Finite Group Databasebeta

← #14426216

Subgroups — #14426216

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#135C211yesmaximal, characteristic, complemented
2#11756591C211yesmaximal, characteristic, complemented
3#41×Dic15C211yesmaximal, characteristic, complemented
4C2×#91839C211yesmaximal, characteristic, complemented
5#11751334C211yesmaximal, characteristic, complemented
6#11751286C211yesmaximal, characteristic, complemented
7#11751283C211yesmaximal, characteristic, complemented
8#11751267C211yesmaximal, characteristic, complemented
9#11751266C211yesmaximal, characteristic, complemented
10#11751264C211yesmaximal, characteristic, complemented
11#11751263C211yesmaximal, characteristic, complemented
12#11751254C211yesmaximal, characteristic, complemented
13#11751251C211yesmaximal, characteristic, complemented
14#11751214C211yesmaximal, characteristic, complemented
15C2×#91098C211yesmaximal, characteristic, complemented
16#10615631—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×#41C2211yescharacteristic
19C2×#6817C2211yescharacteristic
20C3×C5×#135—24no—
21C2×C3×C5×Q16C2211yescharacteristic
22C2×C3×C5×SD16C2211yescharacteristic
23C2×C3×C5×SD16C2211yescharacteristic
24C2×C3×C5×D8C2211yescharacteristic
25C22×C3×C5×C8C2211yescharacteristic
26#91839—24no—
27#91836C2211yescharacteristic
28Q8×Dic15C2211yescharacteristic
29Q8×Dic15C2211yescharacteristic
30#91833C2211yescharacteristic
31C2×#6718C2211yescharacteristic
32C2×#6717C2211yescharacteristic
33#91829C2211yescharacteristic
34#91828—21no—
35#91828—21no—
36#91825C2211yescharacteristic
37D4×Dic15—21no—
38D4×Dic15—21no—
39D4×Dic15C2211yescharacteristic
40D4×Dic15C2211yescharacteristic
41C2×#6716C2211yescharacteristic
42C2×#6715C2211yescharacteristic
43C4×#1220—21no—
44C4×#1220—21no—
45#91815—21no—
46#91815C2211yescharacteristic
47C2×C4×Dic15—21no—
48C2×C4×Dic15C2211yescharacteristic
49C22×C3⋊#168C2211yescharacteristic
50#91119C2211yescharacteristic
51#91119C2211yescharacteristic
52#91116C2211yescharacteristic
53#91116C2211yescharacteristic
54#91105C2211yescharacteristic
55#91105C2211yescharacteristic
56#91100C2211yescharacteristic
57#91100C2211yescharacteristic
58#91098C2211yescharacteristic
59#91098C2211yescharacteristic
60#91098C2211yescharacteristic
61#91098C2211yescharacteristic
62#83900—51nomaximal, Hall
63C2×C5×#135D311yescharacteristic, complemented
64#66166—31no—
65#41×Dic5—31no—
66C2×#4096—31no—
67#65522—31no—
68#65474—31no—
69#65471—31no—
70#65455—31no—
71#65454—31no—
72#65452—31no—
73#65451—31no—
74#65442—31no—
75#65439—31no—
76#65402—31no—
77C2×#3946—31no—
78C3×C5×#41—22no—
79C3×C5×#41—22no—
80C3×C5×#41—22no—
81C3×C5×#41D414yescomplemented
82C2×C3×C5×Q8C2311yescharacteristic
83C2×C3×C5×Q8C2311yescharacteristic
84C2×C3×C5×D4—21no—
85C2×C3×C5×D4—21no—
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5C2311yescharacteristic
91C2×#1220—21no—
92C2×#1220—21no—
93C2×#1220—21no—
