Finite Group Databasebeta

← C4×#91502 #14416714

Subgroups — C4×#91502 #14416714

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×#713C211yesmaximal, characteristic, complemented
2C2×#91502C211yesmaximal, characteristic
3C4×D5×D12C211yesmaximal, characteristic, complemented
4C4×#6717C211yesmaximal, characteristic, complemented
5C4×C5×#215C211yesmaximal, characteristic, complemented
6#11749225C211yesmaximal, characteristic, complemented
7#11749223C211yesmaximal, characteristic, complemented
8#11749198C211yesmaximal, characteristic, complemented
9#11747475C211yesmaximal, characteristic, complemented
10#11747469C211yesmaximal, characteristic, complemented
11#11747468C211yesmaximal, characteristic, complemented
12#11747189C211yesmaximal, characteristic, complemented
13C4×#6653C211yesmaximal, characteristic, complemented
14C4×#6652C211yesmaximal, characteristic, complemented
15C4×#6649C211yesmaximal, characteristic, complemented
16C4×#4060—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C2×C4×D3×D5—21no—
20C3×C4×C5×Q8C2211yescharacteristic, complemented
21C2×#6717C2211yescharacteristic
22C4×D60C2211yescharacteristic
23C2×C5×#215C2211yescharacteristic
24C4×C5×D12C2211yescharacteristic
25C3×Q8×Dic5C2211yescharacteristic, complemented
26C3×#4039—21no—
27C3×#4039C2211yescharacteristic, complemented
28C3×#4038—21no—
29C3×#4038C2211yescharacteristic
30C3×C4×D20—21no—
31C3×C4×D20C2211yescharacteristic, complemented
32C3×C42×D5—21no—
33C3×C42×D5C2211yescharacteristic
34#91502C418yesdirect product factor
35D5×(C2×D3)⋊C4—21no—
36C4×#1203—21no—
37#91418C2211yescharacteristic
38Dic5×D12C2211yescharacteristic
39D5×C4⋊Dic3C2211yescharacteristic
40#91405—21no—
41C2×#6653C2211yescharacteristic
42C2×#6652C2211yescharacteristic
43C2×#6649C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91093C2211yescharacteristic
47#91092C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#809C2211yescharacteristic
51C5×#808C2211yescharacteristic, complemented
52C4×C5×C3⋊C8C2211yescharacteristic, complemented
53#90990C2211yescharacteristic, complemented
54#90989C2211yescharacteristic, complemented
55#90968C2211yescharacteristic
56#90966C2211yescharacteristic
57#90965C2211yescharacteristic, complemented
58#90964C2211yescharacteristic, complemented
59#90952C2211yescharacteristic, complemented
60#90952C2211yescharacteristic, complemented
61C4×#949—51nomaximal, Hall
62C2×#4060—31no—
63C4×#713D311yescharacteristic, complemented
64C4×D4×D5—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67C4×#688—31no—
68C4×#686—31no—
69#65158—31no—
70#65150—31no—
71#65106—31no—
72#65092—31no—
73#65074—31no—
74#65059—31no—
75C4×D40—31no—
76C4×#676—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×D5—21no—
90C2×C3×C4×D5D411yescharacteristic
91C2×C3×C4×D5D411yescharacteristic
92C2×C3×C4×D5C2311yescharacteristic
93C2×#1203—21no—
94C2×#1200—21no—
95C2×D3×Dic5—21no—
96C2×D5×Dic3—21no—
97D5×D12—22no—
98D5×D12C2×C414yescomplemented
99C4×D3×D5—44no—
100C3×C5×C4⋊C4—21no—
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C42×C5—21no—
103C3×C42×C5C2311yescharacteristic
104#6717C2×C414yescomplemented
105#6714—21no—
106C4⋊Dic15C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109C5×#215C2×C414yescomplemented
110C5×(C2×D3)⋊C4—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C3×#685—21no—
115C3×#685—21no—
116C3×#685—21no—
117C3×C4⋊Dic5—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5D411yescharacteristic
122C3×C4×Dic5D411yescharacteristic
123C3×C4×Dic5C2311yescharacteristic
124#6668—21no—
125#6667—21no—
126(C2×D3)⋊Dic5—21no—
127#6653C2×C414yescomplemented
128#6652C2×C414yescomplemented
129#6649—22no—
