Finite Group Databasebeta

← #14416764

Subgroups — #14416764

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×#91249C211yesmaximal, characteristic
2D5×#893C211yesmaximal, characteristic, complemented
3#11753403C211yesmaximal, characteristic, complemented
4#11750973C211yesmaximal, characteristic, complemented
5C5×#4889C211yesmaximal, characteristic, complemented
6C3×#65170C211yesmaximal, characteristic, complemented
7#11747807C211yesmaximal, characteristic, complemented
8#11747796C211yesmaximal, characteristic, complemented
9#11747601C211yesmaximal, characteristic, complemented
10#11747500C211yesmaximal, characteristic, complemented
11#11747475C211yesmaximal, characteristic, complemented
12#11747470C211yesmaximal, characteristic, complemented
13#11747279C211yesmaximal, characteristic, complemented
14#11747233C211yesmaximal, characteristic, complemented
15#11747231C211yesmaximal, characteristic, complemented
16#10611504—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18C2×C4×D3×D5—21no—
19C2×#6773C2211yescharacteristic
20C2×D120C2211yescharacteristic
21#91782C2211yescharacteristic
22#91782C2211yescharacteristic, complemented
23C2×C5×#204C2211yescharacteristic
24C5×#893C2211yescharacteristic
25C5×#887C2211yescharacteristic, complemented
26C2×C3×#676C2211yescharacteristic
27C3×#4038C2211yescharacteristic
28C3×D5×C4⋊C4C2211yescharacteristic
29D5×(C2×D3)⋊C4—21no—
30#91446—21no—
31#91435C2211yescharacteristic
32#91428C2211yescharacteristic
33#91428C2211yescharacteristic, complemented
34#91406—21no—
35#91402—21no—
36C4×#1200—21no—
37#91396—21no—
38#91395—21no—
39C4×D5×Dic3C2211yescharacteristic
40#91344C2211yescharacteristic, complemented
41C2×#6660C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44#91249C418yescomplemented
45C3×C5×#107C2211yescharacteristic, complemented
46C8×Dic15C2211yescharacteristic, complemented
47#91093C2211yescharacteristic
48#91093C2211yescharacteristic, complemented
49C5×#815C2211yescharacteristic, complemented
50C5×#810C2211yescharacteristic, complemented
51C5×#809C2211yescharacteristic
52C3×#3949C2211yescharacteristic, complemented
53C3×#3940C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90972C2211yescharacteristic, complemented
56#90968C2211yescharacteristic
57#90968C2211yescharacteristic, complemented
58#90966C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#79199—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#65170D311yescharacteristic, complemented
70#65161—31no—
71#65092—31no—
72#65077—31no—
73#65059—31no—
74#65045—31no—
75#65000—31no—
76#64996—31no—
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C4×D15—21no—
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C5×Dic6C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5C2311yescharacteristic
87C2×#1203—21no—
88C2×#1202—21no—
89C2×#1200—21no—
90C2×#1200—21no—
91C2×#1200—21no—
92C2×D3×Dic5—21no—
93C2×D5×Dic3D411yescharacteristic
94C2×D5×Dic3D411yescharacteristic
95D5×D12—22no—
96D5×D12C2×C414yescomplemented
97C4×D3×D5—44no—
98#6773—22no—
99#6773C2×C414yescomplemented
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103#6714—21no—
104#6714—21no—
105C4×Dic15C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107D120C2×C414yescomplemented
108C5×(C2×D3)⋊C4—21no—
109C5×Dic3⋊C4—21no—
110C4×C5×Dic3—21no—
111C4×C5×Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C5×#204C2×C414yescomplemented
114C3×#685—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C3×C4×Dic5—21no—
119C2×C3×#168C2311yescharacteristic
120C3×#676C2×C414yescomplemented
121Dic3⋊Dic5—21no—
