Finite Group Databasebeta

← #14416782

Subgroups — #14416782

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
1Dic3×#713C211yesmaximal, characteristic, complemented
2C2×#91502C211yesmaximal, characteristic
3D5×#893C211yesmaximal, characteristic, complemented
4#11750889C211yesmaximal, characteristic, complemented
5C5×#4817C211yesmaximal, characteristic, complemented
6C3×#65092C211yesmaximal, characteristic, complemented
7#11749240C211yesmaximal, characteristic, complemented
8#11749235C211yesmaximal, characteristic, complemented
9#11748105C211yesmaximal, characteristic, complemented
10#11747741C211yesmaximal, characteristic, complemented
11#11747733C211yesmaximal, characteristic, complemented
12#11747601C211yesmaximal, characteristic, complemented
13#11747452C211yesmaximal, characteristic, complemented
14#11747226C211yesmaximal, characteristic, complemented
15#11747220C211yesmaximal, characteristic, complemented
16#10611504—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C2×C4×D3×D5—21no—
20Q8×Dic15C2211yescharacteristic, complemented
21C2×#6717C2211yescharacteristic
22#91782C2211yescharacteristic
23C5×Q8×Dic3C2211yescharacteristic, complemented
24C2×C5×#215C2211yescharacteristic
25C5×#893C2211yescharacteristic
26C2×C3×#676C2211yescharacteristic
27C3×D5×C4⋊C4C2211yescharacteristic
28#91502C418yescomplemented
29D5×(C2×D3)⋊C4—21no—
30#91446—21no—
31#91435C2211yescharacteristic
32#91434—21no—
33#91434C2211yescharacteristic, complemented
34#91428C2211yescharacteristic
35Dic3×D20—21no—
36Dic3×D20C2211yescharacteristic, complemented
37#91406—21no—
38C4×D5×Dic3—21no—
39C4×D5×Dic3C2211yescharacteristic
40#91358—21no—
41#91358C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6652C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47C8×Dic15C2211yescharacteristic, complemented
48#91092C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×#815C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C3×#3967C2211yescharacteristic, complemented
53C3×#3953C2211yescharacteristic, complemented
54C3×#3941C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90987C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90967C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#78866—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#65092D311yescharacteristic, complemented
72#65077—31no—
73#65059—31no—
74#65045—31no—
75#65000—31no—
76#64996—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C5×D12C2311yescharacteristic
82C2×C4×C5×D3—21no—
83C3×#713—22no—
84C3×#713C2×C414yescomplemented
85C2×C3×D20—21no—
86C2×C3×D20C2311yescharacteristic
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5C2311yescharacteristic
90C2×#1203—21no—
91C2×#1200—21no—
92C2×D3×Dic5—21no—
93C2×D5×Dic3—21no—
94C2×D5×Dic3—21no—
95C2×D5×Dic3D411yescharacteristic
96C2×D5×Dic3D411yescharacteristic
97D5×D12—22no—
98D5×D12C2×C414yescomplemented
99C4×D3×D5—44no—
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102#6717C2×C414yescomplemented
103#6714—21no—
104C4⋊Dic15—21no—
105C4⋊Dic15C2311yescharacteristic
106C4×Dic15—21no—
107C4×Dic15C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109C5×#215C2×C414yescomplemented
110C5×(C2×D3)⋊C4—21no—
111C5×C4⋊Dic3—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C4×C5×Dic3—21no—
114C4×C5×Dic3C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×#683—21no—
118C2×C3×#168C2311yescharacteristic
119C3×#676—22no—
120#6667—21no—
121(C2×D3)⋊Dic5—21no—
122#6665—21no—
123#6665—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6653C2×C414yescomplemented
129#6652C2×C414yescomplemented
130#6649C2×C414yescomplemented
131Dic3×#41—51no—
132C2×#949—51no—
133C2×#893—51no—
134C3×#417—51no—
135#5131—51no—
136Dic3×M16—51no—
137#4964—51no—
138#4817—51no—
139#4817D511yescharacteristic, complemented
140#4788—51no—