130#6649C2×C414yescomplemented
131C3×C4×#41—51no—
132C2×#949—51no—
133C2×C4×D12—51no—
134#5232—51no—
135#5026—51no—
136#5026—51no—
137C4×#215—51no—
138C4×#215D511yescharacteristic, complemented
139#5014—51no—
140#5014—51no—
141C4×#213—51no—
142C4×#213—51no—
143#5001—51no—
144#4995—51no—
145C4×#208—51no—
146C2×#713C2×D311yescharacteristic
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×SD16—31no—
150C4×C5×Q8C2×D311yescharacteristic, complemented
151C4×C5×D4—31no—
152Q8×Dic5C2×D311yescharacteristic, complemented
153C2×#688—31no—
154D4×Dic5—31no—
155C2×#686—31no—
156C4×C22⋊D5—61no—
157#4060—38no—
158C2×D40—31no—
159C2×#676—31no—
160C2×#676—31no—
161#4039—21no—
162#4039—31no—
163#4039C2×D311yescharacteristic, complemented
164#4038—21no—
165#4038C2×D311yescharacteristic
166D5×C4⋊C4—31no—
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—21no—
170C4×D20—31no—
171C4×D20C2×D311yescharacteristic, complemented
172C42×D5—21no—
173C42×D5C2×D311yescharacteristic
174C5×#106—31no—
175C5×#103—31no—
176C5×#102—31no—
177C4×C5×C8—31no—
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3953—31no—
182#3950—31no—
183#3947—31no—
184#3947—31no—
185#3941—31no—
186#3941—31no—
187#3940—31no—
188#3939—31no—
189C4×#168—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×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205C2×Dic15—21no—
206D60—21no—
207D60C22×C412yes—
208C4×D15—42no—
209C2×C5×Dic3—21no—
210C5×D12—21no—
211C5×D12C22×C412yes—
212C4×C5×D3—42no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×D20—24no—
218C3×D20—21no—
219C3×D20C22×C412yescomplemented
220C3×C4×D5—22no—
221C3×C4×D5—24no—
222C3×C4×D5—41no—
223C3×C4×D5—42no—
224C3×C4×D5—42no—
225C3×C4×D5C22×C412yes—
226C3×C4×D5#4112yes—
227#1203—24no—
228#1200—42no—
229D3×Dic5—42no—
230D5×Dic3—42no—
231C3⋊#168—21no—
232C3⋊#168C22×C412yescomplemented
233C5×C3⋊C8—21no—
234C5×C3⋊C8C22×C412yescomplemented
235C2×C3×#41—51no—
236C22×D12—51no—
237C22×C4×D3—101no—
238C3×C4×Q8—51no—
239C3×C4×Q8C2×D511yescharacteristic, complemented
240C3×C4×D4—51no—
241C3×C4×D4—51no—
242C3×C4×D4—101no—
243C3×C4×D4—101no—
244C3×#117—51no—
245C3×#117—101no—
246C2×C3×C42—51no—
247C2×C3×C42—101no—
248#949—58no—
249C2×#215—51no—
250C2×#215C2×D511yescharacteristic
251C2×#213—51no—
252C2×#213—51no—
253C2×(C2×D3)⋊C4—101no—
254C2×C4⋊Dic3—51no—
255C2×#208—51no—
256C2×#208—51no—
257C4×D12—51no—
258C4×D12—51no—
259C4×D12—51no—
260C4×D12—101no—
261C4×D12—101no—
262C4×D12C2×D511yescharacteristic
263#835—51no—
264#835C2×D511yescharacteristic, complemented
265#832—51no—
266#832—51no—
267#809—51no—
268#809—51no—
269#809—51no—
270#809C2×D511yescharacteristic
271#808—51no—
272#808C2×D511yescharacteristic, complemented
273#807—51no—
274#807—51no—
275#803—51no—
276#803—51no—
277C4×C3⋊C8—51no—
278C4×C3⋊C8C2×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—21no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—124no—
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—21no—
306C5×C4⋊C4—31no—
307C5×C4⋊C4C22×D311yescharacteristic
308C5×C22⋊C4—61no—
309C42×C5—21no—
310C42×C5C22×D311yescharacteristic
311C22⋊Dic5—61no—
312#688—34no—
313#686—34no—
314#685—21no—
315#685—21no—
316#685—21no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—21no—
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—61no—
323C4×Dic5—21no—
324C4×Dic5—21no—
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—51no—
335C2×C4×D4—151no—
336#442—151no—
337#442—151no—
338#440—151no—
339#440—151no—
340C4×SD16—31no—
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—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—21no—
364C3×C4×C5—41no—
365C3×C4×C5AGL(1,ℤ/8)12yescomplemented
