Finite Group Databasebeta

← #14416786

Subgroups — #14416786

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
1C3×C4×D4×D5C211yesmaximal, characteristic, complemented
2C2×#91491C211yesmaximal, characteristic
3C4×#6773C211yesmaximal, characteristic, complemented
4#11751115C211yesmaximal, characteristic, complemented
5C5×#5018C211yesmaximal, characteristic, complemented
6Dic5×#214C211yesmaximal, characteristic, complemented
7#11748975C211yesmaximal, characteristic, complemented
8#11748962C211yesmaximal, characteristic, complemented
9#11747500C211yesmaximal, characteristic, complemented
10#11747452C211yesmaximal, characteristic, complemented
11#11747261C211yesmaximal, characteristic, complemented
12#11747223C211yesmaximal, characteristic, complemented
13#11747048C211yesmaximal, characteristic, complemented
14#11747023C211yesmaximal, characteristic, complemented
15#11747003C211yesmaximal, characteristic, complemented
16#10611504—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C22×C3×C4×D5—21no—
19C2×#6773C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C2×#6715C2211yescharacteristic
22C4×D60C2211yescharacteristic, complemented
23C2×C5×#214C2211yescharacteristic
24C4×C5×Dic6C2211yescharacteristic, complemented
25C3×D4×Dic5C2211yescharacteristic
26C3×C4×C22⋊D5—21no—
27C3×#4039C2211yescharacteristic
28C3×D5×C4⋊C4C2211yescharacteristic
29C3×#4027—21no—
30C3×D5×C22⋊C4—21no—
31C3×C4×D20C2211yescharacteristic
32C3×C42×D5C2211yescharacteristic
33#91491C418yescomplemented
34#91444—21no—
35C4×#1202—21no—
36#91418C2211yescharacteristic, complemented
37#91402—21no—
38C4×#1200—21no—
39#91358C2211yescharacteristic
40Dic5×Dic6C2211yescharacteristic, complemented
41C2×#6655C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45#91116C2211yescharacteristic
46#91093C2211yescharacteristic, complemented
47#91092C2211yescharacteristic, complemented
48#91087C2211yescharacteristic, complemented
49C5×#832C2211yescharacteristic
50C5×#810C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C5×#803C2211yescharacteristic, complemented
53#90989C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90972C2211yescharacteristic, complemented
56#90968C2211yescharacteristic, complemented
57#90965C2211yescharacteristic
58#90964C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61C4×#932—51nomaximal, Hall
62C2×#4060—31no—
63C4×#713—31no—
64C4×D4×D5D311yescharacteristic, complemented
65C5×#440—31no—
66SD16×Dic5—31no—
67#65315—31no—
68#65303—31no—
69#65170—31no—
70#65161—31no—
71#65092—31no—
72#65077—31no—
73#65059—31no—
74#65045—31no—
75#65000—31no—
76#64996—31no—
77C23×C3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×C5×Dic6C2311yescharacteristic
83C2×C3×C22⋊D5—21no—
84C22×C3×Dic5—21no—
85C3×D4×D5—22no—
86C3×D4×D5C2×C414yescomplemented
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—44no—
92C2×C3×C4×D5D411yescharacteristic
93C2×C3×C4×D5D411yescharacteristic
94C2×C3×C4×D5C2311yescharacteristic
95C2×#1202—21no—
96C2×#1200—21no—
97C2×#1200—21no—
98#6773—22no—
99#6773C2×C414yescomplemented
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C22⋊C4—21no—
102C3×C42×C5C2311yescharacteristic
103#6715C2×C414yescomplemented
104#6714—21no—
105C4⋊Dic15C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C5×#214C2×C414yescomplemented
109C5×C4⋊Dic3C2311yescharacteristic
110C5×Dic3⋊C4—21no—
111C4×C5×Dic3—21no—
112C2×C5×C3⋊C8C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C3×C22⋊Dic5—21no—
115C3×#685—21no—
116C3×#685—21no—
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×C4×Dic5D411yescharacteristic