141#4788—51no—
142#4785—51no—
143#4785—51no—
144#4756—51no—
145#4756—51no—
146C2×#713C2×D311yescharacteristic
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—31no—
165#4038—61no—
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×#107—31no—
175C5×#103C2×D311yescharacteristic, complemented
176C5×#102—31no—
177C5×#97—31no—
178#3967C2×D311yescharacteristic, complemented
179#3964—31no—
180#3953—31no—
181#3953C2×D311yescharacteristic, complemented
182#3949—31no—
183C8×Dic5—31no—
184C8×Dic5—31no—
185#3941—31no—
186#3941C2×D311yescharacteristic, complemented
187#3940—31no—
188#3939—31no—
189#3935—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C3×D5—21no—
194C22×C3×D5C2×D411yescharacteristic
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
205C2×Dic15C2×D411yescharacteristic
206D60—21no—
207D60C22×C412yes—
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—
215C2×C3×Dic5—21no—
216C2×C3×Dic5C2×D411yescharacteristic
217C3×D20—24no—
218C3×D20—21no—
219C3×D20C22×C412yescomplemented
220C3×C4×D5—24no—
221C3×C4×D5—42no—
222C3×C4×D5C22×C412yes—
223C3×C4×D5#4112yes—
224#1203—24no—
225#1200—42no—
226D3×Dic5—42no—
227D5×Dic3—22no—
228D5×Dic3—41no—
229D5×Dic3—42no—
230D5×Dic3—42no—
231C3×C5×C8—21no—
232C3⋊#168C22×C412yescomplemented
233C3×#168—21no—
234C5×C3⋊C8C22×C412yescomplemented
235C2×C3×#41—51no—
236C22×D12—51no—
237C22×C4×D3—101no—
238C2×C3×M16—51no—
239C2×C3×C4⋊C4—51no—
240#949—58no—
241Q8×Dic3—51no—
242Q8×Dic3C2×D511yescharacteristic, complemented
243C2×#215—51no—
244C2×#215C2×D511yescharacteristic
245D4×Dic3—51no—
246D4×Dic3—51no—
247D4×Dic3—101no—
248D4×Dic3—101no—
249C2×#213—51no—
250C2×#213—51no—
251C2×(C2×D3)⋊C4—101no—
252#926—51no—
253#926—101no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—101no—
256C2×#208—51no—
257#893—51no—
258#893—51no—
259#893—51no—
260#893—101no—
261#893—101no—
262#893C2×D511yescharacteristic
263C3×#103—51no—
264C3×#103C2×D511yescharacteristic, complemented
265C3×#102—51no—
266C3×#102—51no—
267#821—51no—
268#821—51no—
269#821—51no—
270#821C2×D511yescharacteristic
271#815—51no—
272#815C2×D511yescharacteristic, complemented
273C8×Dic3—51no—
274C8×Dic3—51no—
275#808—51no—
276#808—51no—
277#807—51no—
278#807C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C2×C5×Q8C22×D311yescharacteristic
281C2×C5×D4—31no—
282C22×C4×C5—61no—
283C2×C22⋊D5—61no—
284C22×Dic5—61no—
285#713—22no—
286#713C4×D314yescomplemented
287D4×D5—34no—
288D4×D5—62no—
289C2×D20—21no—
290C2×D20—31no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—21no—
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—124no—
301C2×C4×D5C22×D311yescharacteristic
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#688—34no—
313#686—34no—
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—61no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—21no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C4×Dic5—61no—
327C4×Dic5—61no—
328C2×#168—31no—
329C2×#168C22×D311yescharacteristic
330D40—34no—
331#676—22no—
332#676—34no—
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—151no—
345#418—151no—
346#417—51no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—22no—
350C2×D15—41no—
351C2×D15—41no—
352C2×C5×D3—22no—
353C2×C5×D3—41no—
354C2×C5×D3—41no—
355C2×C3×D5—21no—
356C2×C3×D5—21no—
357C2×C3×D5—22no—
358C2×C3×D5—41no—
359C2×C3×D5—41no—
360C2×C3×D5C4×D412yes—
361D3×D5—48no—
362C3×C4×C5—22no—
363C3×C4×C5—41no—
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—21no—
367Dic15—41no—
368Dic15AGL(1,ℤ/8)12yescomplemented
369C3×Dic5—41no—
370C3×Dic5C4×D412yes—
371C5×Dic3—21no—
372C5×Dic3—21no—
373C5×Dic3—41no—
374C23×D3—101no—
375C3×#41—54no—
376C3×#41—102no—
377C2×C3×Q8C22×D511yescharacteristic
378C2×C3×D4—51no—
379C2×C3×D4—101no—
380C22×C3×C4—51no—
381C22×C3×C4—101no—
382C22×C3×C4—101no—