366C3×C4×C5C23×C411yescharacteristic
367C3×C4×C5C2×#4111yescharacteristic
368Dic15—41no—
369C3×Dic5—21no—
370C3×Dic5—21no—
371C3×Dic5—41no—
372C3×Dic5C4×D412yes—
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—51no—
382C22×C3×C4—51no—
383C22×C3×C4—101no—
384C22×C3×C4—101no—
385C22×C3×C4—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×C4⋊C4—21no—
398C3×C4⋊C4—51no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C42—21no—
405C3×C42—51no—
406C3×C42—51no—
407C3×C42—51no—
408C3×C42—101no—
409C3×C42—101no—
410C3×C42C22×D511yescharacteristic
411#215—54no—
412#215C4×D514yescomplemented
413#213—54no—
414#213—54no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—101no—
417(C2×D3)⋊C4—101no—
418(C2×D3)⋊C4—101no—
419C4⋊Dic3—51no—
420C4⋊Dic3—101no—
421C4⋊Dic3C22×D511yescharacteristic
422#208—54no—
423#208—102no—
424C2×C3⋊C8—51no—
425C2×C3⋊C8—51no—
426C2×C3⋊C8C22×D511yescharacteristic
427C2×C3⋊C8C22×D511yescharacteristic
428C23×C5—61no—
429C22×D5—21no—
430C22×D5—61no—
431C22×D5—64no—
432C22×D5—122no—
433C22×D5—122no—
434C22×D5C2×#6711yescharacteristic
435C5×Q8—21no—
436C5×Q8C2×C4×D312yescomplemented
437C5×D4—32no—
438C5×D4—61no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—61no—
442C2×C4×C5—122no—
443C2×C4×C5C2×#6711yescharacteristic
444C2×C4×C5C2×#6711yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C2×Dic5—21no—
448C2×Dic5—61no—
449C2×Dic5—122no—
450C2×Dic5C2×#6711yescharacteristic
451C2×Dic5C2×#6711yescharacteristic
452C2×Dic5C2×#6711yescharacteristic
453D20—24no—
454D20—21no—
455D20—32no—
456D20—61no—
457D20C2×C4×D312yescomplemented
458C4×D5—22no—
459C4×D5—24no—
460C4×D5—41no—
461C4×D5—42no—
462C4×D5—42no—
463C4×D5—122no—
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—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—151no—
481C2×M16—151no—
482C4×Q8—51no—
483C4×Q8D3×D511yescharacteristic, complemented
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—51no—
487C4×D4—101no—
488C4×D4—101no—
489C4×D4—151no—
490C4×D4—151no—
491C4×D4—151no—
492C4×D4—301no—
493C4×D4—301no—
494#117—51no—
495#117—101no—
496C2×C4⋊C4—151no—
497C2×C22⋊C4—301no—
498C2×C42—51no—
499C2×C42—101no—
500#107—151no—
501#107—151no—
502#106—31no—
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—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—
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—51no—
541C2×C3×C4—51no—
542C2×C3×C4—104no—
543C2×C3×C4—102no—
544C2×C3×C4—101no—
545C2×C3×C4—201no—
546C2×C3×C4—202no—
547C2×C3×C4—202no—
548C2×C3×C4D4×D511yescharacteristic
549C2×C3×C4D4×D511yescharacteristic
550C2×C3×C4C23×D511yescharacteristic
551C2×Dic3—21no—
552C2×Dic3—101no—
553C2×Dic3—202no—
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—52no—
565C3⋊C8—101no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—62no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5C22×#6711yescharacteristic
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×D5C4×#6712yes—
581C4×C5—22no—
582C4×C5—21no—
583C4×C5—41no—
584C4×C5—121no—
585C4×C5#94912yescomplemented
586C4×C5C22×C4×D311yescharacteristic
587C4×C5C2×#23511yescharacteristic
588Dic5—21no—
589Dic5—21no—
590Dic5—41no—
591Dic5—121no—
592Dic5C4×#6712yes—
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—51no—
606C22×C4—51no—
607C22×C4—61no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
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—21no—
627C4⋊C4—31no—
628C4⋊C4—51no—
629C4⋊C4—101no—
630C4⋊C4—151no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—61no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4—101no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—21no—
641C42—51no—
642C42—51no—