94C22×Dic15—21no—
95C22×Dic15—21no—
96C22×Dic15D411yescharacteristic
97C22×Dic15D411yescharacteristic
98#6817—22no—
99#6817—22no—
100C2×D60C2311yescharacteristic
101C2×C4×D15—21no—
102C2×Dic30C2311yescharacteristic
103C3×C5×Q16—22no—
104C3×C5×SD16—22no—
105C3×C5×SD16—22no—
106C3×C5×D8—22no—
107C2×C3×C5×C8—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110#6719—21no—
111#6719—21no—
112#6719—21no—
113#6719—21no—
114#6719—21no—
115#6718—22no—
116#6717—22no—
117#6716—22no—
118#6715—22no—
119#6714—21no—
120#6714—21no—
121C4⋊Dic15—21no—
122C4⋊Dic15—21no—
123C4⋊Dic15C2311yescharacteristic
124C4⋊Dic15C2311yescharacteristic
125#6712—21no—
126#6712—21no—
127C4×Dic15—21no—
128C4×Dic15—21no—
129C4×Dic15—21no—
130C4×Dic15D411yescharacteristic
131C4×Dic15D411yescharacteristic
132C4×Dic15C2311yescharacteristic
133C4×Dic15C2311yescharacteristic
134C2×C3⋊#168—22no—
135C2×C3⋊#168C2311yescharacteristic
136C2×C3⋊#168C2311yescharacteristic
137C2×C3×#135D511yescharacteristic, complemented
138#5832—51no—
139Dic3×#41—51no—
140C2×#950—51no—
141#5233—51no—
142#5185—51no—
143#5182—51no—
144#5166—51no—
145#5165—51no—
146#5163—51no—
147#5162—51no—
148#5153—51no—
149#5150—51no—
150#5113—51no—
151C2×Dic3⋊C8—51no—
152C2×C5×#41C2×D311yescharacteristic
153C2×C5×#41C2×D311yescharacteristic
154C2×#709—31no—
155C5×#135—24no—
156C2×C5×Q16C2×D311yescharacteristic
157C2×C5×SD16C2×D311yescharacteristic
158C2×C5×SD16C2×D311yescharacteristic
159C2×C5×D8C2×D311yescharacteristic
160C22×C5×C8C2×D311yescharacteristic
161#4096—64no—
162#4093—31no—
163Q8×Dic5—31no—
164Q8×Dic5—31no—
165#4090—31no—
166C2×#689—31no—
167C2×#688—31no—
168#4086—31no—
169#4085—61no—
170#4085—61no—
171#4082—31no—
172D4×Dic5—31no—
173D4×Dic5—31no—
174D4×Dic5—61no—
175D4×Dic5—61no—
176C2×#687—31no—
177C2×#686—31no—
178C4×C22⋊D5—61no—
179C4×C22⋊D5—61no—
180#4072—31no—
181#4072—61no—
182C2×C4×Dic5—31no—
183C2×C4×Dic5—61no—
184C22×#168—31no—
185#3967—31no—
186#3967—31no—
187#3964—31no—
188#3964—31no—
189#3953—31no—
190#3953—31no—
191#3948—31no—
192#3948—31no—
193#3946—31no—
194#3946—31no—
195#3946—31no—
196#3946—31no—
197#3035—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5C2×D411yescharacteristic
201C22×D15—21no—
202C3×C5×Q8—21no—
203C3×C5×Q8—21no—
204C3×C5×Q8—21no—
205C3×C5×Q8C2×D412yes—
206C3×C5×D4—24no—
207C3×C5×D4—21no—
208C3×C5×D4—21no—
209C3×C5×D4—21no—
210C3×C5×D4—42no—
211C3×C5×D4C2×D412yes—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—24no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—42no—
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2×D412yes—
218C2×C3×C4×C5#4112yes—
219C2×C3×C4×C5C2411yescharacteristic
220#1220—42no—
221#1220—42no—
222#1220—42no—
223C2×Dic15—22no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—41no—
228C2×Dic15—42no—
229C2×Dic15—42no—
230C2×Dic15C2×D411yescharacteristic
231C2×Dic15C2×D411yescharacteristic
232C2×Dic15C2×D411yescharacteristic
