Finite Group Databasebeta

← #14458850

Subgroups — #14458850

Order 1920.

840 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×C5×#553C211yesmaximal, characteristic, complemented
2#11756309C211yesmaximal, characteristic, complemented
3#11751169C211yesmaximal, characteristic, complemented
4#11751167C211yesmaximal, characteristic, complemented
5#11751142C211yesmaximal, characteristic, complemented
6#11751139C211yesmaximal, characteristic, complemented
7#11751138C211yesmaximal, characteristic, complemented
8#11751137C211yesmaximal, characteristic, complemented
9#11751117C211yesmaximal, characteristic, complemented
10C4×#6715C211yesmaximal, characteristic, complemented
11D4×C3⋊#168C211yesmaximal, characteristic, complemented
12#11751104C211yesmaximal, characteristic, complemented
13#11751103C211yesmaximal, characteristic, complemented
14#11751071C211yesmaximal, characteristic, complemented
15C2×#91093C211yesmaximal, characteristic, complemented
16#10615345—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C3×C5×#126—21no—
20C3×C5×#125C2211yescharacteristic, complemented
21C3×C5×#123—21no—
22C3×C5×#121—21no—
23C3×C5×#121C2211yescharacteristic
24C3×C5×#121C2211yescharacteristic, complemented
25C3×C4×C5×D4—21no—
26C3×C4×C5×D4C2211yescharacteristic
27C3×C4×C5×D4C2211yescharacteristic, complemented
28C3×C5×#117C2211yescharacteristic, complemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30#91826—21no—
31C2×#6716C2211yescharacteristic, complemented
32C2×#6715C2211yescharacteristic
33C2×#6715C2211yescharacteristic
34#91819C2211yescharacteristic
35#91813C2211yescharacteristic
36C22×C3⋊#168C2211yescharacteristic
37C22×C3⋊#168C2211yescharacteristic, complemented
38#91783—21no—
39#91773—21no—
40C22⋊C4×D15—21no—
41#91764C2211yescharacteristic
42C4×D60C2211yescharacteristic
43#91116C2211yescharacteristic, complemented
44#91114C2211yescharacteristic
45#91114C2211yescharacteristic, complemented
46#91094C2211yescharacteristic, complemented
47#91094C2211yescharacteristic, complemented
48#91094C2211yescharacteristic, complemented
49#91093C2211yescharacteristic
50#91093C2211yescharacteristic
51#91093C2211yescharacteristic
52#91093C2211yescharacteristic
53#91093C2211yescharacteristic
54#91093C2211yescharacteristic
55#91092C2211yescharacteristic, complemented
56#91091C2211yescharacteristic, complemented
57#91091C2211yescharacteristic, complemented
58C4⋊(C3⋊#168)C2211yescharacteristic, complemented
59C4×C3⋊#168C2211yescharacteristic, complemented
60#83614—51nomaximal, Hall
61C5×#553D311yescharacteristic, complemented
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65330—31no—
66#65327—31no—
67#65326—31no—
68#65325—31no—
69#65305—31no—
70C4×#686—31no—
71D4×#168—31no—
72#65292—31no—
73#65291—31no—
74#65259—31no—
75C2×#3941—31no—
76C23×D15—21no—
77C2×C3×C5×D4—21no—
78C2×C3×C5×D4—21no—
79C2×C3×C5×D4D411yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5—21no—
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C2×#1220—21no—
86C2×#1220—21no—
87#6817—22no—
88#6817—41no—
89C2×D60—22no—
90C2×D60—21no—
91C2×D60—41no—
92C2×D60C2311yescharacteristic
93C2×D60C2311yescharacteristic
94C2×C4×D15—21no—
95C2×C4×D15—21no—
96C2×Dic30C2311yescharacteristic
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4—21no—
99C3×C5×C4⋊C4—21no—
100C3×C5×C4⋊C4D411yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C22⋊C4—21no—
105C3×C5×C22⋊C4—21no—
106C3×C5×C22⋊C4—21no—
107C3×C5×C22⋊C4—21no—
108C3×C5×C22⋊C4D411yescharacteristic
109C3×C5×C22⋊C4D411yescharacteristic
110C3×C42×C5—21no—
111C3×C42×C5C2311yescharacteristic
112#6719—21no—
113#6716—41no—
114#6715—22no—
115#6715—41no—
116#6714—21no—
117#6714—21no—
118#6714—21no—
119#6714—21no—
120C4⋊Dic15C2311yescharacteristic
121#6712—21no—
122C2×C3⋊#168—41no—
123C2×C3⋊#168—41no—
124C2×C3⋊#168C2311yescharacteristic
125C2×C3⋊#168C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128C3×#553D511yescharacteristic, complemented
129#5550—51no—
