Finite Group Databasebeta

← #14458868

Subgroups — #14458868

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×#546C211yesmaximal, characteristic, complemented
2#11756324C211yesmaximal, characteristic, complemented
3#11751339C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic, complemented
5#11751318C211yesmaximal, characteristic, complemented
6C2×#91116C211yesmaximal, characteristic, complemented
7#11751158C211yesmaximal, characteristic, complemented
8#11751157C211yesmaximal, characteristic, complemented
9#11751149C211yesmaximal, characteristic, complemented
10#11751145C211yesmaximal, characteristic, complemented
11#11751139C211yesmaximal, characteristic, complemented
12#11751136C211yesmaximal, characteristic, complemented
13C4×#6715C211yesmaximal, characteristic, complemented
14D4×C3⋊#168C211yesmaximal, characteristic, complemented
15#11751110C211yesmaximal, characteristic, complemented
16#10615226—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C3×C5×#124C2211yescharacteristic
20C3×C5×#123—21no—
21C3×C5×C22⋊Q8C2211yescharacteristic
22C3×C5×#121—21no—
23C3×C5×#121C2211yescharacteristic
24C3×C5×#120—21no—
25C3×C4×C5×D4C2211yescharacteristic
26C3×C4×C5×D4C2211yescharacteristic
27C2×C3×C5×C22⋊C4—21no—
28C2×#6717C2211yescharacteristic, complemented
29#91828—21no—
30C2×#6715C2211yescharacteristic
31C2×#6715C2211yescharacteristic
32#91819C2211yescharacteristic
33#91819C2211yescharacteristic, complemented
34#91815C2211yescharacteristic, complemented
35C2×C4⋊Dic15C2211yescharacteristic
36C22×C3⋊#168C2211yescharacteristic
37C22×C3⋊#168C2211yescharacteristic, complemented
38#91787—21no—
39#91772—21no—
40#91770—21no—
41C4×D60C2211yescharacteristic, complemented
42#91759C2211yescharacteristic, complemented
43#91119C2211yescharacteristic, complemented
44#91119C2211yescharacteristic, complemented
45#91119C2211yescharacteristic, complemented
46#91116C2211yescharacteristic
47#91116C2211yescharacteristic
48#91116C2211yescharacteristic
49#91116C2211yescharacteristic
50#91116C2211yescharacteristic
51#91116C2211yescharacteristic
52#91114C2211yescharacteristic
53#91114C2211yescharacteristic, complemented
54#91093C2211yescharacteristic, complemented
55#91092C2211yescharacteristic, complemented
56#91091C2211yescharacteristic, complemented
57#91091C2211yescharacteristic, complemented
58C4⋊(C3⋊#168)C2211yescharacteristic, complemented
59C4×C3⋊#168C2211yescharacteristic, complemented
60#83495—51nomaximal, Hall
61C5×#546D311yescharacteristic, complemented
62#65899—31no—
63#65527—31no—
64#65522—31no—
65#65506—31no—
66C2×#3964—31no—
67#65346—31no—
68#65345—31no—
69#65337—31no—
70#65333—31no—
71#65327—31no—
72#65324—31no—
73C4×#686—31no—
74D4×#168—31no—
75#65298—31no—
76C24×C3×C5—21no—
77C3×C5×#41—22no—
78C3×C5×#41—41no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4—22no—
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4—21no—
83C2×C3×C5×D4—21no—
84C2×C3×C5×D4—41no—
85C2×C3×C5×D4D411yescharacteristic
86C2×C3×C5×D4C2311yescharacteristic
87C2×C3×C5×D4C2311yescharacteristic
88C22×C3×C4×C5—21no—
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C2×#1220—21no—
93C2×#1220—21no—
94C22×Dic15—21no—
95C2×D60C2311yescharacteristic
96C2×C4×D15—21no—
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4D411yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4—21no—
103C3×C5×C22⋊C4—21no—
104C3×C5×C22⋊C4—21no—
105C3×C5×C22⋊C4D411yescharacteristic
106C3×C5×C22⋊C4D411yescharacteristic
107C3×C42×C5C2311yescharacteristic
108#6719—21no—
109#6717—41no—
110#6715—22no—
111#6715—41no—
112#6714—21no—
113#6714—21no—
114#6714—21no—
115C4⋊Dic15—21no—
116C4⋊Dic15C2311yescharacteristic
117C4⋊Dic15C2311yescharacteristic
118C4⋊Dic15C2311yescharacteristic
119#6712—21no—
120#6712—21no—
121C4×Dic15—21no—
122C2×C3⋊#168—41no—
123C2×C3⋊#168—41no—
124C2×C3⋊#168C2311yescharacteristic
