Finite Group Databasebeta

← C4×#91257 #14416709

Subgroups — C4×#91257 #14416709

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×#91257C211yesmaximal, characteristic
2C4×#6777C211yesmaximal, characteristic, complemented
3C4×#6768C211yesmaximal, characteristic, complemented
4C4×#6705C211yesmaximal, characteristic, complemented
5C4×C5×D24C211yesmaximal, characteristic, complemented
6C3×C4×#677C211yesmaximal, characteristic, complemented
7#11748146C211yesmaximal, characteristic, complemented
8#11748109C211yesmaximal, characteristic, complemented
9#11747813C211yesmaximal, characteristic, complemented
10#11747812C211yesmaximal, characteristic, complemented
11#11747738C211yesmaximal, characteristic, complemented
12#11747734C211yesmaximal, characteristic, complemented
13#11747638C211yesmaximal, characteristic, complemented
14C4×#6656C211yesmaximal, characteristic, complemented
15C4×#6652C211yesmaximal, characteristic, complemented
16C4×#4057—31nomaximal, Hall
17C2×#6777C2211yescharacteristic
18C2×C4×D3×D5—21no—
19C2×#6768C2211yescharacteristic
20C2×#6705C2211yescharacteristic
21C2×#6705C2211yescharacteristic
22C42×D15C2211yescharacteristic
23C2×C5×D24C2211yescharacteristic
24C4×C5×D12C2211yescharacteristic
25C4×C5×D12C2211yescharacteristic, complemented
26C2×C3×#677C2211yescharacteristic
27C3×C4×D20C2211yescharacteristic
28C3×C4×Dic10C2211yescharacteristic, complemented
29#91473—21no—
30C4×#1203—21no—
31#91442—21no—
32C4×#1201—21no—
33#91437C2211yescharacteristic
34#91435C2211yescharacteristic
35#91435C2211yescharacteristic, complemented
36#91434C2211yescharacteristic
37#91406—21no—
38#91400—21no—
39C4×D3×Dic5—21no—
40#91347C2211yescharacteristic
41#91331C2211yescharacteristic, complemented
42C2×#6656C2211yescharacteristic
43C2×#6652C2211yescharacteristic
44#91257C418yesdirect product factor
45C3×C4×C5×C8C2211yescharacteristic, complemented
46#91099C2211yescharacteristic, complemented
47#91099C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×#821C2211yescharacteristic, complemented
51C5×#818C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×#3949C2211yescharacteristic, complemented
54C3×#3948C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90986C2211yescharacteristic, complemented
57#90970C2211yescharacteristic, complemented
58#90966C2211yescharacteristic
59#90966C2211yescharacteristic, complemented
60#90964C2211yescharacteristic
61C4×#914—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#65170—31no—
71#65074—31no—
72#65060—31no—
73#65059—31no—
74#65046—31no—
75C4×#677D311yescharacteristic, complemented
76C4×#676—31no—
77C22×D3×D5—21no—
78C2×C4×D15D411yescharacteristic
79C2×C4×D15D411yescharacteristic
80C2×C4×D15C2311yescharacteristic
81C2×C5×D12C2311yescharacteristic
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C3×D20C2311yescharacteristic
86C2×C3×C4×D5—21no—
87C2×C3×Dic10C2311yescharacteristic
88C2×#1203—21no—
89C2×#1201—21no—
90C2×#1200—21no—
91C2×D3×Dic5—21no—
92C2×D3×Dic5—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95#6777—22no—
96#6777C2×C414yescomplemented
97C4×D3×D5—44no—
98#6768—22no—
99#6768C2×C414yescomplemented
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102C3×C42×C5C2311yescharacteristic
103C4×Dic15D411yescharacteristic
104C4×Dic15D411yescharacteristic