122#6667—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6660C2×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#4889D511yescharacteristic, complemented
140#4872—51no—
141#4872—51no—
142#4869—51no—
143#4869—51no—
144#4852—51no—
145#4852—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×Dic5—31no—
153C2×#688—31no—
154D4×Dic5—31no—
155C2×#686—31no—
156C4×C22⋊D5—61no—
157#4060—38no—
158C2×D40—31no—
159C2×#676—31no—
160C2×#676C2×D311yescharacteristic
161#4039—31no—
162#4039—31no—
163#4039—61no—
164#4038—61no—
165#4038C2×D311yescharacteristic
166D5×C4⋊C4C2×D311yescharacteristic
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C4×D20—31no—
171C4×D20—61no—
172C42×D5—31no—
173C42×D5—61no—
174C5×#107C2×D311yescharacteristic, complemented
175C5×#103—31no—
176C5×#102—31no—
177C5×#97—31no—
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3953—31no—
182#3949C2×D311yescharacteristic, complemented
183C8×Dic5—31no—
184C8×Dic5—31no—
185#3941—31no—
186#3941—31no—
187#3940C2×D311yescharacteristic, complemented
188#3939C2×D311yescharacteristic, complemented
189#3935—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×D15—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×Dic15C2×D411yescharacteristic
202C2×Dic15C2×D411yescharacteristic
203D60—21no—
204D60—21no—
205D60C22×C412yes—
206D60C22×C412yescomplemented
207C4×D15—42no—
208C4×D15—42no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C5×D12—21no—
213C5×D12C22×C412yes—
214C4×C5×D3—42no—
215C5×Dic6—21no—
216C5×Dic6C22×C412yescomplemented
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#1202—24no—
225#1200—24no—
226#1200—42no—
227#1200—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×D24—51no—
247C2×#204—51no—
248C2×#204C2×D511yescharacteristic
249#893—51no—
250#893—51no—
251#893—51no—
252#893—51no—
253#893—51no—
254#893—101no—
255#893—101no—
256#893C2×D511yescharacteristic
257#887—51no—
258#887C2×D511yescharacteristic, complemented
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#815C2×D511yescharacteristic, complemented
269C8×Dic3—51no—
270C8×Dic3—51no—
271#810—51no—
272#810C2×D511yescharacteristic, complemented
273#809—51no—
274#809—51no—
275#809—51no—
276#809—51no—
277#809—51no—
278#809C2×D511yescharacteristic
279C23×D5—61no—
280C2×C5×Q8—31no—
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—31no—
291C2×D20—61no—
292C2×C4×D5—21no—
293C2×C4×D5—31no—
294C2×C4×D5—31no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—124no—
301C2×C4×D5C22×D311yescharacteristic
302C5×SD16—34no—
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—61no—
306C5×C4⋊C4C22×D311yescharacteristic
307C5×C4⋊C4C22×D311yescharacteristic
308C5×C22⋊C4—61no—
309C42×C5—31no—
310C42×C5—61no—
311C22⋊Dic5—61no—
312#688—34no—
313#686—34no—
314#685—21no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—61no—
320C4⋊Dic5C22×D311yescharacteristic
321C4⋊Dic5C22×D311yescharacteristic
322#683—21no—
323C4×Dic5—21no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C4×Dic5—31no—
327C4×Dic5—61no—
328C2×#168—31no—
329C2×#168C22×D311yescharacteristic
330D40—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—31no—
339#440—151no—
340C4×SD16—151no—
341C4×SD16—151no—
342C4×D8—151no—
343C4×D8—151no—
344#428—51no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—22no—
350C2×D15—22no—
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—41no—
355C2×C5×D3—22no—
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—21no—
367Dic15AGL(1,ℤ/8)12yescomplemented
368C3×Dic5—41no—
369C3×Dic5—41no—
370C3×Dic5C4×D412yes—
371C5×Dic3—22no—
372C5×Dic3—21no—
373C5×Dic3—21no—
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—51no—
384C2×D12—54no—
