Finite Group Databasebeta

← #14459046

Subgroups — #14459046

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×#65946C211yesmaximal, characteristic, complemented
2#11754406C211yesmaximal, characteristic, complemented
3#11751136C211yesmaximal, characteristic, complemented
4C5×#5038C211yesmaximal, characteristic, complemented
5#11749085C211yesmaximal, characteristic, complemented
6#11749021C211yesmaximal, characteristic, complemented
7#11748978C211yesmaximal, characteristic, complemented
8D5×#832C211yesmaximal, characteristic, complemented
9#11748511C211yesmaximal, characteristic, complemented
10C3⋊C8×C22⋊D5C211yesmaximal, characteristic, complemented
11#11748365C211yesmaximal, characteristic, complemented
12#11747389C211yesmaximal, characteristic, complemented
13#11747309C211yesmaximal, characteristic, complemented
14#11747216C211yesmaximal, characteristic, complemented
15#11747194C211yesmaximal, characteristic, complemented
16#10612456—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18C2×C3×#709C2211yescharacteristic
19C3×C5×#121C2211yescharacteristic
20#91815C2211yescharacteristic, complemented
21C2×C5×#213C2211yescharacteristic
22C5×#930C2211yescharacteristic, complemented
23C22×C5×C3⋊C8C2211yescharacteristic, complemented
24C3×#4084—21no—
25C3×#4083—21no—
26C3×#4082C2211yescharacteristic
27C3×C4×C22⋊D5C2211yescharacteristic
28C3×#4043C2211yescharacteristic
29C3×#4039C2211yescharacteristic
30C3×#4029—21no—
31C3×D5×C22⋊C4—21no—
32#91555—21no—
33#91549—21no—
34#91449C2211yescharacteristic
35#91442—21no—
36Dic5×D12C2211yescharacteristic, complemented
37D5×C4⋊Dic3C2211yescharacteristic
38#91388C2211yescharacteristic, complemented
39#91367—21no—
40C2×#6656C2211yescharacteristic, complemented
41C2×#6652C2211yescharacteristic
42C2×D5×C3⋊C8C2211yescharacteristic
43#91116C2211yescharacteristic
44#91116C2211yescharacteristic
45#91114C2211yescharacteristic, complemented
46#91092C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C5×#832C2211yescharacteristic
49C5×#809C2211yescharacteristic, complemented
50C5×#807C2211yescharacteristic, complemented
51#90982C2211yescharacteristic, complemented
52#90971C2211yescharacteristic, complemented
53#90971C2211yescharacteristic, complemented
54#90970C2211yescharacteristic, complemented
55#90965C2211yescharacteristic
56#90965C2211yescharacteristic
57#90964C2211yescharacteristic
58#90955C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic, complemented
60#83495—51nomaximal, Hall
61#65948—31no—
62#65946D311yescharacteristic, complemented
63C5×#466—31no—
64#65445—31no—
65#65442—31no—
66#65402—31no—
67C8×C22⋊D5—31no—
68#65326—31no—
69#65324—31no—
70#65180—31no—
71#65173—31no—
72#65067—31no—
73D5×#102—31no—
74#65057—31no—
75#65045—31no—
76C23×C3×D5—21no—
77C2×C3×C5×D4—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×D12C2311yescharacteristic
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5—21no—
84C2×C3×C22⋊D5D411yescharacteristic
85C3×D4×D5—22no—
86C3×D4×D5—41no—
87C3×#709—22no—
88C3×#709—41no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5C2311yescharacteristic
93C2×C3×Dic10C2311yescharacteristic
94C2×#1201—21no—
95C2×D3×Dic5—21no—
96C2×D5×Dic3—21no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C22⋊C4—21no—