105C4×Dic15C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108#6705—22no—
109#6705C2×C414yescomplemented
110C5×(C2×D3)⋊C4—21no—
111C5×(C2×D3)⋊C4—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×C4⋊Dic3C2311yescharacteristic
114C5×D24C2×C414yescomplemented
115C3×#685—21no—
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×#677C2×C414yescomplemented
121#6669—21no—
122#6668—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125(C2×D3)⋊Dic5—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128Dic3×Dic5—21no—
129#6656C2×C414yescomplemented
130#6652C2×C414yescomplemented
131C2×#914—51no—
132C4×#239—51no—
133C4×D3×D4—51no—
134C3×C4×SD16—51no—
135#5164—51no—
136C4×#215—51no—
137C4×#213—51no—
138#4869—51no—
139#4861—51no—
140#4817—51no—
141#4803—51no—
142#4785—51no—
143#4770—51no—
144C4×D24D511yescharacteristic, complemented
145C4×ΓL(1,𝔽25)—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×#677C2×D311yescharacteristic
161C2×#676—31no—
162C2×#676—31no—
163#4039—31no—
164#4038—31no—
165D5×C4⋊C4—31no—
166#4033—31no—
167#4027—61no—
168#4027—61no—
169D5×C22⋊C4—61no—
170#4023—61no—
171C4×D20C2×D311yescharacteristic
172C42×D5—31no—
173C4×Dic10C2×D311yescharacteristic, complemented
174C5×#107—31no—
175C5×#102—31no—
176C5×#102—31no—
177C4×C5×C8C2×D311yescharacteristic, complemented
178#3964—31no—
179#3964—31no—
180#3953C2×D311yescharacteristic
181#3949C2×D311yescharacteristic, complemented
182#3948C2×D311yescharacteristic, complemented
183#3947—31no—
184#3947—31no—
185#3942—31no—
186#3941—31no—
187#3940—31no—
188#3939—31no—
189C4×#168—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15C2×D411yescharacteristic
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C3×D5—21no—
195C2×D3×D5—24no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2411yescharacteristic
201C2×Dic15C2×D411yescharacteristic
202C2×Dic15C2×D411yescharacteristic
203C2×Dic15C2×D411yescharacteristic
204C4×D15—22no—
205C4×D15—41no—
206C4×D15C22×C412yes—
207C4×D15#4112yes—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C5×D12—21no—
211C5×D12—21no—
212C5×D12C22×C412yes—
213C5×D12C22×C412yescomplemented
214C4×C5×D3—42no—
215C4×C5×D3—42no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C3×D20—21no—
220C3×D20C22×C412yes—
221C3×C4×D5—42no—
222C3×Dic10—21no—
223C3×Dic10C22×C412yescomplemented
224#1203—24no—
225#1201—24no—
226#1200—42no—
227D3×Dic5—24no—
228D3×Dic5—42no—
229D3×Dic5—42no—
230D5×Dic3—42no—
231C3×C5×C8—21no—
232C3×C5×C8C22×C412yescomplemented
233C3⋊#168—21no—
234C3⋊#168C22×C412yescomplemented
235C2×#239—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×SD16—51no—
239C3×C4×Q8—51no—
240C3×C4×D4—51no—
241Q8×Dic3—51no—
242C2×#215—51no—
243D4×Dic3—51no—
244C2×#213—51no—
245C4×#67—101no—
246#914—58no—
247C2×D24C2×D511yescharacteristic
248C2×ΓL(1,𝔽25)—51no—
249C2×ΓL(1,𝔽25)—51no—
250#893—51no—
251#893—51no—
252#893—101no—
253#892—51no—
254#892—101no—
255D3×C4⋊C4—51no—
256#67⋊C4—101no—
257D3×C22⋊C4—101no—
258C4×D12—101no—
259C4×D12C2×D511yescharacteristic
260C4×D12C2×D511yescharacteristic, complemented
261C42×D3—51no—
262C42×D3—101no—
263C3×#106—51no—
264C3×#103—51no—
265C3×#102—51no—
266C3×C4×C8C2×D511yescharacteristic, complemented
267#835—51no—
268#832—51no—
269#821C2×D511yescharacteristic
270#821C2×D511yescharacteristic, complemented