383C22×Dic3—51no—
384C22×Dic3—51no—
385C22×Dic3—101no—
386C22×Dic3—101no—
387C2×D12—51no—
388C2×D12—54no—
389C2×D12—102no—
390C2×D12—101no—
391C2×D12C22×D511yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—204no—
397C3×M16—102no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4C22×D511yescharacteristic
403#217—101no—
404#217—101no—
405#217—101no—
406#215—54no—
407#215C4×D514yescomplemented
408#213—54no—
409#213—54no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414C4⋊Dic3—21no—
415C4⋊Dic3—51no—
416C4⋊Dic3—101no—
417C4⋊Dic3C22×D511yescharacteristic
418C4×Dic3—21no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—51no—
422C4×Dic3—101no—
423C4×Dic3—101no—
424C4×Dic3C22×D511yescharacteristic
425#208—54no—
426C2×C3⋊C8—51no—
427C2×C3⋊C8C22×D511yescharacteristic
428C23×C5—61no—
429C22×D5—21no—
430C22×D5—61no—
431C22×D5—64no—
432C22×D5—122no—
433C22×D5—122no—
434C22×D5D3×D411yescharacteristic
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—31no—
450C2×Dic5—61no—
451C2×Dic5—122no—
452C2×Dic5D3×D411yescharacteristic
453D20—24no—
454D20—21no—
455D20—32no—
456D20—61no—
457D20C2×C4×D312yescomplemented
458C4×D5—24no—
459C4×D5—42no—
460C4×D5—62no—
461C4×D5—122no—
462C4×D5—122no—
463C4×D5—122no—
464C4×D5—121no—
465C4×D5—122no—
466C4×D5C2×C4×D312yes—
467C4×D5#23712yes—
468C5×C8—21no—
469C5×C8—32no—
470#168—21no—
471#168—32no—
472C2×#41—51no—
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—151no—
495#117—301no—
496C2×C4⋊C4—51no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—31no—
501#107—151no—
502#106—151no—
503#106—151no—
504#103—51no—
505#103D3×D511yescharacteristic, complemented
506#102—31no—
507#102—51no—
508#102—51no—
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—
520C3×D5—22no—
521C3×D5—42no—
522C5×D3—42no—
523C23×C3—51no—
524C23×C3—101no—
525C22×D3—21no—
526C22×D3—104no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C3×Q8—21no—
531C3×Q8C2×C4×D512yescomplemented
532C3×D4—52no—
533C3×D4—104no—
534C3×D4—101no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—51no—
538C2×C3×C4—52no—
539C2×C3×C4—52no—
540C2×C3×C4—104no—
541C2×C3×C4—101no—
542C2×C3×C4—202no—
543C2×C3×C4C23×D511yescharacteristic
544C2×Dic3—21no—
545C2×Dic3—51no—
546C2×Dic3—51no—
547C2×Dic3—102no—
548C2×Dic3—101no—
549C2×Dic3—201no—
550C2×Dic3—202no—
551C2×Dic3—202no—
552C2×Dic3D4×D511yescharacteristic
553C2×Dic3D4×D511yescharacteristic
554D12—21no—
555D12—52no—
556D12—104no—
557D12—101no—
558D12C2×C4×D512yes—
559C4×D3—42no—
560C4×D3—202no—
561C4×D3—202no—
562C4×D3—202no—
563C3×C8—21no—
564C3×C8—101no—
565C3⋊C8—52no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—62no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5C2×D3×D411yescharacteristic
571C2×D5—21no—
572C2×D5—21no—
573C2×D5—22no—
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—62no—
577C2×D5—128no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5#67⋊C412yes—
581C4×C5—22no—
582C4×C5—41no—
583C4×C5—61no—
584C4×C5—61no—
585C4×C5—121no—
586C4×C5C22×C4×D311yescharacteristic
587C4×C5C2×#23711yescharacteristic
588Dic5—32no—
589Dic5—41no—
590Dic5—61no—
591Dic5—121no—
592Dic5#67⋊C412yes—
593C24—301no—
594#41—54no—
595#41—102no—
596C2×Q8C2×D3×D511yescharacteristic
597C2×D4—31no—
598C2×D4—51no—
599C2×D4—101no—
600C2×D4—154no—
601C2×D4—151no—
602C2×D4—302no—
603C2×D4—301no—
604C22×C4—51no—
605C22×C4—61no—
606C22×C4—101no—
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—34no—
617SD16—154no—
618D8—154no—
619D8—154no—
620M16—102no—
621M16—154no—
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—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—61no—
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×C3—102no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—102no—
659C2×D3—208no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—22no—