99#6719—21no—
100C4⋊Dic15C2311yescharacteristic
101C4⋊Dic15C2311yescharacteristic
102C4×Dic15—21no—
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×#213—41no—
106C5×(C2×D3)⋊C4—21no—
107C5×C4⋊Dic3C2311yescharacteristic
108C2×C5×C3⋊C8—41no—
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C22⋊Dic5—21no—
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5D411yescharacteristic
114C3×#685—21no—
115C3×#685—21no—
116C3×#685D411yescharacteristic
117C3×C4⋊Dic5—21no—
118C3×#683D411yescharacteristic
119C3×C4×Dic5C2311yescharacteristic
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123(C2×D3)⋊Dic5—21no—
124(C2×D3)⋊Dic5—21no—
125#6656—41no—
126#6652—22no—
127D5×C3⋊C8—41no—
128C3×#546—51no—
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#5038D511yescharacteristic, complemented
139#5035—51no—
140C4×#213—51no—
141D4×C3⋊C8—51no—
142#5009—51no—
143C2×D4×D5C2×D311yescharacteristic
144C2×#709C2×D311yescharacteristic
145C2×C5×D8—31no—
146C22×C5×C8—31no—
147C5×#121—31no—
148C5×#121C2×D311yescharacteristic
149#4084—21no—
150#4084—31no—
151#4084—61no—
152#4083—21no—
153#4082C2×D311yescharacteristic
154#4081—61no—
155D4×Dic5—31no—
156C2×#687—31no—
157C2×#686—31no—
158C4×C22⋊D5C2×D311yescharacteristic
159#4072—31no—
160C2×C8×D5—31no—
161#4043C2×D311yescharacteristic
162#4039C2×D311yescharacteristic
163D5×C4⋊C4—31no—
164#4036—31no—
165#4029—21no—
166#4027—61no—
167D5×C22⋊C4—21no—
168#4025—61no—
169C5×#107—31no—
170C5×#102—31no—
171C5×#102—31no—
172#3964—31no—
173#3964—31no—
174C22⋊#168—31no—
175#3953—31no—
176#3953—31no—
177#3952—31no—
178#3948—31no—
179#3948—31no—
180#3946—31no—
181C8×Dic5—31no—
182#3942—31no—
183#3941—31no—
184#3940—31no—
185#3939—31no—
186#3297—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5C2×D411yescharacteristic
189C22×C5×D3—21no—
190C22×C3×D5—21no—
191C22×C3×D5—42no—
192C22×C3×D5—42no—
193C22×C3×D5—81no—
194C22×C3×D5C2×D411yescharacteristic
195C3×C5×D4—21no—
196C3×C5×D4—21no—
197C3×C5×D4—81no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C2×Dic15—21no—
204C2×Dic15—21no—
205C5×#67—81no—
206C2×C5×Dic3—21no—
207C5×D12—21no—
208C5×D12—21no—
209C3×C22⋊D5—22no—
210C3×C22⋊D5—42no—
211C3×C22⋊D5—42no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×D20—21no—
217C3×D20#4112yes—
218C3×C4×D5—21no—
219C3×C4×D5—21no—
220C3×C4×D5—42no—
221C3×C4×D5—81no—
222C3×Dic10—21no—
223C3×Dic10—21no—
224#1201—42no—
225D3×Dic5—81no—
226D5×Dic3—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C5×C3⋊C8—21no—
230C5×C3⋊C8—21no—
231C2×C3×#41—51no—
232C22×C3×D4—51no—
233C3×#124—51no—
234C3×#123—101no—
235C3×C22⋊Q8—51no—
236C3×#121—101no—
237C3×#121C2×D511yescharacteristic
238C3×#120—101no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C2×C3×C22⋊C4—101no—
242C2×#215—51no—
243#939—101no—
244C2×#213—51no—
245C2×#213C2×D511yescharacteristic
246#930—51no—
247#930C2×D511yescharacteristic, complemented
248#926—51no—
249C2×C4⋊Dic3—51no—
250C22×C3⋊C8—51no—
251C22×C3⋊C8C2×D511yescharacteristic, complemented
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#832C2×D511yescharacteristic
266#830—51no—
267#830—51no—
268#809C2×D511yescharacteristic, complemented
269#808—51no—
270#807—51no—
271#807C2×D511yescharacteristic, complemented
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C23×D5—21no—