120C3×C4×Dic5D411yescharacteristic
121C3×C4×Dic5C2311yescharacteristic
122Dic3⋊Dic5—21no—
123#6667—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6655C2×C414yescomplemented
128#6653C2×C414yescomplemented
129#6649—22no—
130#6649C2×C414yescomplemented
131C2×C3×C4×D4—51no—
132C2×#932—51no—
133C4×#235—51no—
134#5215—51no—
135#5018—51no—
136#5018D511yescharacteristic, complemented
137C4×#214—51no—
138C4×#214—51no—
139#5014—51no—
140#5014—51no—
141C4×#213—51no—
142C4×#213—51no—
143#4966—51no—
144#4964—51no—
145C4×#208—51no—
146C2×#713—31no—
147C2×D4×D5C2×D311yescharacteristic
148C22×C4×D5—21no—
149C2×C5×SD16—31no—
150C4×C5×Q8—31no—
151C4×C5×D4C2×D311yescharacteristic
152Q8×Dic5—31no—
153C2×#688—31no—
154D4×Dic5C2×D311yescharacteristic
155C2×#686—31no—
156C4×C22⋊D5—21no—
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⋊C4C2×D311yescharacteristic
167#4027—21no—
168D5×C22⋊C4—21no—
169C4×D20—31no—
170C4×D20—61no—
171C4×D20C2×D311yescharacteristic
172C42×D5—61no—
173C42×D5C2×D311yescharacteristic
174C5×#107—31no—
175C5×#103—31no—
176C5×#102—31no—
177C5×#97—31no—
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3953—31no—
182#3949—31no—
183C8×Dic5—31no—
184C8×Dic5—31no—
185#3941—31no—
186#3941—31no—
187#3940—31no—
188#3939—31no—
189#3935—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C23×C3×C5—21no—
192C22×D15—21no—
193C22×C3×D5—21no—
194C22×C3×D5—24no—
195C22×C3×D5—42no—
196C22×C3×D5—42no—
197C22×C3×D5C2×D411yescharacteristic
198C3×C5×D4—21no—
199C3×C5×D4C22×C412yes—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—42no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205C2×Dic15—21no—
206D60—21no—
207D60C22×C412yescomplemented
208C4×D15—42no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C5×Dic6—21no—
212C5×Dic6C22×C412yescomplemented
213C3×C22⋊D5—24no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—42no—
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C3×D20—21no—
220C3×D20C22×C412yes—
221C3×C4×D5—22no—
222C3×C4×D5—41no—
223C3×C4×D5—42no—
224C3×C4×D5—42no—
225C3×C4×D5—42no—
226C3×C4×D5C22×C412yes—
227C3×C4×D5#4112yes—
228#1202—24no—
229#1200—24no—
230#1200—42no—
231C3⋊#168—21no—
232C3⋊#168C22×C412yescomplemented
233C5×C3⋊C8—21no—
234C5×C3⋊C8C22×C412yescomplemented
235C22×C3×D4—51no—
236C23×C3×C4—101no—
237C2×#235—51no—
238C3×C4×D4—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—101no—
242C3×C4×D4—101no—
243C3×C4×D4C2×D511yescharacteristic
244C2×C3×C4⋊C4—51no—
245C2×C3×C22⋊C4—101no—
246C2×C3×C42—51no—
247C2×#214—51no—
248C2×#214C2×D511yescharacteristic
249#932—58no—
250C2×#213—51no—
251C2×#213—51no—
252C4×#67—101no—
253C4×#67—101no—
254#926—51no—
255C2×#208—51no—
256C2×#208—51no—
257C4×D12—51no—
258C4×D12—51no—
259#872—101no—
260C42×D3—101no—
261C4×Dic6—51no—
262C4×Dic6C2×D511yescharacteristic, complemented
263#832—51no—
264#832—51no—
265#832—51no—
266#832C2×D511yescharacteristic
267#810—51no—
268#810C2×D511yescharacteristic, complemented
269#809—51no—
270#809—51no—
271#808—51no—
272#808—51no—
273#807—51no—
274#807C2×D511yescharacteristic, complemented
275#803—51no—
276#803C2×D511yescharacteristic, complemented
277C4×C3⋊C8—51no—
278C4×C3⋊C8—51no—
279C23×D5—21no—
280C2×C5×Q8—31no—
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—21no—
283C2×C22⋊D5—21no—
284C22×Dic5—21no—
285#713—34no—
286#713—62no—
287D4×D5—22no—
288D4×D5C4×D314yescomplemented
289C2×D20—31no—
290C2×D20—61no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—21no—
294C2×C4×D5—21no—