233C2×Dic15C2×D411yescharacteristic
234D60—21no—
235D60—21no—
236C4×D15—42no—
237Dic30—21no—
238Dic30—21no—
239C3×C5×C8—21no—
240C3×C5×C8—21no—
241C3⋊#168—21no—
242C3⋊#168—21no—
243C2×C3×#41C2×D511yescharacteristic
244C2×C3×#41C2×D511yescharacteristic
245C2×#235—51no—
246C3×#135—24no—
247C2×C3×Q16C2×D511yescharacteristic
248C2×C3×SD16C2×D511yescharacteristic
249C2×C3×SD16C2×D511yescharacteristic
250C2×C3×D8C2×D511yescharacteristic
251C22×C3×C8C2×D511yescharacteristic
252#950—104no—
253#947—51no—
254Q8×Dic3—51no—
255Q8×Dic3—51no—
256#944—51no—
257C2×#216—51no—
258C2×#215—51no—
259#940—51no—
260#939—101no—
261#939—101no—
262#936—51no—
263D4×Dic3—51no—
264D4×Dic3—51no—
265D4×Dic3—101no—
266D4×Dic3—101no—
267C2×#214—51no—
268C2×#213—51no—
269C4×#67—101no—
270C4×#67—101no—
271#926—51no—
272#926—101no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—101no—
275C22×C3⋊C8—51no—
276#835—51no—
277#835—51no—
278#832—51no—
279#832—51no—
280#821—51no—
281#821—51no—
282#816—51no—
283#816—51no—
284Dic3⋊C8—51no—
285Dic3⋊C8—51no—
286Dic3⋊C8—51no—
287Dic3⋊C8—51no—
288C5×#41—22no—
289C5×#41—22no—
290C5×#41—22no—
291C5×#41#6714yescomplemented
292C2×C5×Q8C22×D311yescharacteristic
293C2×C5×Q8C22×D311yescharacteristic
294C2×C5×D4—21no—
295C2×C5×D4—21no—
296C2×C5×D4C22×D311yescharacteristic
297C2×C5×D4C22×D311yescharacteristic
298C22×C4×C5—21no—
299C22×C4×C5—21no—
300C22×C4×C5C22×D311yescharacteristic
301C2×C22⋊D5—61no—
302C2×C22⋊D5—61no—
303C2×C22⋊D5—61no—
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5—61no—
307C22×Dic5—61no—
308#709—62no—
309#709—62no—
310C2×D20—31no—
311C2×C4×D5—61no—
312C2×Dic10—31no—
313C5×Q16—22no—
314C5×SD16—22no—
315C5×SD16—22no—
316C5×D8—22no—
317C2×C5×C8—22no—
318C2×C5×C8C22×D311yescharacteristic
319C2×C5×C8C22×D311yescharacteristic
320C22⋊Dic5—61no—
321C22⋊Dic5—61no—
322C22⋊Dic5—61no—
323C22⋊Dic5—61no—
324C22⋊Dic5—61no—
325#689—62no—
326#688—62no—
327#687—62no—
328#686—62no—
329#685—61no—
330#685—61no—
331C4⋊Dic5—31no—
332C4⋊Dic5—31no—
333C4⋊Dic5—61no—
334C4⋊Dic5—61no—
335#683—61no—
336#683—61no—
337C4×Dic5—31no—
338C4×Dic5—31no—
339C4×Dic5—31no—
340C4×Dic5—31no—
341C4×Dic5—61no—
342C4×Dic5—61no—
343C4×Dic5—61no—
344C2×#168—31no—
345C2×#168—31no—
346C2×#168—62no—
347C2×#135—151no—
348C2×#135D1511yescharacteristic, complemented
349#532—151no—
350C4×#41—151no—
351#464—151no—
352#464—151no—
353#463—151no—
354#463—151no—
355#462—151no—
356#461—151no—
357#460—151no—
358#459—151no—
359C2×C4⋊C8—151no—
360#416—151no—
361#416—151no—
362C22×C3×C5—21no—
363C22×C3×C5—21no—
364C22×C3×C5—22no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5—41no—
369C22×C3×C5—41no—
370C22×C3×C5#12112yes—
371C22×C3×C5C22×D411yescharacteristic
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C3×C4×C5—22no—
376C3×C4×C5—41no—
377C3×C4×C5#12112yes—
378C3×C4×C5C22×D411yescharacteristic
379C3×C4×C5C2×#4111yescharacteristic
380Dic15—21no—
381Dic15—21no—