275C2×C5×D4—21no—
276C2×C5×D4—31no—
277C2×C5×D4—61no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5C22×D311yescharacteristic
280C2×C22⋊D5—21no—
281C2×C22⋊D5—21no—
282C2×C22⋊D5—61no—
283C2×C22⋊D5#6711yescharacteristic
284C22×Dic5—61no—
285D4×D5—22no—
286D4×D5—41no—
287#709—22no—
288#709—41no—
289C2×D20C22×D311yescharacteristic
290C2×C4×D5—21no—
291C2×C4×D5—21no—
292C2×C4×D5—61no—
293C2×C4×D5C22×D311yescharacteristic
294C2×Dic10C22×D311yescharacteristic
295C5×D8—121no—
296C2×C5×C8—31no—
297C2×C5×C8—31no—
298C2×C5×C8—121no—
299C5×C4⋊C4—31no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C22⋊C4—21no—
302C5×C22⋊C4—61no—
303C22⋊Dic5—21no—
304C22⋊Dic5—21no—
305C22⋊Dic5—61no—
306C22⋊Dic5—61no—
307C22⋊Dic5—61no—
308C22⋊Dic5#6711yescharacteristic
309#687—121no—
310#686—62no—
311#685—21no—
312#685—21no—
313#685#6711yescharacteristic
314C4⋊Dic5—21no—
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—61no—
318#683—61no—
319#683—61no—
320#683#6711yescharacteristic
321C4×Dic5—61no—
322C4×Dic5C22×D311yescharacteristic
323C2×#168—31no—
324C2×#168—31no—
325C8×D5—121no—
326#553—151no—
327#546—51no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—31no—
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—41no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×C5×D3—41no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C3×D5—21no—
352C2×C3×D5—21no—
353C2×C3×D5—22no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—84no—
357C2×C3×D5#13512yes—
358C3×C4×C5—21no—
359C3×C4×C5—41no—
360C3×C4×C5C2×#4111yescharacteristic
361C3×C4×C5H(5,𝔽2)11yescharacteristic
362Dic15—41no—
363Dic15—41no—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—41no—
368C5×Dic3—41no—
369C24×C3—101no—
370C3×#41—102no—
371C3×#41—201no—
372C2×C3×Q8—51no—
373C2×C3×D4—21no—
374C2×C3×D4—51no—
375C2×C3×D4—51no—
376C2×C3×D4—101no—
377C2×C3×D4—102no—
378C2×C3×D4—101no—
379C2×C3×D4—201no—
380C2×C3×D4C22×D511yescharacteristic
381C22×C3×C4—51no—
382C22×C3×C4—101no—
383C22×C3×C4—101no—
384C22×C3×C4C22×D511yescharacteristic
385C2×#67—21no—
386C2×#67—101no—
387C22×Dic3—101no—
388C2×D12C22×D511yescharacteristic
389C2×C4×D3—101no—
390C3×C4⋊C4—51no—
391C3×C4⋊C4—101no—
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—51no—
395C3×C22⋊C4—51no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C42—51no—
401#217—101no—
402#215—201no—
403#213—41no—
404#213—102no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408C4⋊Dic3—51no—
409C4⋊Dic3—51no—
410C4⋊Dic3—101no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—101no—
415C2×C3⋊C8—41no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—201no—
419C2×C3⋊C8C22×D511yescharacteristic
420C2×C3⋊C8C22×D511yescharacteristic
421C23×C5—21no—
422C23×C5—61no—
423C23×C5C2×#6711yescharacteristic
424C22×D5—21no—
425C22×D5—42no—
426C22×D5—42no—
427C22×D5—81no—
428C22×D5C2×#6711yescharacteristic
429C5×D4—21no—
430C5×D4—21no—
431C5×D4—61no—
432C5×D4—61no—
433C5×D4—81no—
434C5×D4—241no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—61no—
439C2×C4×C5C2×#6711yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—22no—
442C22⋊D5—42no—
443C22⋊D5—42no—
444C22⋊D5—122no—
445C2×Dic5—21no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—241no—