130#5068—51no—
131#5066—51no—
132#5041—51no—
133#5038—51no—
134#5037—51no—
135#5036—51no—
136#5016—51no—
137C4×#213—51no—
138D4×C3⋊C8—51no—
139#5003—51no—
140#5002—51no—
141#4970—51no—
142C2×#809—51no—
143C2×#709—31no—
144C22×D20—31no—
145C5×#126—21no—
146C5×#125C2×D311yescharacteristic, complemented
147C5×#123—21no—
148C5×#121—21no—
149C5×#121C2×D311yescharacteristic
150C5×#121C2×D311yescharacteristic, complemented
151C4×C5×D4—21no—
152C4×C5×D4C2×D311yescharacteristic
153C4×C5×D4C2×D311yescharacteristic, complemented
154C5×#117C2×D311yescharacteristic, complemented
155C2×C5×C4⋊C4C2×D311yescharacteristic
156#4083—61no—
157C2×#687—31no—
158C2×#686—31no—
159C2×#686—31no—
160#4076—31no—
161#4070—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021—31no—
168C4×D20—31no—
169#3964—31no—
170C22⋊#168—31no—
171C22⋊#168—31no—
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
180#3941—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5C2×D411yescharacteristic
189C23×C3×C5C2×D411yescharacteristic
190C22×D15—21no—
191C22×D15—21no—
192C22×D15—42no—
193C22×D15—42no—
194C22×D15—81no—
195C3×C5×D4—22no—
196C3×C5×D4—21no—
197C3×C5×D4—21no—
198C3×C5×D4—42no—
199C3×C5×D4—81no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—81no—
208C2×C3×C4×C5—81no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D411yescharacteristic
211C2×C3×C4×C5C2×D411yescharacteristic
212C2×C3×C4×C5C2×D411yescharacteristic
213C2×C3×C4×C5C2411yescharacteristic
214#1220—42no—
215#1220—81no—
216C2×Dic15—21no—
217C2×Dic15—21no—
218D60—21no—
219D60—21no—
220D60—21no—
221D60—42no—
222D60#4112yes—
223C4×D15—42no—
224C4×D15—81no—
225Dic30—21no—
226Dic30—21no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3⋊#168—21no—
230C3⋊#168—21no—
231C2×#235—51no—
232C22×D12—51no—
233C3×#126—21no—
234C3×#125C2×D511yescharacteristic, complemented
235C3×#123—21no—
236C3×#121—21no—
237C3×#121C2×D511yescharacteristic
238C3×#121C2×D511yescharacteristic, complemented
239C3×C4×D4—21no—
240C3×C4×D4C2×D511yescharacteristic
241C3×C4×D4C2×D511yescharacteristic, complemented
242C3×#117C2×D511yescharacteristic, complemented
243C2×C3×C4⋊C4C2×D511yescharacteristic
244#937—101no—
245C2×#214—51no—
246C2×#213—51no—
247C2×#213—51no—
248#930—51no—
249#924—51no—
250C22×C3⋊C8—51no—
251C22×C3⋊C8—51no—
252#894—101no—
253#884—101no—
254D3×C22⋊C4—101no—
255#875—51no—
256C4×D12—51no—
257#832—51no—
258#830—51no—
259#830—51no—
260#810—51no—
261#810—51no—
262#810—51no—
263#809—51no—
264#809—51no—
265#809—51no—
266#809—51no—
267#809—51no—
268#809—51no—
269#808—51no—
270#807—51no—
271#807—51no—
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C23×D5—61no—
275C2×C5×D4—21no—
276C2×C5×D4—21no—
277C2×C5×D4#6711yescharacteristic
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—21no—
280C22×C4×C5—21no—
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—61no—
284C2×C22⋊D5—61no—
285#709—62no—
286#709—121no—
287C2×D20—31no—
288C2×D20—31no—
289C2×D20—62no—
290C2×D20—61no—
291C2×D20—121no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×Dic10—31no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4—21no—
297C5×C4⋊C4—21no—
298C5×C4⋊C4#6711yescharacteristic
299C5×C4⋊C4C22×D311yescharacteristic
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C5×C22⋊C4—21no—
305C5×C22⋊C4—21no—
306C5×C22⋊C4#6711yescharacteristic
307C5×C22⋊C4#6711yescharacteristic
308C42×C5—21no—
309C42×C5C22×D311yescharacteristic
310C22⋊Dic5—61no—
311#687—121no—
312#686—62no—
313#686—121no—
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—31no—
319#683—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—31no—
323C2×#168—31no—
324C2×#168—121no—
325C2×#168—121no—
326#553D1511yescharacteristic, complemented
327#546—151no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—151no—
335#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—21no—
346C22×C3×C5—41no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5#13512yes—
350C22×C3×C5C22×D411yescharacteristic