643C42—51no—
644C42—101no—
645C42—101no—
646C42C2×D3×D511yescharacteristic
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—21no—
663C3×C4—22no—
664C3×C4—41no—
665C3×C4—52no—
666C3×C4—101no—
667C3×C4—101no—
668C3×C4—201no—
669C3×C4#406012yescomplemented
670C3×C4C22×C4×D511yescharacteristic
671C3×C4D5×#4111yescharacteristic
672Dic3—41no—
673Dic3—201no—
674C2×C5—122no—
675C2×C5C2×C4×#6711yescharacteristic
676C2×C5C2×#94911yescharacteristic
677C2×C5#582211yescharacteristic
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—51no—
701C2×C4—52no—
702C2×C4—52no—
703C2×C4—51no—
704C2×C4—51no—
705C2×C4—61no—
706C2×C4—104no—
707C2×C4—102no—
708C2×C4—101no—
709C2×C4—122no—
710C2×C4—201no—
711C2×C4—202no—
712C2×C4—202no—
713C2×C4—301no—
714C2×C4—602no—
715C2×C4—602no—
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—102no—
726C2×C3—202no—
727C2×C3C4×D4×D511yescharacteristic
728C2×C3C2×#406011yescharacteristic
729C2×C3#6610211yescharacteristic
730D3—42no—
731D3—202no—
732C5C4×#94911yescharacteristic, 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—
746C22C2×D5×#6711yescharacteristic
747C4—21no—
748C4—22no—
749C4—41no—
750C4—52no—
751C4—101no—
752C4—101no—
753C4—121no—
754C4—201no—
755C4—601no—
756C4#9150212yesdirect product factor
757C4C2×C4×D3×D511yescharacteristic
758C4D5×#23511yescharacteristic
759C3C4×#406011yescharacteristic, complemented, Sylow
760C2—102no—
761C2—122no—
762C2—202no—
763C2—602no—
764C2C4×D5×#6711yescharacteristic
765C2C2×#9150211yescharacteristic
766C2#1175531511yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91502C2
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C4×#713C2semidirect
3. C4×D5×D12C2semidirect
4. C4×#6717C2semidirect
5. C4×C5×#215C2semidirect
6. #11749225C2semidirect
7. #11749223C2semidirect
8. #11749198C2semidirect
9. #11747475C2semidirect
10. #11747469C2semidirect
11. #11747468C2semidirect
12. #11747189C2semidirect
13. C4×#6653C2semidirect
14. C4×#6652C2semidirect
15. C4×#6649C2semidirect
20. C3×C4×C5×Q8C22semidirect
25. C3×Q8×Dic5C22semidirect
27. C3×#4039C22semidirect
31. C3×C4×D20C22semidirect
34. #91502C4direct (N × H)
45. #91119C22semidirect
47. #91092C22semidirect
48. C4×C3⋊#168C22semidirect
49. C5×#835C22semidirect
51. C5×#808C22semidirect
52. C4×C5×C3⋊C8C22semidirect
53. #90990C22semidirect
54. #90989C22semidirect
57. #90965C22semidirect
58. #90964C22semidirect
59. #90952C22semidirect
60. #90952C22semidirect
63. C4×#713D3semidirect
84. C3×#713C2×C4semidirect
98. D5×D12C2×C4semidirect
104. #6717C2×C4semidirect
109. C5×#215C2×C4semidirect
127. #6653C2×C4semidirect
128. #6652C2×C4semidirect
130. #6649C2×C4semidirect
138. C4×#215D5semidirect
150. C4×C5×Q8C2×D3semidirect
152. Q8×Dic5C2×D3semidirect
163. #4039C2×D3semidirect
171. C4×D20C2×D3semidirect
199. C3×C5×Q8C22×C4semidirect
219. C3×D20C22×C4semidirect
232. C3⋊#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
239. C3×C4×Q8C2×D5semidirect
264. #835C2×D5semidirect
272. #808C2×D5semidirect
278. C4×C3⋊C8C2×D5semidirect
286. #713C4×D3semidirect
365. C3×C4×C5AGL(1,ℤ/8)semidirect
412. #215C4×D5semidirect
436. C5×Q8C2×C4×D3semidirect
457. D20C2×C4×D3semidirect
483. C4×Q8D3×D5semidirect
531. C3×Q8C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
585. C4×C5#949semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
669. C3×C4#4060semidirect
689. Q8C4×D3×D5semidirect
732. C5C4×#949semidirect
756. C4#91502direct (N × H)
759. C3C4×#4060semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#7132
C2×#915022
C4×D5×D122
C4×#67172
C4×C5×#2152
#117492252
#117492232
#117491982
#117474752
#117474692
#117474682
#117471892
C4×#66532
C4×#66522
C4×#66492
C4×#40603
C4×#9495