385C2×D12—102no—
386C2×D12—101no—
387C2×D12C22×D511yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3—101no—
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×Dic6C22×D511yescharacteristic
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—101no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413Dic3⋊C4—21no—
414Dic3⋊C4—101no—
415C4×Dic3—21no—
416C4×Dic3—51no—
417C4×Dic3—51no—
418C4×Dic3—51no—
419C4×Dic3—101no—
420C4×Dic3C22×D511yescharacteristic
421#208—102no—
422C2×C3⋊C8—51no—
423C2×C3⋊C8C22×D511yescharacteristic
424D24—54no—
425D24—54no—
426#204—54no—
427#204C4×D514yescomplemented
428C23×C5—61no—
429C22×D5—61no—
430C22×D5—61no—
431C22×D5—64no—
432C22×D5—122no—
433C22×D5—122no—
434C22×D5D3×D411yescharacteristic
435C5×Q8—32no—
436C5×Q8—61no—
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—21no—
449C2×Dic5—31no—
450C2×Dic5—31no—
451C2×Dic5—122no—
452C2×Dic5D3×D411yescharacteristic
453D20—32no—
454D20—32no—
455D20—64no—
456D20—61no—
457D20—61no—
458C4×D5—42no—
459C4×D5—62no—
460C4×D5—64no—
461C4×D5—122no—
462C4×D5—122no—
463C4×D5—122no—
464C4×D5—122no—
465C4×D5—121no—
466C4×D5C2×C4×D312yes—
467C4×D5#23912yes—
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—31no—
477C2×SD16—151no—
478C2×D8—151no—
479C2×D8—151no—
480C2×M16—51no—
481C2×M16—151no—
482C4×Q8—31no—
483C4×Q8—151no—
484C4×D4—31no—
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—
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—31no—
505#103—151no—
506#102—31no—
507#102—151no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—31no—
513#97—151no—
514C4×C8—151no—
515C4×C8—151no—
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—42no—
520D15—42no—
521C3×D5—22no—
522C5×D3—42no—
523C23×C3—51no—
524C22×D3—21no—
525C22×D3—104no—
526C22×D3—101no—
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—21no—
541C2×Dic3—51no—
542C2×Dic3—51no—
543C2×Dic3—102no—
544C2×Dic3—201no—
545C2×Dic3D4×D511yescharacteristic
546C2×Dic3D4×D511yescharacteristic
547D12—21no—
548D12—52no—
549D12—52no—
550D12—104no—
551D12—101no—
552D12—101no—
553D12C2×C4×D512yes—
554C4×D3—42no—
555C4×D3—104no—
556C4×D3—202no—
557C4×D3—202no—
558C4×D3—202no—
559C4×D3—202no—
560C4×D3—202no—
561Dic6—21no—
562Dic6C2×C4×D512yescomplemented
563C3×C8—52no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—21no—
566C3⋊C8—101no—
567C22×C5—62no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5C2×D3×D411yescharacteristic
571C2×D5—21no—
572C2×D5—21no—
573C2×D5—62no—
574C2×D5—62no—
575C2×D5—128no—
576C2×D5—121no—
577C2×D5—121no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5#89312yes—
581C4×C5—41no—
582C4×C5—41no—
583C4×C5—62no—
584C4×C5—61no—
585C4×C5—61no—
586C4×C5C22×C4×D311yescharacteristic
587C4×C5C2×#23911yescharacteristic
588Dic5—32no—
589Dic5—41no—
590Dic5—41no—
591Dic5—61no—
592Dic5#89312yes—
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—31no—
597C2×D4—31no—
598C2×D4—154no—
599C2×D4—151no—
600C2×D4—151no—
601C2×D4—302no—
602C2×D4—301no—
603C2×D4—301no—
604C22×C4—51no—
605C22×C4—61no—
606C22×C4—101no—
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—154no—
618D8—154no—
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—61no—
629C4⋊C4—101no—
630C4⋊C4—301no—
631C4⋊C4C2×D3×D511yescharacteristic
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—61no—
642C42—101no—
643C42—151no—
644C42—151no—
645C42—151no—
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—41no—
654C2×D3—41no—
655C2×D3—102no—
656C2×D3—102no—
657C2×D3—208no—
658C2×D3—201no—
659C2×D3—201no—
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—21no—
671Dic3—22no—
672Dic3—52no—
673Dic3—101no—