125C2×C3⋊#168C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128C3×#546D511yescharacteristic, complemented
129#5565—51no—
130#5238—51no—
131#5233—51no—
132#5217—51no—
133C2×#832—51no—
134#5057—51no—
135#5056—51no—
136#5048—51no—
137#5044—51no—
138#5038—51no—
139#5035—51no—
140C4×#213—51no—
141D4×C3⋊C8—51no—
142#5009—51no—
143C2×C5×#41C2×D311yescharacteristic
144C22×C5×D4C2×D311yescharacteristic
145C5×#124C2×D311yescharacteristic
146C5×#123—21no—
147C5×C22⋊Q8C2×D311yescharacteristic
148C5×#121—21no—
149C5×#121C2×D311yescharacteristic
150C5×#120—21no—
151C4×C5×D4C2×D311yescharacteristic
152C4×C5×D4C2×D311yescharacteristic
153C2×C5×C22⋊C4—21no—
154C2×#688—31no—
155#4085—61no—
156C2×#686—31no—
157C2×#686—31no—
158#4076—31no—
159#4076—31no—
160#4072—31no—
161C2×C4⋊Dic5—31no—
162C22×#168—31no—
163C22×#168—31no—
164#4044—61no—
165#4029—61no—
166#4027—61no—
167C4×D20—31no—
168#4016—31no—
169#3967—31no—
170#3967—31no—
171#3967—31no—
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178C22⋊#168—31no—
179C22⋊#168—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×C5—21no—
189C23×C3×C5—42no—
190C23×C3×C5—42no—
191C23×C3×C5—81no—
192C23×C3×C5C2×D411yescharacteristic
193C23×C3×C5C2×D411yescharacteristic
194C22×D15—21no—
195C3×C5×Q8—21no—
196C3×C5×Q8—21no—
197C3×C5×D4—22no—
198C3×C5×D4—21no—
199C3×C5×D4—21no—
200C3×C5×D4—21no—
201C3×C5×D4—42no—
202C3×C5×D4—42no—
203C3×C5×D4—81no—
204C3×C5×D4#4112yes—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—42no—
212C2×C3×C4×C5—81no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218#1220—42no—
219#1220—81no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—81no—
224D60—21no—
225D60—21no—
226C4×D15—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3⋊#168—21no—
230C3⋊#168—21no—
231C2×C3×#41C2×D511yescharacteristic
232C22×C3×D4C2×D511yescharacteristic
233C3×#124C2×D511yescharacteristic
234C3×#123—21no—
235C3×C22⋊Q8C2×D511yescharacteristic
236C3×#121—21no—
237C3×#121C2×D511yescharacteristic
238C3×#120—21no—
239C3×C4×D4C2×D511yescharacteristic
240C3×C4×D4C2×D511yescharacteristic
241C2×C3×C22⋊C4—21no—
242C2×#215—51no—
243#939—101no—
244C2×#213—51no—
245C2×#213—51no—
246#930—51no—
247#930—51no—
248#926—51no—
249C2×C4⋊Dic3—51no—
250C22×C3⋊C8—51no—
251C22×C3⋊C8—51no—
252#898—101no—
253#883—101no—
254#67⋊C4—101no—
255C4×D12—51no—
256#870—51no—
257#835—51no—
258#835—51no—
259#835—51no—
260#832—51no—
261#832—51no—
262#832—51no—
263#832—51no—
264#832—51no—
265#832—51no—
266#830—51no—
267#830—51no—
268#809—51no—
269#808—51no—
270#807—51no—
271#807—51no—
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C24×C5—21no—
275C5×#41—22no—
276C5×#41—41no—
277C2×C5×Q8C22×D311yescharacteristic
278C2×C5×D4—22no—
279C2×C5×D4—21no—
280C2×C5×D4—21no—
281C2×C5×D4—21no—
282C2×C5×D4—41no—
283C2×C5×D4#6711yescharacteristic
284C2×C5×D4C22×D311yescharacteristic
285C2×C5×D4C22×D311yescharacteristic
286C22×C4×C5—21no—
287C22×C4×C5—21no—
288C22×C4×C5C22×D311yescharacteristic
289C22×C4×C5C22×D311yescharacteristic
290C2×C22⋊D5—61no—
291C2×C22⋊D5—61no—
292C22×Dic5—61no—
293C2×D20—31no—
294C2×C4×D5—61no—
295C5×C4⋊C4—21no—
296C5×C4⋊C4#6711yescharacteristic
297C5×C4⋊C4C22×D311yescharacteristic
298C5×C22⋊C4—21no—
299C5×C22⋊C4—21no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4#6711yescharacteristic
304C5×C22⋊C4#6711yescharacteristic
305C42×C5C22×D311yescharacteristic
306C22⋊Dic5—61no—
307#688—121no—
308#686—62no—
309#686—121no—
310#685—61no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5—31no—
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317#683—61no—
318#683—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—31no—
323C2×#168—31no—
324C2×#168—121no—
325C2×#168—121no—
326#553—151no—
327#546D1511yescharacteristic, complemented
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—22no—