295C2×C4×D5—44no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5#6711yescharacteristic
300C2×C4×D5#6711yescharacteristic
301C2×C4×D5C22×D311yescharacteristic
302C5×SD16—34no—
303C2×C5×C8—31no—
304C2×C5×C8—31no—
305C5×C4⋊C4—31no—
306C5×C4⋊C4—61no—
307C5×C4⋊C4C22×D311yescharacteristic
308C5×C22⋊C4—21no—
309C42×C5—61no—
310C42×C5C22×D311yescharacteristic
311C22⋊Dic5—21no—
312#688—34no—
313#686—34no—
314#685—21no—
315#685—21no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—61no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—21no—
323C4×Dic5—61no—
324C4×Dic5—61no—
325C4×Dic5#6711yescharacteristic
326C4×Dic5#6711yescharacteristic
327C4×Dic5C22×D311yescharacteristic
328C2×#168—31no—
329C2×#168—31no—
330D40—34no—
331#676—34no—
332#676—62no—
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—51no—
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—151no—
347C4×M16—151no—
348C22×C3×C5—22no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5C22×D411yescharacteristic
352C2×D15—22no—
353C2×D15—41no—
354C2×D15—41no—
355C2×C3×D5—21no—
356C2×C3×D5—21no—
357C2×C3×D5—22no—
358C2×C3×D5—48no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361C2×C3×D5C4×D412yes—
362C3×C4×C5—21no—
363C3×C4×C5—21no—
364C3×C4×C5—41no—
365C3×C4×C5C23×C411yescharacteristic
366C3×C4×C5C2×#4111yescharacteristic
367Dic15—41no—
368C3×Dic5—21no—
369C3×Dic5—41no—
370C3×Dic5C4×D412yes—
371C3×Dic5AGL(1,ℤ/8)12yescomplemented
372C5×Dic3—22no—
373C5×Dic3—41no—
374C24×C3—101no—
375C2×C3×D4—54no—
376C2×C3×D4—51no—
377C2×C3×D4—102no—
378C2×C3×D4—101no—
379C2×C3×D4C22×D511yescharacteristic
380C22×C3×C4—21no—
381C22×C3×C4—51no—
382C22×C3×C4—51no—
383C22×C3×C4—51no—
384C22×C3×C4—101no—
385C22×C3×C4—101no—
386C22×C3×C4—101no—
387C22×C3×C4—101no—
388C22×C3×C4—204no—
389C2×#67—101no—
390#235—54no—
391#235—102no—
392C2×D12—51no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×Dic6C22×D511yescharacteristic
397C3×C4⋊C4—51no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4C22×D511yescharacteristic
400C3×C22⋊C4—21no—
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C42—51no—
405C3×C42—51no—
406C3×C42—51no—
407C3×C42C22×D511yescharacteristic
408#217—101no—
409#214—54no—
410#214C4×D514yescomplemented
411#213—54no—
412#213—54no—
413(C2×D3)⋊C4—101no—
414(C2×D3)⋊C4—101no—
415C4⋊Dic3—51no—
416C4⋊Dic3C22×D511yescharacteristic
417Dic3⋊C4—21no—
418Dic3⋊C4—101no—
419C4×Dic3—21no—
420C4×Dic3—101no—
421C4×Dic3—101no—
422#208—54no—
423#208—102no—
424C2×C3⋊C8—51no—
425C2×C3⋊C8—51no—
426C2×C3⋊C8C22×D511yescharacteristic
427C2×C3⋊C8C22×D511yescharacteristic
428C23×C5—21no—
429C22×D5—21no—
430C22×D5—24no—
431C22×D5—42no—
432C22×D5—42no—
433C22×D5—61no—
434C22×D5C2×#6711yescharacteristic
435C5×Q8—32no—
436C5×Q8—61no—
437C5×D4—21no—
438C5×D4C2×C4×D312yes—
439C2×C4×C5—21no—
440C2×C4×C5—42no—
441C2×C4×C5—61no—
442C2×C4×C5—61no—
443C2×C4×C5C2×#6711yescharacteristic
444C2×C4×C5C2×#6711yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—24no—
447C2×Dic5—21no—
448C2×Dic5—42no—
449C2×Dic5—61no—
450C2×Dic5C2×#6711yescharacteristic
451C2×Dic5C2×#6711yescharacteristic
452C2×Dic5C2×#6711yescharacteristic
453D20—21no—
454D20—32no—
455D20—64no—
456D20—61no—
457D20C2×C4×D312yes—
458C4×D5—22no—
459C4×D5—41no—
460C4×D5—42no—
461C4×D5—42no—
462C4×D5—42no—
463C4×D5—64no—
464C4×D5—122no—
465C4×D5—122no—
466C4×D5C2×C4×D312yes—
467C4×D5#23512yes—
468C5×C8—32no—
469C5×C8—61no—
470#168—32no—
471#168—61no—
472C2×#41—151no—
473C22×D4—51no—
474C23×C4—101no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—31no—
477C2×SD16—151no—
478C2×D8—151no—
479C2×D8—151no—