271#818C2×D511yescharacteristic, complemented
272#815—51no—
273#815—51no—
274#809—51no—
275#809—51no—
276#808—51no—
277#807—51no—
278C4×C3⋊C8—51no—
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×D20C22×D311yescharacteristic
294C2×C4×D5—21no—
295C2×C4×D5—31no—
296C2×C4×D5—31no—
297C2×C4×D5—31no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—124no—
301C2×Dic10C22×D311yescharacteristic
302C5×D8—34no—
303C2×C5×C8C22×D311yescharacteristic
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—31no—
307C5×C22⋊C4—61no—
308C5×C22⋊C4—61no—
309C42×C5C22×D311yescharacteristic
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×#168—31no—
330#677C4×D314yescomplemented
331#676—34no—
332#676—62no—
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—51no—
341C4×SD16—151no—
342C4×D8—31no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—21no—
350C2×D15—21no—
351C2×D15C4×D412yes—
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—22no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361D3×D5—48no—
362C3×C4×C5—21no—
363C3×C4×C5AGL(1,ℤ/8)12yescomplemented
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—21no—
367Dic15—21no—
368Dic15C4×D412yes—
369C3×Dic5—22no—
370C3×Dic5—41no—
371C3×Dic5—41no—
372C5×Dic3—41no—
373C5×Dic3—41no—
374C23×D3—101no—
375C2×C3×Q8—51no—
376C2×C3×D4—51no—
377C22×C3×C4—101no—
378C2×#67—101no—
379C22×Dic3—101no—
380#239—54no—
381#239—102no—
382D3×D4—54no—
383D3×D4—102no—
384C2×D12—101no—
385C2×D12C22×D511yescharacteristic
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—51no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—204no—
397C3×SD16—54no—
398C2×C3×C8C22×D511yescharacteristic
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C42—101no—
405C3×C42C22×D511yescharacteristic
406#217—101no—
407#215—54no—
408#213—54no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414C4⋊Dic3—101no—
415C4⋊Dic3C22×D511yescharacteristic
416C4⋊Dic3C22×D511yescharacteristic
417Dic3⋊C4—101no—
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—101no—
422C4×Dic3—101no—
423C2×C3⋊C8—51no—
424C2×C3⋊C8—51no—
425D24C4×D514yescomplemented
426ΓL(1,𝔽25)—54no—
427ΓL(1,𝔽25)—102no—
428C23×C5—61no—
429C23×C5—61no—
430C22×D5—21no—
431C22×D5—31no—
432C22×D5—64no—
433C22×D5—122no—
434C22×D5—122no—
435C5×D4—32no—
436C5×D4—32no—
437C5×D4—61no—
438C5×D4—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—122no—
442C2×C4×C5—122no—
443C2×C4×C5D3×D411yescharacteristic
444C2×C4×C5D3×D411yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C22⋊D5—64no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—21no—
451C2×Dic5—31no—
452C2×Dic5—31no—
453C2×Dic5—31no—
454C2×Dic5—64no—
455C2×Dic5—122no—
456C2×Dic5—122no—
457D20—21no—
458D20C2×C4×D312yes—
459C4×D5—32no—
460C4×D5—32no—
461C4×D5—42no—
462C4×D5—62no—
463C4×D5—122no—
464C4×D5—121no—
465C4×D5—122no—
466Dic10—21no—
467Dic10C2×C4×D312yescomplemented
468C5×C8—21no—
469C5×C8C2×C4×D312yescomplemented
470#168—32no—
471#168—61no—
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—51no—
477C2×SD16—151no—
478C2×D8—31no—
479C2×D8—151no—
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—51no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—51no—
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—151no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—31no—