345C22×C3×C5—21no—
346C22×C3×C5—21no—
347C22×C3×C5—41no—
348C22×C3×C5—41no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5—84no—
353C22×C3×C5#13512yes—
354C22×C3×C5C22×D411yescharacteristic
355C2×D15—41no—
356C2×D15—41no—
357C2×D15—41no—
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×C5C2×#4111yescharacteristic
365C3×C4×C5H(5,𝔽2)11yescharacteristic
366Dic15—41no—
367Dic15—41no—
368Dic15—41no—
369C24×C3—21no—
370C3×#41—22no—
371C3×#41—41no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—22no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—41no—
378C2×C3×D4C22⋊D511yescharacteristic
379C2×C3×D4C22×D511yescharacteristic
380C2×C3×D4C22×D511yescharacteristic
381C22×C3×C4—21no—
382C22×C3×C4—21no—
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—101no—
386C2×#67—101no—
387C22×Dic3—101no—
388C2×D12—51no—
389C2×C4×D3—101no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4C22⋊D511yescharacteristic
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4C22⋊D511yescharacteristic
399C3×C22⋊C4C22⋊D511yescharacteristic
400C3×C42C22×D511yescharacteristic
401#217—101no—
402#215—201no—
403#213—102no—
404#213—201no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410C4⋊Dic3—51no—
411C4⋊Dic3—101no—
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—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×C5—21no—
423C23×C5—42no—
424C23×C5—42no—
425C23×C5—81no—
426C23×C5C2×#6711yescharacteristic
427C23×C5C2×#6711yescharacteristic
428C22×D5—61no—
429C5×Q8—21no—
430C5×Q8—21no—
431C5×D4—22no—
432C5×D4—21no—
433C5×D4—21no—
434C5×D4—21no—
435C5×D4—42no—
436C5×D4—42no—
437C5×D4—81no—
438C5×D4#23712yes—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—42no—
446C2×C4×C5—81no—
447C2×C4×C5C2×#6711yescharacteristic
448C2×C4×C5C2×#6711yescharacteristic
449C2×C4×C5C2×#6711yescharacteristic
450C2×C4×C5C2×#6711yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—122no—
453C22⋊D5—241no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458D20—61no—
459D20—61no—
460C4×D5—241no—
461#168—61no—
462#168—61no—
463#168—61no—
464#168—61no—
465C2×#41C2×D1511yescharacteristic
466C22×D4C2×D1511yescharacteristic
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—301no—
473#125—151no—
474#124C2×D1511yescharacteristic
475#123—21no—
476#123—301no—
477C22⋊Q8C2×D1511yescharacteristic
478#121—21no—
479#121—151no—
480#121—151no—
481#121—301no—
482#121C2×D1511yescharacteristic
483#120—21no—
484C4×D4—151no—
485C4×D4—301no—
486C4×D4C2×D1511yescharacteristic
487C4×D4C2×D1511yescharacteristic
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—21no—
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—42no—
511C2×C3×C5—81no—
512C2×C3×C5#54611yescharacteristic
513C2×C3×C5C2×#13511yescharacteristic
514C2×C3×C5#57611yescharacteristic
515D15—81no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—42no—
519C23×C3—42no—
520C23×C3—81no—
521C23×C3C2×C22⋊D511yescharacteristic
522C23×C3C2×C22⋊D511yescharacteristic
523C22×D3—101no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×D4—22no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—42no—
531C3×D4—42no—
532C3×D4—81no—
533C3×D4#71112yes—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—42no—
541C2×C3×C4—81no—
542C2×C3×C4C2×C22⋊D511yescharacteristic
543C2×C3×C4C2×C22⋊D511yescharacteristic
544C2×C3×C4C2×C22⋊D511yescharacteristic
545C2×C3×C4C2×C22⋊D511yescharacteristic
546C2×C3×C4C23×D511yescharacteristic
547#67—202no—
548#67—401no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—401no—
553D12—101no—
554D12—101no—
555C4×D3—401no—
556C3⋊C8—101no—
557C3⋊C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—22no—
564C22×C5—21no—
565C22×C5—21no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5—41no—
571C22×C5—84no—
572C22×C5#95012yes—
573C22×C5C22×#6711yescharacteristic
