Finite Group Databasebeta

← #14453687

Subgroups — #14453687

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#137C211yesmaximal, characteristic, complemented
2#11756588C211yesmaximal, characteristic
3Q8×#1220C211yesmaximal, characteristic, complemented
4C2×SD16×D15C211yesmaximal, characteristic, complemented
5#11751340C211yesmaximal, characteristic, complemented
6#11751328C211yesmaximal, characteristic, complemented
7#11751291C211yesmaximal, characteristic, complemented
8#11751289C211yesmaximal, characteristic, complemented
9#11751287C211yesmaximal, characteristic, complemented
10#11751286C211yesmaximal, characteristic, complemented
11#11751270C211yesmaximal, characteristic, complemented
12#11751265C211yesmaximal, characteristic, complemented
13#11751263C211yesmaximal, characteristic, complemented
14#11751235C211yesmaximal, characteristic, complemented
15#11751228C211yesmaximal, characteristic, complemented
16#10615718—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C2×Q8×D15C2211yescharacteristic
20C2×D4×D15C2211yescharacteristic
21C3×C5×#137—24no—
22C2×C3×C5×Q16C2211yescharacteristic, complemented
23C2×C3×C5×Q16C2211yescharacteristic, complemented
24C2×C3×C5×SD16C2211yescharacteristic
25C2×C3×C5×SD16C2211yescharacteristic
26C2×C3×C5×M16C2211yescharacteristic, complemented
27#91836C2211yescharacteristic
28#91835—21no—
29#91835C2211yescharacteristic
30#91835C2211yescharacteristic
31Q8×Dic15C2211yescharacteristic, complemented
32#91833—21no—
33#91833C2211yescharacteristic, complemented
34C2×#6718C2211yescharacteristic, complemented
35C2×#6717C2211yescharacteristic
36C2×#6717C2211yescharacteristic
37#91828—21no—
38#91826—21no—
39D4×Dic15C2211yescharacteristic
40C2×#6716C2211yescharacteristic
41#91819C2211yescharacteristic
42#91818—21no—
43C4×#1220—21no—
44C4×#1220C2211yescharacteristic
45C2×#6714—21no—
46#91813—21no—
47#91813C2211yescharacteristic, complemented
48SD16×D15—24no—
49C2×#6706C2211yescharacteristic
50C2×C8×D15C2211yescharacteristic
51#91119C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91119C2211yescharacteristic, complemented
54#91116C2211yescharacteristic
55#91114C2211yescharacteristic, complemented
56#91105C2211yescharacteristic
57#91104C2211yescharacteristic
58#91102C2211yescharacteristic, complemented
59#91100C2211yescharacteristic, complemented
60#91099C2211yescharacteristic, complemented
61#91098C2211yescharacteristic, complemented
62#83987—51nomaximal, Hall
63C2×C5×#137D311yescharacteristic, complemented
64#66163—31no—
65Q8×C22⋊D5—31no—
66C2×D5×SD16—31no—
67#65528—31no—
68#65516—31no—
69#65479—31no—
70#65477—31no—
71#65475—31no—
72#65474—31no—
73#65458—31no—
74#65453—31no—
75#65451—31no—
76#65423—31no—
77#65416—31no—
78C23×D15—21no—
79C3×C5×#41—22no—
80C3×C5×#41—41no—
81C2×C3×C5×Q8—21no—
82C2×C3×C5×Q8—22no—
83C2×C3×C5×Q8—41no—
84C2×C3×C5×Q8C2311yescharacteristic
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×Q8C2311yescharacteristic
87C2×C3×C5×D4—21no—