501#107—151no—
502#106—51no—
503#106—151no—
504#103—51no—
505#103—151no—
506#102—31no—
507#102—31no—
508#102—51no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—151no—
513#97—151no—
514C4×C8—151no—
515C4×C8D3×D511yescharacteristic, complemented
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—22no—
520C3×D5—42no—
521C5×D3—42no—
522C5×D3—42no—
523C23×C3—101no—
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—51no—
527C22×D3—104no—
528C22×D3—202no—
529C22×D3—202no—
530C3×Q8—52no—
531C3×Q8—101no—
532C3×D4—52no—
533C3×D4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—202no—
538C2×C3×C4D4×D511yescharacteristic
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—51no—
545C2×Dic3—51no—
546C2×Dic3—51no—
547C2×Dic3—202no—
548D12—21no—
549D12—21no—
550D12—104no—
551D12C2×C4×D512yes—
552D12C2×C4×D512yescomplemented
553C4×D3—42no—
554C4×D3—42no—
555C4×D3—52no—
556C4×D3—52no—
557C4×D3—104no—
558C4×D3—102no—
559C4×D3—202no—
560C4×D3—201no—
561C4×D3—202no—
562C4×D3—202no—
563C3×C8—21no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—52no—
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—22no—
575C2×D5—32no—
576C2×D5—41no—
577C2×D5—41no—
578C2×D5—61no—
579C2×D5—61no—
580C2×D5—128no—
581C4×C5—21no—
582C4×C5—121no—
583C4×C5—121no—
584C4×C5#91412yescomplemented
585C4×C5C22×C4×D311yescharacteristic
586C4×C5D3×#4111yescharacteristic
587Dic5—22no—
588Dic5—32no—
589Dic5—41no—
590Dic5—41no—
591Dic5—61no—
592Dic5—61no—
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—51no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—51no—
600C2×D4—154no—
601C2×D4—301no—
602C2×D4—302no—
603C2×D4—301no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—101no—
607C22×C4—151no—
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—54no—
617SD16—154no—
618D8—34no—
619D8—154no—
620M16—154no—
621M16—302no—
622C2×C8—151no—
623C2×C8—151no—
624C2×C8C2×D3×D511yescharacteristic
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—51no—
629C4⋊C4—51no—
630C4⋊C4—101no—
631C4⋊C4—301no—
632C4⋊C4—301no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—101no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—101no—
641C42—151no—
642C42—151no—
643C42—151no—
644C42—301no—
645C42—301no—
646C42C2×D3×D511yescharacteristic
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—102no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3C2×D4×D511yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—52no—
659C2×D3—101no—
660C2×D3—101no—
661C2×D3—208no—
662C3×C4—21no—
663C3×C4—102no—
664C3×C4—201no—
665C3×C4—201no—
666C3×C4#405712yescomplemented
667C3×C4C22×C4×D511yescharacteristic
668C3×C4D5×#4111yescharacteristic
669Dic3—41no—
670Dic3—41no—
671Dic3—52no—
672Dic3—101no—
673Dic3—101no—
674C2×C5—122no—
675C2×C5—122no—
676C2×C5C4×D3×D411yescharacteristic
677C2×C5C2×#91411yescharacteristic
678C2×C5#576811yescharacteristic
679D5—42no—
680D5—62no—
681C23—61no—
682C23—61no—
683C23—101no—
684C23—151no—
685C23—304no—
686C23—602no—
687C23—602no—
688Q8—52no—
689Q8—101no—
690D4—32no—
691D4—32no—
692D4—52no—
693D4—61no—
694D4—61no—
695D4—101no—
696D4—304no—
697D4—304no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—101no—
701C2×C4—101no—
702C2×C4—101no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—151no—
706C2×C4—152no—
707C2×C4—152no—