382Dic15—21no—
383Dic15—41no—
384Dic15—41no—
385Dic15—41no—
386Dic15#13512yescomplemented
387C3×#41—22no—
388C3×#41—22no—
389C3×#41—22no—
390C3×#41C22⋊D514yescomplemented
391C2×C3×Q8C22×D511yescharacteristic
392C2×C3×Q8C22×D511yescharacteristic
393C2×C3×D4—21no—
394C2×C3×D4—21no—
395C2×C3×D4C22×D511yescharacteristic
396C2×C3×D4C22×D511yescharacteristic
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4C22×D511yescharacteristic
400C2×#67—101no—
401C2×#67—101no—
402C2×#67—101no—
403C22×Dic3—51no—
404C22×Dic3—51no—
405C22×Dic3—101no—
406C22×Dic3—101no—
407#235—102no—
408#235—102no—
409C2×D12—51no—
410C2×C4×D3—101no—
411C2×Dic6—51no—
412C3×Q16—22no—
413C3×SD16—22no—
414C3×SD16—22no—
415C3×D8—22no—
416C2×C3×C8—22no—
417C2×C3×C8C22×D511yescharacteristic
418C2×C3×C8C22×D511yescharacteristic
419#217—101no—
420#217—101no—
421#217—101no—
422#217—101no—
423#217—101no—
424#216—102no—
425#215—102no—
426#214—102no—
427#213—102no—
428(C2×D3)⋊C4—101no—
429(C2×D3)⋊C4—101no—
430C4⋊Dic3—51no—
431C4⋊Dic3—51no—
432C4⋊Dic3—101no—
433C4⋊Dic3—101no—
434Dic3⋊C4—101no—
435Dic3⋊C4—101no—
436C4×Dic3—51no—
437C4×Dic3—51no—
438C4×Dic3—51no—
439C4×Dic3—51no—
440C4×Dic3—101no—
441C4×Dic3—101no—
442C4×Dic3—101no—
443C2×C3⋊C8—51no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446C23×C5—21no—
447C23×C5—21no—
448C23×C5D3×D411yescharacteristic
449C22×D5—61no—
450C5×Q8—21no—
451C5×Q8—21no—
452C5×Q8—21no—
453C5×Q8C2×#6712yes—
454C5×D4—24no—
455C5×D4—21no—
456C5×D4—21no—
457C5×D4—21no—
458C5×D4—42no—
459C5×D4C2×#6712yes—
460C2×C4×C5—21no—
461C2×C4×C5—24no—
462C2×C4×C5—21no—
463C2×C4×C5—42no—
464C2×C4×C5D3×D411yescharacteristic
465C2×C4×C5#23712yes—
466C2×C4×C5C2×#6712yes—
467C2×C4×C5C23×D311yescharacteristic
468C22⋊D5—122no—
469C22⋊D5—122no—
470C22⋊D5—122no—
471C2×Dic5—31no—
472C2×Dic5—31no—
473C2×Dic5—31no—
474C2×Dic5—31no—
475C2×Dic5—62no—
476C2×Dic5—61no—
477C2×Dic5—61no—
478C2×Dic5—61no—
479C2×Dic5—122no—
480C2×Dic5—121no—
481C2×Dic5—122no—
482D20—61no—
483D20—61no—
484C4×D5—122no—
485Dic10—61no—
486Dic10—61no—
487C5×C8—21no—
488C5×C8—21no—
489#168—61no—
490#168—61no—
491C2×#41—151no—
492C2×#41C2×D1511yescharacteristic
493C2×#41C2×D1511yescharacteristic
494#135—24no—
495#135—304no—
496C2×Q16—151no—
497C2×Q16C2×D1511yescharacteristic
498C2×SD16—151no—
499C2×SD16—151no—
500C2×SD16C2×D1511yescharacteristic
501C2×SD16C2×D1511yescharacteristic
502C2×D8—151no—
503C2×D8C2×D1511yescharacteristic
504C22×C8—151no—
505C22×C8C2×D1511yescharacteristic
506C4⋊Q8—151no—
507#127—151no—
508#124—151no—
509#124—151no—
510#121—301no—
511#121—301no—
512C4×Q8—151no—
513C4×Q8—151no—
514C4×D4—151no—
515C4×D4—151no—
516C4×D4—301no—
517C4×D4—301no—
518C4×D4—301no—
519C4×D4—301no—
520#117—151no—
521#117—301no—
522C2×C42—151no—
523C2×C42—301no—
524C4⋊C8—151no—
525C4⋊C8—151no—
526C4⋊C8—151no—
527C4⋊C8—151no—
528#103—151no—
529#103—151no—
530#103—151no—
531#103—151no—
532#102—151no—