88C2×C3×C5×D4C2311yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C2×#1220—21no—
93C2×#1220—21no—
94C2×#1220D411yescharacteristic
95C22×Dic15—21no—
96Q8×D15—22no—
97Q8×D15—41no—
98D4×D15—22no—
99D4×D15—41no—
100C2×D60C2311yescharacteristic
101C2×C4×D15—21no—
102C2×C4×D15C2311yescharacteristic
103C2×Dic30—21no—
104C2×Dic30C2311yescharacteristic
105C3×C5×Q16—22no—
106C3×C5×Q16—22no—
107C3×C5×SD16—22no—
108C3×C5×SD16D414yescomplemented
109C3×C5×M16—22no—
110C2×C3×C5×C8C2311yescharacteristic
111C2×C3×C5×C8C2311yescharacteristic
112#6719—21no—
113#6719—21no—
114#6719D411yescharacteristic
115#6718—41no—
116#6717—22no—
117#6717—41no—
118#6716—22no—
119#6714—21no—
120#6714—21no—
121#6714—21no—
122#6714—21no—
123#6714—21no—
124#6714D411yescharacteristic
125C4⋊Dic15—21no—
126C4⋊Dic15C2311yescharacteristic
127C4⋊Dic15C2311yescharacteristic
128#6712—21no—
129#6712—21no—
130#6712—21no—
131#6712—21no—
132#6712—21no—
133#6712D411yescharacteristic
134C4×Dic15—21no—
135C4×Dic15C2311yescharacteristic
136C2×C3⋊#168C2311yescharacteristic
137C2×C3⋊#168C2311yescharacteristic
138#6706—22no—
139C8×D15—22no—
140C2×C3×#137D511yescharacteristic, complemented
141#5829—51no—
142Q8×#67—51no—
143C2×D3×SD16—51no—
144#5239—51no—
145#5227—51no—
146#5190—51no—
147#5188—51no—
148#5186—51no—
149#5185—51no—
150#5169—51no—
151#5164—51no—
152#5162—51no—
153#5134—51no—
154#5127—51no—
155C2×C5×#41C2×D311yescharacteristic
156C22×C5×Q8C2×D311yescharacteristic, complemented
157C2×Q8×D5—31no—
158C2×D4×D5—31no—
159C5×#137—24no—
160C2×C5×Q16C2×D311yescharacteristic, complemented
161C2×C5×Q16C2×D311yescharacteristic, complemented
162C2×C5×SD16C2×D311yescharacteristic
163C2×C5×SD16C2×D311yescharacteristic
164C2×C5×M16C2×D311yescharacteristic, complemented
165#4093—31no—
166#4092—31no—
167#4092—31no—
168#4092—61no—
169Q8×Dic5—31no—
170#4090—31no—
171#4090—61no—
172C2×#689—31no—
173C2×#688—31no—
174C2×#688—31no—
175#4085—61no—
176#4083—61no—
177D4×Dic5—31no—
178C2×#687—31no—
179#4076—31no—
180#4075—61no—
181C4×C22⋊D5—31no—
182C4×C22⋊D5—61no—
183C2×#685—61no—
184#4070—31no—
185#4070—61no—
186D5×SD16—64no—
187C2×#677—31no—
188C2×C8×D5—31no—
189#3967—31no—
190#3967—31no—
191#3967—31no—
192#3964—31no—
193C22⋊#168—31no—
194#3953—31no—
195#3952—31no—
196#3950—31no—
197#3948—31no—
198#3947—31no—
199#3946—31no—
200#3266—151noSylow
201C23×C3×C5—21no—
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—42no—
205C22×D15—42no—
206C22×D15—81no—
207C22×D15C2×D411yescharacteristic
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×Q8—42no—
214C3×C5×Q8C2×D412yes—
215C3×C5×D4—21no—
216C3×C5×D4—42no—
217C3×C5×D4C2×D412yes—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—42no—
224C2×C3×C4×C5—42no—
225C2×C3×C4×C5C2×D411yescharacteristic
226C2×C3×C4×C5C2411yescharacteristic
227#1220—22no—
228#1220—42no—
229#1220—81no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15—21no—
233C2×Dic15—81no—
234C2×Dic15C2×D411yescharacteristic
235C2×Dic15C2×D411yescharacteristic