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—121no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—41no—
582C4×C5—41no—
583C4×C5C2×#23711yescharacteristic
584C4×C5#100411yescharacteristic
585Dic5—121no—
586Dic5—121no—
587Dic5—121no—
588C24—21no—
589#41—22no—
590#41—41no—
591C2×Q8C22×D1511yescharacteristic
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—41no—
597C2×D4—151no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4#122011yescharacteristic
601C2×D4C22×D1511yescharacteristic
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—151no—
620C4⋊C4—151no—
621C4⋊C4—151no—
622C4⋊C4—301no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4#122011yescharacteristic
626C4⋊C4C22×D1511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4#122011yescharacteristic
637C22⋊C4#122011yescharacteristic
638C42—301no—
639C42C22×D1511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—84no—
653C22×C3#409612yes—
654C22×C3C22×C22⋊D511yescharacteristic
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—201no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4C2×#71111yescharacteristic
665C3×C4#414411yescharacteristic
666Dic3—201no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5—42no—
672C2×C5—81no—
673C2×C5#580611yescharacteristic
674C2×C5C2×#95011yescharacteristic
675C2×C5#583511yescharacteristic
676D5—241no—
677C23—21no—
678C23—21no—
679C23—42no—
680C23—42no—
681C23—81no—
682C23—301no—
683C23C2×#122011yescharacteristic
684C23C2×#122011yescharacteristic
685Q8—21no—
686Q8—21no—
687D4—22no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—42no—
692D4—42no—
693D4—81no—
694D4—301no—
695D4—301no—
696D4—602no—
697D4—1201no—
698D4#681912yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—42no—
706C2×C4—81no—
707C2×C4—301no—
708C2×C4—301no—
709C2×C4—301no—
710C2×C4—1201no—
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—42no—
724C2×C3—81no—
725C2×C3#6614011yescharacteristic
726C2×C3C2×#409611yescharacteristic
727C2×C3#6616911yescharacteristic
728D3—401no—
729C5#8349511yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—84no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22#9183912yes—
746C22C22×#122011yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—41no—
752C4—41no—
753C4—601no—
754C4—601no—
755C4—601no—
756C4C2×#681911yescharacteristic
757C4#9209511yescharacteristic
758C3#1061522611yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—42no—
762C2—81no—
763C2—1201no—
764C2#1175656511yescharacteristic
765C2C2×#9183911yescharacteristic
766C2#1175659411yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#546C2
socleC22×C3×C5C22×D4
hypercenter#546D15
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C3×C5×#546C2semidirect
2. #11756324C2semidirect
3. #11751339C2semidirect
4. #11751334C2semidirect
5. #11751318C2semidirect
6. C2×#91116C2semidirect
7. #11751158C2semidirect
8. #11751157C2semidirect
9. #11751149C2semidirect
10. #11751145C2semidirect
11. #11751139C2semidirect
12. #11751136C2semidirect
13. C4×#6715C2semidirect
14. D4×C3⋊#168C2semidirect
15. #11751110C2semidirect
28. C2×#6717C22semidirect
33. #91819C22semidirect
34. #91815C22semidirect
37. C22×C3⋊#168C22semidirect
41. C4×D60C22semidirect
42. #91759C22semidirect
43. #91119C22semidirect
44. #91119C22semidirect
45. #91119C22semidirect
53. #91114C22semidirect
54. #91093C22semidirect
55. #91092C22semidirect
56. #91091C22semidirect
57. #91091C22semidirect
58. C4⋊(C3⋊#168)C22semidirect
59. C4×C3⋊#168C22semidirect
61. C5×#546D3semidirect
128. C3×#546D5semidirect
327. #546D15semidirect
640. C3×C5#3297semidirect
729. C5#83495semidirect
758. C3#10615226semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5462
#117563242
#117513392
#117513342
#117513182
C2×#911162
#117511582
#117511572
#117511492
#117511452
#117511392
#117511362
C4×#67152
D4×C3⋊#1682
#117511102
#106152263
#834955