708C2×C4—151no—
709C2×C4—151no—
710C2×C4—202no—
711C2×C4—304no—
712C2×C4—302no—
713C2×C4—601no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4#677711yescharacteristic
719C2×C4#677711yescharacteristic
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—152no—
723C8—301no—
724C8C4×D3×D512yescomplemented
725C2×C3—202no—
726C2×C3C4×D4×D511yescharacteristic
727C2×C3C2×#405711yescharacteristic
728C2×C3#6610211yescharacteristic
729D3—42no—
730D3—42no—
731D3—102no—
732C5C4×#91411yescharacteristic, complemented, Sylow
733C22—62no—
734C22—62no—
735C22—102no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—152no—
741C22—201no—
742C22—201no—
743C22—301no—
744C22—301no—
745C22—608no—
746C22C2×#677711yescharacteristic
747C4—21no—
748C4—102no—
749C4—121no—
750C4—121no—
751C4—152no—
752C4—201no—
753C4—201no—
754C4—301no—
755C4—301no—
756C4#9125712yesdirect product factor
757C4C2×C4×D3×D511yescharacteristic
758C4#9201611yescharacteristic
759C3C4×#405711yescharacteristic, complemented, Sylow
760C2—122no—
761C2—122no—
762C2—202no—
763C2—302no—
764C2C4×#677711yescharacteristic
765C2C2×#9125711yescharacteristic
766C2#1175397911yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91257C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×#6777C2semidirect
3. C4×#6768C2semidirect
4. C4×#6705C2semidirect
5. C4×C5×D24C2semidirect
6. C3×C4×#677C2semidirect
7. #11748146C2semidirect
8. #11748109C2semidirect
9. #11747813C2semidirect
10. #11747812C2semidirect
11. #11747738C2semidirect
12. #11747734C2semidirect
13. #11747638C2semidirect
14. C4×#6656C2semidirect
15. C4×#6652C2semidirect
25. C4×C5×D12C22semidirect
28. C3×C4×Dic10C22semidirect
35. #91435C22semidirect
41. #91331C22semidirect
44. #91257C4direct (N × H)
45. C3×C4×C5×C8C22semidirect
46. #91099C22semidirect
47. #91099C22semidirect
48. C4×C3⋊#168C22semidirect
50. C5×#821C22semidirect
51. C5×#818C22semidirect
53. C3×#3949C22semidirect
54. C3×#3948C22semidirect
55. #90989C22semidirect
56. #90986C22semidirect
57. #90970C22semidirect
59. #90966C22semidirect
75. C4×#677D3semidirect
96. #6777C2×C4semidirect
99. #6768C2×C4semidirect
109. #6705C2×C4semidirect
114. C5×D24C2×C4semidirect
120. C3×#677C2×C4semidirect
129. #6656C2×C4semidirect
130. #6652C2×C4semidirect
144. C4×D24D5semidirect
173. C4×Dic10C2×D3semidirect
177. C4×C5×C8C2×D3semidirect
181. #3949C2×D3semidirect
182. #3948C2×D3semidirect
213. C5×D12C22×C4semidirect
223. C3×Dic10C22×C4semidirect
232. C3×C5×C8C22×C4semidirect
234. C3⋊#168C22×C4semidirect
260. C4×D12C2×D5semidirect
266. C3×C4×C8C2×D5semidirect
270. #821C2×D5semidirect
271. #818C2×D5semidirect
330. #677C4×D3semidirect
363. C3×C4×C5AGL(1,ℤ/8)semidirect
425. D24C4×D5semidirect
467. Dic10C2×C4×D3semidirect
469. C5×C8C2×C4×D3semidirect
515. C4×C8D3×D5semidirect
552. D12C2×C4×D5semidirect
564. C3×C8C2×C4×D5semidirect
584. C4×C5#914semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
666. C3×C4#4057semidirect
724. C8C4×D3×D5semidirect
732. C5C4×#914semidirect
756. C4#91257direct (N × H)
759. C3C4×#4057semidirect

Maximal subgroups

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

subgroupindex
C2×#912572
C4×#67772
C4×#67682
C4×#67052
C4×C5×D242
C3×C4×#6772
#117481462
#117481092
#117478132
#117478122
#117477382
#117477342
#117476382
C4×#66562
C4×#66522
C4×#40573
C4×#9145