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—41no—
355C2×D15—41no—
356C2×D15—41no—
357C2×D15—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5—41no—
363C3×C4×C5—41no—
364C3×C4×C5—41no—
365C3×C4×C5C2×#4111yescharacteristic
366C3×C4×C5H(5,𝔽2)11yescharacteristic
367Dic15—41no—
368Dic15—41no—
369C23×D3—101no—
370C2×C3×D4—21no—
371C2×C3×D4—21no—
372C2×C3×D4C22⋊D511yescharacteristic
373C2×C3×D4C22×D511yescharacteristic
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—101no—
379C2×#67—101no—
380#235—102no—
381#235—201no—
382C2×D12—51no—
383C2×D12—51no—
384C2×D12—102no—
385C2×D12—101no—
386C2×D12—201no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4C22⋊D511yescharacteristic
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4C22⋊D511yescharacteristic
402C3×C22⋊C4C22⋊D511yescharacteristic
403C3×C42—21no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#214—201no—
407#213—102no—
408#213—201no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413C4⋊Dic3—51no—
414Dic3⋊C4—101no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8—201no—
420C2×C3⋊C8—201no—
421C23×C5—21no—
422C23×C5C2×#6711yescharacteristic
423C23×C5C2×#6711yescharacteristic
424C22×D5—61no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
429C5×D4—22no—
430C5×D4—21no—
431C5×D4—21no—
432C5×D4—42no—
433C5×D4—81no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—81no—
442C2×C4×C5—81no—
443C2×C4×C5C2×#6711yescharacteristic
444C2×C4×C5C2×#6711yescharacteristic
445C2×C4×C5C2×#6711yescharacteristic
446C2×C4×C5C2×#6711yescharacteristic
447C2×C4×C5C23×D311yescharacteristic
448C22⋊D5—122no—
449C22⋊D5—241no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452D20—32no—
453D20—61no—
454D20—61no—
455D20—61no—
456D20—122no—
457C4×D5—122no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461#168—61no—
462#168—61no—
463#168—61no—
464#168—61no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—21no—
473#125C2×D1511yescharacteristic, complemented
474#124—151no—
475#123—21no—
476#123—301no—
477C22⋊Q8—151no—
478#121—21no—
479#121—151no—
480#121—301no—
481#121C2×D1511yescharacteristic
482#121C2×D1511yescharacteristic, complemented
483#120—301no—
484C4×D4—21no—
485C4×D4—151no—
486C4×D4C2×D1511yescharacteristic
487C4×D4C2×D1511yescharacteristic, complemented
488#117C2×D1511yescharacteristic, complemented
489C2×C4⋊C4C2×D1511yescharacteristic
490C2×C22⋊C4—301no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5—81no—
511C2×C3×C5#54611yescharacteristic
512C2×C3×C5C2×#13511yescharacteristic
513C2×C3×C5#57611yescharacteristic
514D15—42no—
515D15—81no—
516C23×C3—21no—
517C23×C3C2×C22⋊D511yescharacteristic
518C23×C3C2×C22⋊D511yescharacteristic
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
524C3×D4—22no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—42no—
528C3×D4—81no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—81no—
537C2×C3×C4—81no—
538C2×C3×C4C2×C22⋊D511yescharacteristic
539C2×C3×C4C2×C22⋊D511yescharacteristic
540C2×C3×C4C2×C22⋊D511yescharacteristic
541C2×C3×C4C2×C22⋊D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543#67—202no—
544#67—401no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547D12—52no—
548D12—101no—
549D12—101no—
550D12—101no—
551D12—202no—
552C4×D3—202no—
553C4×D3—401no—
554Dic6—101no—
555Dic6—101no—
556C3⋊C8—101no—
557C3⋊C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5—41no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5#95012yes—
569C22×C5C22×#6711yescharacteristic
570C2×D5—62no—
571C2×D5—121no—
572C2×D5—121no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—41no—
582C4×C5—41no—
583C4×C5—41no—
584C4×C5D3×#4111yescharacteristic
585C4×C5#100911yescharacteristic
586Dic5—121no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—151no—
595C2×D4—151no—
596C2×D4—302no—
597C2×D4—301no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—601no—
601C2×D4#122011yescharacteristic
602C2×D4C22×D1511yescharacteristic