236C2×Dic15C2×D411yescharacteristic
237D60—21no—
238D60—21no—
239C4×D15—21no—
240C4×D15—21no—
241C4×D15—42no—
242Dic30—21no—
243Dic30—21no—
244Dic30—42no—
245C3×C5×C8—21no—
246C3×C5×C8C2×D412yes—
247C3⋊#168—21no—
248C3⋊#168—21no—
249C2×C3×#41C2×D511yescharacteristic
250C22×C3×Q8C2×D511yescharacteristic, complemented
251C2×D3×Q8—51no—
252C2×D3×D4—51no—
253C3×#137—24no—
254C2×C3×Q16C2×D511yescharacteristic, complemented
255C2×C3×Q16C2×D511yescharacteristic, complemented
256C2×C3×SD16C2×D511yescharacteristic
257C2×C3×SD16C2×D511yescharacteristic
258C2×C3×M16C2×D511yescharacteristic, complemented
259#947—51no—
260#946—51no—
261#946—51no—
262#946—101no—
263Q8×Dic3—51no—
264#944—51no—
265#944—101no—
266C2×#216—51no—
267C2×#215—51no—
268C2×#215—51no—
269#939—101no—
270#937—101no—
271D4×Dic3—51no—
272C2×#214—51no—
273#930—51no—
274#929—101no—
275C4×#67—51no—
276C4×#67—101no—
277C2×(C2×D3)⋊C4—101no—
278#924—51no—
279#924—101no—
280D3×SD16—104no—
281C2×#204—51no—
282C2×D3×C8—51no—
283#835—51no—
284#835—51no—
285#835—51no—
286#832—51no—
287#830—51no—
288#821—51no—
289(C2×D3)⋊C8—51no—
290#818—51no—
291#816—51no—
292#815—51no—
293Dic3⋊C8—51no—
294C23×D5—61no—
295C5×#41—22no—
296C5×#41—41no—
297C2×C5×Q8—21no—
298C2×C5×Q8—22no—
299C2×C5×Q8—41no—
300C2×C5×Q8C22×D311yescharacteristic
301C2×C5×Q8C22×D311yescharacteristic
302C2×C5×Q8C22×D311yescharacteristic
303C2×C5×D4—21no—
304C2×C5×D4C22×D311yescharacteristic
305C22×C4×C5—21no—
306C22×C4×C5—21no—
307C22×C4×C5C22×D311yescharacteristic
308C2×C22⋊D5—31no—
309C2×C22⋊D5—61no—
310C2×C22⋊D5—61no—
311C22×Dic5—61no—
312Q8×D5—62no—
313Q8×D5—121no—
314D4×D5—62no—
315D4×D5—121no—
316C2×D20—31no—
317C2×C4×D5—31no—
318C2×C4×D5—61no—
319C2×Dic10—31no—
320C2×Dic10—61no—
321C5×Q16—22no—
322C5×Q16—22no—
323C5×SD16—22no—
324C5×SD16#6714yescomplemented
325C5×M16—22no—
326C2×C5×C8C22×D311yescharacteristic
327C2×C5×C8C22×D311yescharacteristic
328C22⋊Dic5—31no—
329C22⋊Dic5—61no—
330C22⋊Dic5—61no—
331#689—121no—
332#688—62no—
333#688—121no—
334#687—62no—
335#685—31no—
336#685—61no—
337#685—61no—
338#685—61no—
339#685—61no—
340#685—61no—
341C4⋊Dic5—31no—
342C4⋊Dic5—31no—
343C4⋊Dic5—61no—
344#683—31no—
345#683—61no—
346#683—61no—
347#683—61no—
348#683—61no—
349#683—61no—
350C4×Dic5—31no—
351C4×Dic5—61no—
352C2×#168—31no—
353C2×#168—31no—
354#677—62no—
355C8×D5—62no—
356C2×#137D1511yescharacteristic, complemented
357C22×SD16—151no—
358D4×Q8—151no—
359#546—151no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—22no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5C22×D411yescharacteristic
378C2×D15—21no—
379C2×D15—21no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—84no—
384C2×D15#13712yescomplemented
385C3×C4×C5—22no—
386C3×C4×C5—21no—
387C3×C4×C5—41no—
388C3×C4×C5—41no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391Dic15—21no—
392Dic15—21no—
393Dic15—21no—
394Dic15—41no—
395Dic15—41no—
396Dic15—41no—
397C23×D3—101no—
398C3×#41—22no—
399C3×#41—41no—
