×C8C22×C4semidirect
233. C3×#168C22×C4semidirect
256. #893C2×D5semidirect
264. C3×#107C2×D5semidirect
270. C8×Dic3C2×D5semidirect
278. #809C2×D5semidirect
332. #676C4×D3semidirect
373. C5×Dic3AGL(1,ℤ/8)semidirect
425. D24C4×D5semidirect
469. C5×C8C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
501. #107D3×D5semidirect
553. D12C2×C4×D5semidirect
564. C3×C8C2×C4×D5semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
673. Dic3#4057semidirect
724. C8C4×D3×D5semidirect
732. C5#79199semidirect
759. C3C4×#4057semidirect

Maximal subgroups

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

subgroupindex
C2×#912502
D5×#8932
#117534022
#117509902
C5×#48722
C3×#651702
#117478132
#117477892
Dic3×#6762
#117474982
#117474752
#117472772
#117472362
#117472352
#117472302
C4×#40573
#791995