449C2×Dic5C2×#6711yescharacteristic
450C2×Dic5C2×#6711yescharacteristic
451C2×Dic5C2×#6711yescharacteristic
452D20—21no—
453D20#23712yes—
454C4×D5—21no—
455C4×D5—21no—
456C4×D5—42no—
457C4×D5—81no—
458C4×D5—241no—
459Dic10—21no—
460Dic10—21no—
461C5×C8—61no—
462C5×C8—61no—
463#168—61no—
464#168—61no—
465C2×#41—51no—
466C22×D4—51no—
467C2×SD16—151no—
468C2×D8—31no—
469C2×D8—151no—
470C22×C8—31no—
471C22×C8—151no—
472#126—301no—
473#125—151no—
474#124—51no—
475#123—101no—
476#123—301no—
477C22⋊Q8—51no—
478#121—31no—
479#121—101no—
480#121—151no—
481#121—301no—
482#121D3×D511yescharacteristic
483#120—101no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—151no—
487C4×D4—301no—
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—101no—
491#107—31no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—31no—
499#102—31no—
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—41no—
509C2×C3×C5—81no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C3×D5—22no—
514C3×D5—42no—
515C5×D3—81no—
516C23×C3—21no—
517C23×C3—51no—
518C23×C3—101no—
519C23×C3—202no—
520C23×C3—202no—
521C23×C3—401no—
522C23×C3D4×D511yescharacteristic
523C22×D3—21no—
524C3×Q8—101no—
525C3×Q8—101no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—52no—
529C3×D4—81no—
530C3×D4—102no—
531C3×D4—101no—
532C3×D4—202no—
533C3×D4—202no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—51no—
538C2×C3×C4—51no—
539C2×C3×C4—51no—
540C2×C3×C4—101no—
541C2×C3×C4—101no—
542C2×C3×C4—101no—
543C2×C3×C4—202no—
544C2×C3×C4—401no—
545C2×C3×C4D4×D511yescharacteristic
546C2×C3×C4C23×D511yescharacteristic
547#67—81no—
548#67—202no—
549C2×Dic3—21no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—401no—
553D12—21no—
554D12—21no—
555C4×D3—401no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—41no—
564C22×C5—41no—
565C22×C5—41no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5C22×#6711yescharacteristic
570C2×D5—21no—
571C2×D5—21no—
572C2×D5—22no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—84no—
576C2×D5#95012yes—
577C4×C5—21no—
578C4×C5—41no—
579C4×C5—121no—
580C4×C5C2×#23711yescharacteristic
581C4×C5#100411yescharacteristic
582Dic5—21no—
583Dic5—21no—
584Dic5—21no—
585Dic5—41no—
586Dic5—121no—
587Dic5—121no—
588C24—101no—
589#41—102no—
590#41—201no—
591C2×Q8—51no—
592C2×D4—21no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—51no—
596C2×D4—61no—
597C2×D4—101no—
598C2×D4—102no—
599C2×D4—101no—
600C2×D4—201no—
601C2×D4—301no—
602C2×D4C2×D3×D511yescharacteristic
603C22×C4—51no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—301no—
607C22×C4—301no—
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—121no—
611D8—302no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—121no—
615C2×C8—151no—
616C2×C8—151no—
617C2×C8—601no—
618C4⋊C4—31no—
619C4⋊C4—51no—
620C4⋊C4—101no—
621C4⋊C4—151no—
622C4⋊C4—151no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—51no—
629C22⋊C4—51no—
630C22⋊C4—61no—
631C22⋊C4—101no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C42—51no—
639C42—301no—
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—52no—
648C22×C3—101no—
649C22×C3—101no—
650C22×C3—102no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—404no—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—101no—