674C2×C5—122no—
675C2×C5C2×#89311yescharacteristic
676C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
677C2×C5#577711yescharacteristic
678D5—22no—
679D5—122no—
680D5—122no—
681C23—51no—
682C23—61no—
683C23—304no—
684C23—301no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—32no—
689Q8—61no—
690D4—32no—
691D4—61no—
692D4—152no—
693D4—152no—
694D4—304no—
695D4—304no—
696D4—301no—
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—61no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—122no—
709C2×C4—151no—
710C2×C4—151no—
711C2×C4—202no—
712C2×C4—304no—
713C2×C4—302no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4—601no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—52no—
722C8—61no—
723C8—301no—
724C8C4×D3×D512yescomplemented
725C2×C3—102no—
726C2×C3C4×D4×D511yescharacteristic
727C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
728C2×C3#6611111yescharacteristic
729D3—42no—
730D3—202no—
731D3—202no—
732C5#7919911yescharacteristic, complemented, Sylow
733C22—52no—
734C22—62no—
735C22—101no—
736C22—101no—
737C22—121no—
738C22—121no—
739C22—302no—
740C22—302no—
741C22—608no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—41no—
748C4—41no—
749C4—52no—
750C4—61no—
751C4—62no—
752C4—61no—
753C4—152no—
754C4—201no—
755C4—201no—
756C4—301no—
757C4C2×C4×D3×D511yescharacteristic
758C4D5×#23911yescharacteristic
759C3#1061150411yescharacteristic, complemented, Sylow
760C2—102no—
761C2—122no—
762C2—602no—
763C2—602no—
764C2D5×#89311yescharacteristic
765C2#1175404711yescharacteristic
766C2#1175410111yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#91249C2
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. #11753403C2semidirect
4. #11750973C2semidirect
5. C5×#4889C2semidirect
6. C3×#65170C2semidirect
7. #11747807C2semidirect
8. #11747796C2semidirect
9. #11747601C2semidirect
10. #11747500C2semidirect
11. #11747475C2semidirect
12. #11747470C2semidirect
13. #11747279C2semidirect
14. #11747233C2semidirect
15. #11747231C2semidirect
22. #91782C22semidirect
25. C5×#887C22semidirect
33. #91428C22semidirect
40. #91344C22semidirect
44. #91249C4semidirect
45. C3×C5×#107C22semidirect
46. C8×Dic15C22semidirect
48. #91093C22semidirect
49. C5×#815C22semidirect
50. C5×#810C22semidirect
52. C3×#3949C22semidirect
53. C3×#3940C22semidirect
54. C3×#3939C22semidirect
55. #90972C22semidirect
57. #90968C22semidirect
59. #90953C22semidirect
60. #90951C22semidirect
69. #65170D3semidirect
96. D5×D12C2×C4semidirect
99. #6773C2×C4semidirect
107. D120C2×C4semidirect
113. C5×#204C2×C4semidirect
120. C3×#676C2×C4semidirect
128. #6660C2×C4semidirect
129. #6654C2×C4semidirect
139. #4889D5semidirect
174. C5×#107C2×D3semidirect
182. #3949C2×D3semidirect
187. #3940C2×D3semidirect
188. #3939C2×D3semidirect
206. D60C22×C4semidirect
216. C5×Dic6C22×C4semidirect
231. C3×C5×C8C22×C4semidirect
233. C3×#168C22×C4semidirect
258. #887C2×D5semidirect
264. C3×#107C2×D5semidirect
268. #815C2×D5semidirect
272. #810C2×D5semidirect
332. #676C4×D3semidirect
367. Dic15AGL(1,ℤ/8)semidirect
427. #204C4×D5semidirect
469. C5×C8C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
501. #107D3×D5semidirect
562. Dic6C2×C4×D5semidirect
564. C3×C8C2×C4×D5semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
724. C8C4×D3×D5semidirect
732. C5#79199semidirect
759. C3#10611504semidirect

Maximal subgroups

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

subgroupindex
C2×#912492
D5×#8932
#117534032
#117509732
C5×#48892
C3×#651702
#117478072
#117477962
#117476012
#117475002
#117474752
#117474702
#117472792
#117472332
#117472312
#106115043
#791995