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4C22×D1511yescharacteristic
608C22×C4C22×D1511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—151no—
613C2×C8—151no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—151no—
622C4⋊C4—301no—
623C4⋊C4#122011yescharacteristic
624C4⋊C4C22×D1511yescharacteristic
625C4⋊C4C22×D1511yescharacteristic
626C4⋊C4C22×D1511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4#122011yescharacteristic
637C22⋊C4#122011yescharacteristic
638C42—21no—
639C42C22×D1511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3#409612yes—
650C22×C3C22×C22⋊D511yescharacteristic
651C2×D3—102no—
652C2×D3—201no—
653C2×D3—201no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4D5×#4111yescharacteristic
666C3×C4#414911yescharacteristic
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5—81no—
672C2×C5C2×#95011yescharacteristic
673C2×C5#582911yescharacteristic
674C2×C5#583511yescharacteristic
675D5—122no—
676D5—241no—
677C23—21no—
678C23—301no—
679C23—301no—
680C23—602no—
681C23—602no—
682C23—1201no—
683C23C2×#122011yescharacteristic
684C23C2×#122011yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—22no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—81no—
692D4—152no—
693D4—301no—
694D4—301no—
695D4—301no—
696D4—602no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—301no—
709C2×C4—301no—
710C2×C4—602no—
711C2×C4—1201no—
712C2×C4C2×#122011yescharacteristic
713C2×C4C2×#122011yescharacteristic
714C2×C4C2×#122011yescharacteristic
715C2×C4C2×#122011yescharacteristic
716C2×C4C23×D1511yescharacteristic
717C8—301no—
718C8—301no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—81no—
724C2×C3C2×#409611yescharacteristic
725C2×C3#6616311yescharacteristic
726C2×C3#6616911yescharacteristic
727D3—202no—
728D3—401no—
729C5#8361411yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—302no—
739C22—601no—
740C22—601no—
741C22—601no—
742C22—601no—
743C22—601no—
744C22—1204no—
745C22#9183912yes—
746C22C22×#122011yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—601no—
755C4—601no—
756C4#41×D1511yescharacteristic
757C4#9210011yescharacteristic
758C3#1061534511yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—81no—
762C2—602no—
763C2—1201no—
764C2C2×#9183911yescharacteristic
765C2#1175658811yescharacteristic
766C2#1175659411yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#553C2
socleC22×C3×C5C22×D4
hypercenter#553D15
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C3×C5×#553C2semidirect
2. #11756309C2semidirect
3. #11751169C2semidirect
4. #11751167C2semidirect
5. #11751142C2semidirect
6. #11751139C2semidirect
7. #11751138C2semidirect
8. #11751137C2semidirect
9. #11751117C2semidirect
10. C4×#6715C2semidirect
11. D4×C3⋊#168C2semidirect
12. #11751104C2semidirect
13. #11751103C2semidirect
14. #11751071C2semidirect
15. C2×#91093C2semidirect
20. C3×C5×#125C22semidirect
24. C3×C5×#121C22semidirect
27. C3×C4×C5×D4C22semidirect
28. C3×C5×#117C22semidirect
31. C2×#6716C22semidirect
37. C22×C3⋊#168C22semidirect
43. #91116C22semidirect
45. #91114C22semidirect
46. #91094C22semidirect
47. #91094C22semidirect
48. #91094C22semidirect
55. #91092C22semidirect
56. #91091C22semidirect
57. #91091C22semidirect
58. C4⋊(C3⋊#168)C22semidirect
59. C4×C3⋊#168C22semidirect
61. C5×#553D3semidirect
128. C3×#553D5semidirect
146. C5×#125C2×D3semidirect
150. C5×#121C2×D3semidirect
153. C4×C5×D4C2×D3semidirect
154. C5×#117C2×D3semidirect
234. C3×#125C2×D5semidirect
238. C3×#121C2×D5semidirect
241. C3×C4×D4C2×D5semidirect
242. C3×#117C2×D5semidirect
326. #553D15semidirect
473. #125C2×D15semidirect
482. #121C2×D15semidirect
487. C4×D4C2×D15semidirect
488. #117C2×D15semidirect
640. C3×C5#3297semidirect
729. C5#83614semidirect
758. C3#10615345semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5532
#117563092
#117511692
#117511672
#117511422
#117511392
#117511382
#117511372
#117511172
C4×#67152
D4×C3⋊#1682
#117511042
#117511032
#117510712
C2×#910932
#106153453
#836145