533#102—151no—
534#102—151no—
535#102—151no—
536C2×C3×C5—22no—
537C2×C3×C5—42no—
538C2×C3×C5—81no—
539C2×C3×C5C2×#12111yescharacteristic
540C2×C3×C5C2×#13511yescharacteristic
541C2×C3×C5#57511yescharacteristic
542D15—81no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3D4×D511yescharacteristic
546C22×D3—101no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8C2×C22⋊D512yes—
551C3×D4—24no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—42no—
556C3×D4C2×C22⋊D512yes—
557C2×C3×C4—21no—
558C2×C3×C4—24no—
559C2×C3×C4—21no—
560C2×C3×C4—42no—
561C2×C3×C4D4×D511yescharacteristic
562C2×C3×C4#71112yes—
563C2×C3×C4C2×C22⋊D512yes—
564C2×C3×C4C23×D511yescharacteristic
565#67—202no—
566#67—202no—
567#67—202no—
568C2×Dic3—51no—
569C2×Dic3—51no—
570C2×Dic3—51no—
571C2×Dic3—51no—
572C2×Dic3—102no—
573C2×Dic3—101no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—202no—
577C2×Dic3—201no—
578C2×Dic3—202no—
579D12—101no—
580D12—101no—
581C4×D3—202no—
582Dic6—101no—
583Dic6—101no—
584C3×C8—21no—
585C3×C8—21no—
586C3⋊C8—101no—
587C3⋊C8—101no—
588C22×C5—21no—
589C22×C5—21no—
590C22×C5—22no—
591C22×C5—41no—
592C22×C5—41no—
593C22×C5—41no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5#93912yes—
597C22×C5C2×D3×D411yescharacteristic
598C2×D5—121no—
599C2×D5—121no—
600C2×D5—121no—
601C4×C5—22no—
602C4×C5—41no—
603C4×C5#93912yes—
604C4×C5C2×#23711yescharacteristic
605C4×C5C22×#6711yescharacteristic
606Dic5—32no—
607Dic5—61no—
608Dic5—61no—
609Dic5—61no—
610Dic5—121no—
611Dic5—121no—
612Dic5—121no—
613#41—22no—
614#41—22no—
615#41—22no—
616#41—302no—
617#41—302no—
618#41#122014yescomplemented
619C2×Q8—151no—
620C2×Q8C22×D1511yescharacteristic
621C2×Q8C22×D1511yescharacteristic
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—151no—
625C2×D4—301no—
626C2×D4—301no—
627C2×D4—301no—
628C2×D4C22×D1511yescharacteristic
629C2×D4C22×D1511yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—151no—
633C22×C4—151no—
634C22×C4—301no—
635C22×C4—301no—
636C22×C4—301no—
637C22×C4C22×D1511yescharacteristic
638Q16—22no—
639Q16—302no—
640SD16—22no—
641SD16—22no—
642SD16—302no—
643SD16—302no—
644D8—22no—
645D8—302no—
646C2×C8—22no—
647C2×C8—151no—
648C2×C8—151no—
649C2×C8—302no—
650C2×C8C22×D1511yescharacteristic
651C2×C8C22×D1511yescharacteristic
652C4⋊C4—151no—
653C4⋊C4—151no—
654C4⋊C4—301no—
655C4⋊C4—301no—
656C4⋊C4—301no—
657C4⋊C4—301no—
658C22⋊C4—301no—
659C22⋊C4—301no—
660C22⋊C4—301no—
661C22⋊C4—301no—
662C22⋊C4—301no—
663C22⋊C4—301no—
664C22⋊C4—301no—
665C42—151no—
666C42—151no—
667C42—151no—
668C42—151no—
669C42—301no—
670C42—301no—
671C42—301no—
672C3×C5#303511yescharacteristic, complemented, Hall
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—22no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3#408512yes—
682C22×C3C2×D4×D511yescharacteristic
683C2×D3—201no—
684C2×D3—201no—
685C2×D3—201no—
686C3×C4—22no—
687C3×C4—41no—
688C3×C4#408512yes—