400C2×C3×Q8—21no—
401C2×C3×Q8—22no—
402C2×C3×Q8—41no—
403C2×C3×Q8C22×D511yescharacteristic
404C2×C3×Q8C22×D511yescharacteristic
405C2×C3×Q8C22×D511yescharacteristic
406C2×C3×D4—21no—
407C2×C3×D4C22×D511yescharacteristic
408C22×C3×C4—21no—
409C22×C3×C4—21no—
410C22×C3×C4C22×D511yescharacteristic
411C2×#67—51no—
412C2×#67—101no—
413C2×#67—101no—
414C22×Dic3—101no—
415D3×Q8—102no—
416D3×Q8—201no—
417D3×D4—102no—
418D3×D4—201no—
419C2×D12—51no—
420C2×C4×D3—51no—
421C2×C4×D3—101no—
422C2×Dic6—51no—
423C2×Dic6—101no—
424C3×Q16—22no—
425C3×Q16—22no—
426C3×SD16—22no—
427C3×SD16C22⋊D514yescomplemented
428C3×M16—22no—
429C2×C3×C8C22×D511yescharacteristic
430C2×C3×C8C22×D511yescharacteristic
431#217—51no—
432#217—101no—
433#217—101no—
434#216—201no—
435#215—102no—
436#215—201no—
437#214—102no—
438(C2×D3)⋊C4—51no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444C4⋊Dic3—51no—
445C4⋊Dic3—51no—
446C4⋊Dic3—101no—
447Dic3⋊C4—51no—
448Dic3⋊C4—101no—
449Dic3⋊C4—101no—
450Dic3⋊C4—101no—
451Dic3⋊C4—101no—
452Dic3⋊C4—101no—
453C4×Dic3—51no—
454C4×Dic3—101no—
455C2×C3⋊C8—51no—
456C2×C3⋊C8—51no—
457#204—102no—
458D3×C8—102no—
459C23×C5—21no—
460C23×C5D3×D411yescharacteristic
461C22×D5—31no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—21no—
469C5×Q8—21no—
470C5×Q8—21no—
471C5×Q8—42no—
472C5×Q8C2×#6712yes—
473C5×D4—21no—
474C5×D4—42no—
475C5×D4C2×#6712yes—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—42no—
482C2×C4×C5—42no—
483C2×C4×C5D3×D411yescharacteristic
484C2×C4×C5C23×D311yescharacteristic
485C22⋊D5—62no—
486C22⋊D5—122no—
487C22⋊D5—241no—
488C2×Dic5—31no—
489C2×Dic5—31no—
490C2×Dic5—31no—
491C2×Dic5—61no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494C2×Dic5—241no—
495D20—61no—
496D20—61no—
497C4×D5—61no—
498C4×D5—61no—
499C4×D5—122no—
500Dic10—61no—
501Dic10—61no—
502Dic10—122no—
503C5×C8—21no—
504C5×C8C2×#6712yes—
505#168—61no—
506#168—61no—
507C2×#41C2×D1511yescharacteristic
508C22×Q8—151no—
509C22×Q8C2×D1511yescharacteristic, complemented
510C22×D4—151no—
511#137—24no—
512C2×Q16—151no—
513C2×Q16C2×D1511yescharacteristic, complemented
514C2×Q16C2×D1511yescharacteristic, complemented
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—304no—
520C2×SD16C2×D1511yescharacteristic
521C2×SD16C2×D1511yescharacteristic
522C2×M16C2×D1511yescharacteristic, complemented
523C22×C8—151no—
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124—151no—
527#123—301no—
528C22⋊Q8—151no—
529C22⋊Q8—151no—
530C22⋊Q8—151no—
531C22⋊Q8—301no—
532C22⋊Q8—301no—
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—151no—
537C4×D4—151no—
538C4×D4—151no—
539C4×D4—301no—
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—42no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557D15—22no—
558D15—81no—
559C23×C3—21no—
560C23×C3D4×D511yescharacteristic
561C22×D3—51no—
562C22×D3—101no—
563C22×D3—202no—
564C22×D3—202no—
565C22×D3—401no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—42no—
572C3×Q8C2×C22⋊D512yes—