663C3×C4—41no—
664C3×C4—52no—
665C3×C4—201no—
666C3×C4C22×C4×D511yescharacteristic
667C3×C4D5×#4111yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—41no—
671Dic3—52no—
672Dic3—101no—
673Dic3—201no—
674C2×C5—122no—
675C2×C5C2×#67⋊C411yescharacteristic
676C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
677C2×C5#577711yescharacteristic
678D5—22no—
679D5—42no—
680D5—122no—
681C23—51no—
682C23—61no—
683C23—101no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—21no—
689Q8C4×D3×D512yescomplemented
690D4—32no—
691D4—52no—
692D4—61no—
693D4—104no—
694D4—101no—
695D4—152no—
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—61no—
706C2×C4—104no—
707C2×C4—101no—
708C2×C4—122no—
709C2×C4—151no—
710C2×C4—151no—
711C2×C4—202no—
712C2×C4—302no—
713C2×C4—301no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—601no—
717C2×C4—602no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—32no—
723C8—101no—
724C8—152no—
725C2×C3—102no—
726C2×C3—202no—
727C2×C3C4×D4×D511yescharacteristic
728C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
729C2×C3#6611111yescharacteristic
730D3—42no—
731D3—202no—
732C5#7886611yescharacteristic, complemented, Sylow
733C22—52no—
734C22—62no—
735C22—101no—
736C22—101no—
737C22—102no—
738C22—121no—
739C22—121no—
740C22—201no—
741C22—201no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—22no—
748C4—41no—
749C4—52no—
750C4—61no—
751C4—61no—
752C4—121no—
753C4—152no—
754C4—201no—
755C4—301no—
756C4—601no—
757C4C2×C4×D3×D511yescharacteristic
758C4D5×#23711yescharacteristic
759C3#1061150411yescharacteristic, complemented, Sylow
760C2—102no—
761C2—122no—
762C2—202no—
763C2—602no—
764C2D5×#67⋊C411yescharacteristic
765C2#1175406711yescharacteristic
766C2#1175410111yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×#91502C2
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. Dic3×#713C2semidirect
3. D5×#893C2semidirect
4. #11750889C2semidirect
5. C5×#4817C2semidirect
6. C3×#65092C2semidirect
7. #11749240C2semidirect
8. #11749235C2semidirect
9. #11748105C2semidirect
10. #11747741C2semidirect
11. #11747733C2semidirect
12. #11747601C2semidirect
13. #11747452C2semidirect
14. #11747226C2semidirect
15. #11747220C2semidirect
20. Q8×Dic15C22semidirect
23. C5×Q8×Dic3C22semidirect
28. #91502C4semidirect
33. #91434C22semidirect
36. Dic3×D20C22semidirect
45. C3×C5×#103C22semidirect
47. C8×Dic15C22semidirect
48. #91092C22semidirect
50. C5×#815C22semidirect
51. C5×#807C22semidirect
52. C3×#3967C22semidirect
53. C3×#3953C22semidirect
54. C3×#3941C22semidirect
55. #90989C22semidirect
56. #90987C22semidirect
59. #90953C22semidirect
60. #90951C22semidirect
71. #65092D3semidirect
84. C3×#713C2×C4semidirect
98. D5×D12C2×C4semidirect
102. #6717C2×C4semidirect
109. C5×#215C2×C4semidirect
128. #6653C2×C4semidirect
129. #6652C2×C4semidirect
130. #6649C2×C4semidirect
139. #4817D5semidirect
175. C5×#103C2×D3semidirect
178. #3967C2×D3semidirect
181. #3953C2×D3semidirect
186. #3941C2×D3semidirect
199. C3×C5×Q8C22×C4semidirect
219. C3×D20C22×C4semidirect
232. C3⋊#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
242. Q8×Dic3C2×D5semidirect
264. C3×#103C2×D5semidirect
272. #815C2×D5semidirect
278. #807C2×D5semidirect
286. #713C4×D3semidirect
368. Dic15AGL(1,ℤ/8)semidirect
407. #215C4×D5semidirect
436. C5×Q8C2×C4×D3semidirect
457. D20C2×C4×D3semidirect
505. #103D3×D5semidirect
531. C3×Q8C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
689. Q8C4×D3×D5semidirect
732. C5#78866semidirect
759. C3#10611504semidirect

Maximal subgroups

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

subgroupindex
Dic3×#7132
C2×#915022
D5×#8932
#117508892
C5×#48172
C3×#650922
#117492402
#117492352
#117481052
#117477412
#117477332
#117476012
#117474522
#117472262
#117472202
#106115043
#788665