661C3×C4—101no—
662C3×C4—101no—
663C3×C4—201no—
664C3×C4#414411yescharacteristic
665C3×C4D5×#4111yescharacteristic
666Dic3—41no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—41no—
670C2×C5—81no—
671C2×C5—241no—
672C2×C5#580611yescharacteristic
673C2×C5C2×#95011yescharacteristic
674C2×C5#583511yescharacteristic
675D5—22no—
676D5—42no—
677C23—21no—
678C23—51no—
679C23—61no—
680C23—101no—
681C23—202no—
682C23—202no—
683C23—401no—
684C23D5×#6711yescharacteristic
685Q8—101no—
686Q8—101no—
687D4—21no—
688D4—21no—
689D4—52no—
690D4—61no—
691D4—61no—
692D4—81no—
693D4—102no—
694D4—101no—
695D4—202no—
696D4—202no—
697D4—241no—
698D4—602no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—51no—
703C2×C4—51no—
704C2×C4—51no—
705C2×C4—61no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—202no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—401no—
713C2×C4—1201no—
714C2×C4—1201no—
715C2×C4D5×#6711yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—61no—
718C8—61no—
719C8—301no—
720C8—301no—
721C2×C3—41no—
722C2×C3—81no—
723C2×C3—102no—
724C2×C3—202no—
725C2×C3#6594411yescharacteristic
726C2×C3#6609111yescharacteristic
727C2×C3D5×#13511yescharacteristic
728D3—81no—
729C5#8349511yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—52no—
737C22—101no—
738C22—101no—
739C22—102no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—201no—
744C22—201no—
745C22—404no—
746C22C2×D5×#6711yescharacteristic
747C4—21no—
748C4—41no—
749C4—101no—
750C4—101no—
751C4—101no—
752C4—121no—
753C4—201no—
754C4—601no—
755C4—601no—
756C4D5×#23711yescharacteristic
757C4#9202511yescharacteristic
758C3#1061245611yescharacteristic, complemented, Sylow
759C2—41no—
760C2—81no—
761C2—102no—
762C2—202no—
763C2—241no—
764C2#1175469111yescharacteristic
765C2#1175479111yescharacteristic
766C2D5×#95011yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#121C22
socleC22×C3×C5C22×D4
hypercenter#121D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#65946C2semidirect
2. #11754406C2semidirect
3. #11751136C2semidirect
4. C5×#5038C2semidirect
5. #11749085C2semidirect
6. #11749021C2semidirect
7. #11748978C2semidirect
8. D5×#832C2semidirect
9. #11748511C2semidirect
10. C3⋊C8×C22⋊D5C2semidirect
11. #11748365C2semidirect
12. #11747389C2semidirect
13. #11747309C2semidirect
14. #11747216C2semidirect
15. #11747194C2semidirect
20. #91815C22semidirect
22. C5×#930C22semidirect
23. C22×C5×C3⋊C8C22semidirect
36. Dic5×D12C22semidirect
38. #91388C22semidirect
40. C2×#6656C22semidirect
45. #91114C22semidirect
46. #91092C22semidirect
47. #91091C22semidirect
49. C5×#809C22semidirect
50. C5×#807C22semidirect
51. #90982C22semidirect
52. #90971C22semidirect
53. #90971C22semidirect
54. #90970C22semidirect
59. Dic5×C3⋊C8C22semidirect
62. #65946D3semidirect
138. #5038D5semidirect
247. #930C2×D5semidirect
251. C22×C3⋊C8C2×D5semidirect
268. #809C2×D5semidirect
271. #807C2×D5semidirect
640. C3×C5#3297semidirect
729. C5#83495semidirect
758. C3#10612456semidirect

Maximal subgroups

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

subgroupindex
C3×#659462
#117544062
#117511362
C5×#50382
#117490852
#117490212
#117489782
D5×#8322
#117485112
C3⋊C8×C22⋊D52
#117483652
#117473892
#117473092
#117472162
#117471942
#106124563
#834955