573C3×D4—21no—
574C3×D4—42no—
575C3×D4C2×C22⋊D512yes—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—42no—
582C2×C3×C4—42no—
583C2×C3×C4D4×D511yescharacteristic
584C2×C3×C4C23×D511yescharacteristic
585#67—102no—
586#67—202no—
587#67—401no—
588C2×Dic3—51no—
589C2×Dic3—51no—
590C2×Dic3—51no—
591C2×Dic3—101no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594C2×Dic3—401no—
595D12—101no—
596D12—101no—
597C4×D3—101no—
598C4×D3—101no—
599C4×D3—202no—
600Dic6—101no—
601Dic6—101no—
602Dic6—202no—
603C3×C8—21no—
604C3×C8C2×C22⋊D512yes—
605C3⋊C8—101no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—22no—
610C22×C5—21no—
611C22×C5—41no—
612C22×C5—41no—
613C22×C5C2×D3×D411yescharacteristic
614C2×D5—32no—
615C2×D5—61no—
616C2×D5—61no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—22no—
622C4×C5—21no—
623C4×C5—41no—
624C4×C5—41no—
625C4×C5#100411yescharacteristic
626C4×C5C22×#6711yescharacteristic
627Dic5—61no—
628Dic5—61no—
629Dic5—61no—
630Dic5—121no—
631Dic5—121no—
632Dic5—121no—
633C24—301no—
634#41—22no—
635#41—41no—
636C2×Q8—21no—
637C2×Q8—22no—
638C2×Q8—41no—
639C2×Q8—151no—
640C2×Q8—301no—
641C2×Q8—302no—
642C2×Q8—601no—
643C2×Q8C22×D1511yescharacteristic
644C2×Q8C22×D1511yescharacteristic
645C2×Q8C22×D1511yescharacteristic
646C2×D4—21no—
647C2×D4—151no—
648C2×D4—151no—
649C2×D4—301no—
650C2×D4—302no—
651C2×D4—301no—
652C2×D4—601no—
653C2×D4C22×D1511yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—151no—
657C22×C4—301no—
658C22×C4—301no—
659C22×C4C22×D1511yescharacteristic
660Q16—22no—
661Q16—22no—
662Q16—601no—
663SD16—22no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—601no—
668SD16#122014yescomplemented
669M16—22no—
670C2×C8—151no—
671C2×C8—151no—
672C2×C8—302no—
673C2×C8C22×D1511yescharacteristic
674C2×C8C22×D1511yescharacteristic
675C4⋊C4—151no—
676C4⋊C4—151no—
677C4⋊C4—151no—
678C4⋊C4—301no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4—301no—
684C22⋊C4—151no—
685C22⋊C4—151no—
686C22⋊C4—301no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C42—151no—
694C42—301no—
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3C2×D4×D511yescharacteristic
703C2×D3—52no—
704C2×D3—101no—
705C2×D3—101no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—22no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4#414411yescharacteristic
715C3×C4C22×C22⋊D511yescharacteristic
716Dic3—101no—
717Dic3—101no—
718Dic3—101no—
719Dic3—201no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—42no—
723C2×C5—41no—
724C2×C5D3×#13711yescharacteristic
725C2×C5#577811yescharacteristic
726C2×C5D4×#6711yescharacteristic
727D5—62no—
728D5—241no—
729C23—21no—
730C23—151no—
731C23—301no—
732C23—602no—
733C23—602no—
734C23—1201no—
735C23D4×D1511yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—21no—
741Q8—42no—
742Q8—301no—
743Q8—301no—
744Q8—602no—
745Q8C2×#122012yes—
746D4—21no—
747D4—42no—
748D4—302no—
749D4—301no—
750D4—301no—
751D4—602no—
752D4—1201no—