689C3×C4C2×#71111yescharacteristic
690C3×C4C22×C22⋊D511yescharacteristic
691Dic3—52no—
692Dic3—101no—
693Dic3—101no—
694Dic3—101no—
695Dic3—201no—
696Dic3—201no—
697Dic3—201no—
698C2×C5—22no—
699C2×C5—42no—
700C2×C5—81no—
701C2×C5D3×#13511yescharacteristic
702C2×C5#576811yescharacteristic
703C2×C5C2×#93911yescharacteristic
704D5—241no—
705C23—21no—
706C23—21no—
707C23—301no—
708C23D4×D1511yescharacteristic
709Q8—21no—
710Q8—21no—
711Q8—21no—
712Q8—301no—
713Q8—301no—
714Q8C2×#122012yes—
715D4—24no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—42no—
720D4—301no—
721D4—301no—
722D4—602no—
723D4—602no—
724D4—602no—
725D4C2×#122012yes—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—21no—
729C2×C4—42no—
730C2×C4—151no—
731C2×C4—151no—
732C2×C4—151no—
733C2×C4—151no—
734C2×C4—302no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—602no—
739C2×C4—601no—
740C2×C4—602no—
741C2×C4—602no—
742C2×C4D4×D1511yescharacteristic
743C2×C4#681912yes—
744C2×C4C2×#122012yes—
745C2×C4C23×D1511yescharacteristic
746C8—21no—
747C8—21no—
748C8—301no—
749C8—301no—
750C2×C3—22no—
751C2×C3—42no—
752C2×C3—81no—
753C2×C3D5×#13511yescharacteristic
754C2×C3#6610211yescharacteristic
755C2×C3C2×#408511yescharacteristic
756D3—401no—
757C5#8390011yescharacteristic, complemented, Sylow
758C22—21no—
759C22—21no—
760C22—22no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—601no—
767C22—601no—
768C22—601no—
769C22#9182812yes—
770C22C2×D4×D1511yescharacteristic
771C4—22no—
772C4—41no—
773C4—152no—
774C4—301no—
775C4—301no—
776C4—301no—
777C4—601no—
778C4—601no—
779C4—601no—
780C4#9182812yes—
781C4C2×#681911yescharacteristic
782C4C22×#122011yescharacteristic
783C3#1061563111yescharacteristic, complemented, Sylow
784C2—22no—
785C2—42no—
786C2—81no—
787C2—1201no—
788C2D15×#13511yescharacteristic
789C2#1175652711yescharacteristic
790C2C2×#9182811yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#135C2
socleC22×C3×C5C22×D4
hypercenterC2×#135D15
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#135C2semidirect
2. #11756591C2semidirect
3. #41×Dic15C2semidirect
4. C2×#91839C2semidirect
5. #11751334C2semidirect
6. #11751286C2semidirect
7. #11751283C2semidirect
8. #11751267C2semidirect
9. #11751266C2semidirect
10. #11751264C2semidirect
11. #11751263C2semidirect
12. #11751254C2semidirect
13. #11751251C2semidirect
14. #11751214C2semidirect
15. C2×#91098C2semidirect
63. C2×C5×#135D3semidirect
81. C3×C5×#41D4semidirect
137. C2×C3×#135D5semidirect
291. C5×#41#67semidirect
348. C2×#135D15semidirect
386. Dic15#135semidirect
390. C3×#41C22⋊D5semidirect
618. #41#1220semidirect
672. C3×C5#3035semidirect
757. C5#83900semidirect
783. C3#10615631semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1352
#117565912
#41×Dic152
C2×#918392
#117513342
#117512862
#117512832
#117512672
#117512662
#117512642
#117512632
#117512542
#117512512
#117512142
C2×#910982
#106156313
#839005