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—31no—
483C4×Q8—151no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—51no—
487C4×D4—101no—
488C4×D4—101no—
489C4×D4—151no—
490C4×D4—151no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4D3×D511yescharacteristic
494#117—151no—
495#117—301no—
496C2×C4⋊C4—51no—
497C2×C22⋊C4—101no—
498C2×C42—51no—
499C2×C42—301no—
500#107—31no—
501#107—151no—
502#106—151no—
503#106—151no—
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×C5—42no—
517C2×C3×C5C2×C4×D411yescharacteristic
518C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
519C2×C3×C5#57511yescharacteristic
520D15—42no—
521C3×D5—22no—
522C3×D5—42no—
523C23×C3—21no—
524C23×C3—51no—
525C23×C3—104no—
526C23×C3—101no—
527C23×C3—202no—
528C23×C3—202no—
529C22×D3—101no—
530C3×D4—21no—
531C3×D4—52no—
532C3×D4—104no—
533C3×D4—101no—
534C3×D4C2×C4×D512yes—
535C2×C3×C4—21no—
536C2×C3×C4—42no—
537C2×C3×C4—51no—
538C2×C3×C4—51no—
539C2×C3×C4—52no—
540C2×C3×C4—52no—
541C2×C3×C4—51no—
542C2×C3×C4—102no—
543C2×C3×C4—101no—
544C2×C3×C4—201no—
545C2×C3×C4—202no—
546C2×C3×C4—202no—
547C2×C3×C4—202no—
548C2×C3×C4—202no—
549C2×C3×C4D4×D511yescharacteristic
550C2×C3×C4D4×D511yescharacteristic
551C2×C3×C4C23×D511yescharacteristic
552#67—104no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—101no—
556D12—52no—
557D12—101no—
558C4×D3—104no—
559C4×D3—202no—
560C4×D3—202no—
561Dic6—21no—
562Dic6C2×C4×D512yescomplemented
563C3⋊C8—21no—
564C3⋊C8—52no—
565C3⋊C8—101no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—22no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5C22×#6711yescharacteristic
571C2×D5—21no—
572C2×D5—21no—
573C2×D5—22no—
574C2×D5—48no—
575C2×D5—41no—
576C2×D5—41no—
577C2×D5—62no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5C4×#6712yes—
581C4×C5—21no—
582C4×C5—21no—
583C4×C5—41no—
584C4×C5—62no—
585C4×C5—121no—
586C4×C5C22×C4×D311yescharacteristic
587C4×C5C2×#23511yescharacteristic
588Dic5—21no—
589Dic5—41no—
590Dic5—121no—
591Dic5C4×#6712yes—
592Dic5#93212yescomplemented
593C24—101no—
594#41—154no—
595#41—302no—
596C2×Q8—31no—
597C2×D4—54no—
598C2×D4—51no—
599C2×D4—102no—
600C2×D4—101no—
601C2×D4—151no—
602C2×D4—301no—
603C2×D4C2×D3×D511yescharacteristic
604C22×C4—21no—
605C22×C4—51no—
606C22×C4—51no—
607C22×C4—51no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—101no—
612C22×C4—204no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—301no—
616SD16—34no—
617SD16—154no—
618D8—154no—
619D8—154no—
620M16—154no—
621M16—302no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—151no—
625C2×C8—151no—
626C4⋊C4—31no—
627C4⋊C4—51no—
628C4⋊C4—61no—
629C4⋊C4—101no—
630C4⋊C4—151no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—21no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4—101no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—51no—
641C42—51no—
642C42—51no—
643C42—61no—
644C42—301no—
645C42—301no—
646C42C2×D3×D511yescharacteristic
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—22no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—52no—
652C22×C3—101no—
653C22×C3—101no—
654C22×C3—102no—
655C22×C3—208no—
656C22×C3—201no—
657C22×C3—201no—
658C22×C3C2×D4×D511yescharacteristic
659C2×D3—102no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—41no—
665C3×C4—52no—
666C3×C4—52no—
667C3×C4—101no—
668C3×C4—201no—
669C3×C4C22×C4×D511yescharacteristic
670C3×C4D5×#4111yescharacteristic
671Dic3—22no—
672Dic3—41no—
673Dic3—201no—
674C2×C5—42no—
675C2×C5C2×C4×#6711yescharacteristic
676C2×C5C2×#93211yescharacteristic