753D4C2×#122012yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—151no—
762C2×C4—151no—
763C2×C4—151no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—301no—
767C2×C4—301no—
768C2×C4—301no—
769C2×C4—602no—
770C2×C4—1201no—
771C2×C4D4×D1511yescharacteristic
772C2×C4C23×D1511yescharacteristic
773C8—21no—
774C8—301no—
775C8—301no—
776C8C2×#122012yes—
777C2×C3—42no—
778C2×C3—41no—
779C2×C3D5×#13711yescharacteristic
780C2×C3#6611211yescharacteristic
781C2×C3D4×C22⋊D511yescharacteristic
782D3—102no—
783D3—401no—
784C5#8398711yescharacteristic, complemented, Sylow
785C22—21no—
786C22—22no—
787C22—21no—
788C22—21no—
789C22—41no—
790C22—41no—
791C22—152no—
792C22—301no—
793C22—301no—
794C22—601no—
795C22—601no—
796C22—601no—
797C22—1204no—
798C22C2×D4×D1511yescharacteristic
799C4—21no—
800C4—22no—
801C4—41no—
802C4—41no—
803C4—301no—
804C4—301no—
805C4—301no—
806C4—601no—
807C4—601no—
808C4—601no—
809C4#9209511yescharacteristic
810C4C22×#122011yescharacteristic
811C3#1061571811yescharacteristic, complemented, Sylow
812C2—41no—
813C2—42no—
814C2—302no—
815C2—1201no—
816C2D15×#13711yescharacteristic
817C2#1175653711yescharacteristic
818C2D4×#122011yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#137C2
socleC22×C3×C5C22×D4
prime radical#11756588C2
hypercenterC2×#137D15
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#137C2semidirect
3. Q8×#1220C2semidirect
4. C2×SD16×D15C2semidirect
5. #11751340C2semidirect
6. #11751328C2semidirect
7. #11751291C2semidirect
8. #11751289C2semidirect
9. #11751287C2semidirect
10. #11751286C2semidirect
11. #11751270C2semidirect
12. #11751265C2semidirect
13. #11751263C2semidirect
14. #11751235C2semidirect
15. #11751228C2semidirect
18. C22×C3×C5×Q8C22semidirect
22. C2×C3×C5×Q16C22semidirect
23. C2×C3×C5×Q16C22semidirect
26. C2×C3×C5×M16C22semidirect
31. Q8×Dic15C22semidirect
33. #91833C22semidirect
34. C2×#6718C22semidirect
47. #91813C22semidirect
51. #91119C22semidirect
52. #91119C22semidirect
53. #91119C22semidirect
55. #91114C22semidirect
58. #91102C22semidirect
59. #91100C22semidirect
60. #91099C22semidirect
61. #91098C22semidirect
63. C2×C5×#137D3semidirect
108. C3×C5×SD16D4semidirect
140. C2×C3×#137D5semidirect
156. C22×C5×Q8C2×D3semidirect
160. C2×C5×Q16C2×D3semidirect
161. C2×C5×Q16C2×D3semidirect
164. C2×C5×M16C2×D3semidirect
250. C22×C3×Q8C2×D5semidirect
254. C2×C3×Q16C2×D5semidirect
255. C2×C3×Q16C2×D5semidirect
258. C2×C3×M16C2×D5semidirect
324. C5×SD16#67semidirect
356. C2×#137D15semidirect
384. C2×D15#137semidirect
427. C3×SD16C22⋊D5semidirect
509. C22×Q8C2×D15semidirect
513. C2×Q16C2×D15semidirect
514. C2×Q16C2×D15semidirect
522. C2×M16C2×D15semidirect
668. SD16#1220semidirect
695. C3×C5#3266semidirect
784. C5#83987semidirect
811. C3#10615718semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1372
#117565882
Q8×#12202
C2×SD16×D152
#117513402
#117513282
#117512912
#117512892
#117512872
#117512862
#117512702
#117512652
#117512632
#117512352
#117512282
#106157183
#839875