677C2×C5#582211yescharacteristic
678D5—22no—
679D5—42no—
680D5—122no—
681C23—21no—
682C23—51no—
683C23—104no—
684C23—101no—
685C23—202no—
686C23—202no—
687C23—301no—
688Q8—32no—
689Q8—61no—
690D4—21no—
691D4—52no—
692D4—104no—
693D4—101no—
694D4—152no—
695D4—304no—
696D4—301no—
697D4C4×D3×D512yes—
698C2×C4—21no—
699C2×C4—42no—
700C2×C4—51no—
701C2×C4—51no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—51no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—102no—
708C2×C4—101no—
709C2×C4—201no—
710C2×C4—202no—
711C2×C4—202no—
712C2×C4—202no—
713C2×C4—202no—
714C2×C4—304no—
715C2×C4—301no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4D5×#6711yescharacteristic
719C2×C4D5×#6711yescharacteristic
720C2×C4C22×D3×D511yescharacteristic
721C8—32no—
722C8—61no—
723C8—152no—
724C8—301no—
725C2×C3—42no—
726C2×C3—102no—
727C2×C3—202no—
728C2×C3C4×D4×D511yescharacteristic
729C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
730C2×C3#6611111yescharacteristic
731D3—202no—
732C5C4×#93211yescharacteristic, complemented, Sylow
733C22—22no—
734C22—41no—
735C22—41no—
736C22—52no—
737C22—101no—
738C22—101no—
739C22—102no—
740C22—208no—
741C22—201no—
742C22—201no—
743C22—302no—
744C22—601no—
745C22—601no—
746C22C2×D5×#6711yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—52no—
751C4—52no—
752C4—62no—
753C4—101no—
754C4—121no—
755C4—201no—
756C4—601no—
757C4C2×C4×D3×D511yescharacteristic
758C4D5×#23511yescharacteristic
759C3#1061150411yescharacteristic, complemented, Sylow
760C2—42no—
761C2—102no—
762C2—202no—
763C2—602no—
764C2C4×D5×#6711yescharacteristic
765C2D5×#93211yescharacteristic
766C2#1175534411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91491C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
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. C3×C4×D4×D5C2semidirect
3. C4×#6773C2semidirect
4. #11751115C2semidirect
5. C5×#5018C2semidirect
6. Dic5×#214C2semidirect
7. #11748975C2semidirect
8. #11748962C2semidirect
9. #11747500C2semidirect
10. #11747452C2semidirect
11. #11747261C2semidirect
12. #11747223C2semidirect
13. #11747048C2semidirect
14. #11747023C2semidirect
15. #11747003C2semidirect
22. C4×D60C22semidirect
24. C4×C5×Dic6C22semidirect
33. #91491C4semidirect
36. #91418C22semidirect
40. Dic5×Dic6C22semidirect
46. #91093C22semidirect
47. #91092C22semidirect
48. #91087C22semidirect
50. C5×#810C22semidirect
51. C5×#807C22semidirect
52. C5×#803C22semidirect
53. #90989C22semidirect
54. #90987C22semidirect
55. #90972C22semidirect
56. #90968C22semidirect
59. Dic5×C3⋊C8C22semidirect
60. Dic5×C3⋊C8C22semidirect
64. C4×D4×D5D3semidirect
86. C3×D4×D5C2×C4semidirect
99. #6773C2×C4semidirect
103. #6715C2×C4semidirect
108. C5×#214C2×C4semidirect
127. #6655C2×C4semidirect
128. #6653C2×C4semidirect
130. #6649C2×C4semidirect
136. #5018D5semidirect
207. D60C22×C4semidirect
212. C5×Dic6C22×C4semidirect
232. C3⋊#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
262. C4×Dic6C2×D5semidirect
268. #810C2×D5semidirect
274. #807C2×D5semidirect
276. #803C2×D5semidirect
288. D4×D5C4×D3semidirect
371. C3×Dic5AGL(1,ℤ/8)semidirect
410. #214C4×D5semidirect
562. Dic6C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
592. Dic5#932semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
732. C5C4×#932semidirect
759. C3#10611504semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D4×D52
C2×#914912
C4×#67732
#117511152
C5×#50182
Dic5×#2142
#117489752
#117489622
#117475002
#117474522
#117472612
#117472232
#117470482
#117470232
#117470032
#106115043
C4×#9325