Finite Group Databasebeta

← #14479175

Subgroups — #14479175

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92034C211yesmaximal, characteristic
2#11756331C211yesmaximal, characteristic, complemented
3C4×C5×#239C211yesmaximal, characteristic, complemented
4C3×#65908C211yesmaximal, characteristic, complemented
5#11755217C211yesmaximal, characteristic, complemented
6Dic5×#239C211yesmaximal, characteristic, complemented
7#11755124C211yesmaximal, characteristic, complemented
8#11753841C213yesmaximal, complemented
9D5×#892C213yesmaximal, complemented
10#11753671C213yesmaximal, complemented
11#11753398C213yesmaximal, complemented
12#11752729C213yesmaximal, complemented
13D3×#4018C213yesmaximal, complemented
14#11752669C213yesmaximal, complemented
15C4×#6765C213yesmaximal, complemented
16#10617735—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×#239C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic
20#92034C4116yescomplemented
21C2×#6777C2213yes—
22C2×C4×D3×D5C2213yes—
23C2×#6772C2213yes—
24C2×#6765C2213yes—
25C3×C4×C5×Q8C2211yescharacteristic, complemented
26Q8×Dic15C2211yescharacteristic, complemented
27#91781C2213yes—
28#91776C2213yescomplemented
29#91761C2213yes—
30C4×Dic30C2213yescomplemented
31C5×Q8×Dic3C2211yescharacteristic, complemented
32C5×#893C2213yescomplemented
33C5×#892C2213yescomplemented
34C4×C5×D12C2213yescomplemented
35C42×C5×D3C2213yescomplemented
36C3×Q8×Dic5C2211yescharacteristic, complemented
37C3×#4039C2213yescomplemented
38C3×D5×C4⋊C4C2213yescomplemented
39C3×C4×D20C2213yescomplemented
40C3×#4018C2213yescomplemented
41D3×#685C2213yes—
42D3×#685C2213yes—
43D5×(C2×D3)⋊C4C2216yes—
44#91442C2216yescomplemented
45#91441C2216yescomplemented
46#91440C2216yescomplemented
47C4×#1201C2216yescomplemented
48#91435C2213yescomplemented
49#91434C2213yescomplemented
50Dic3×D20C2213yescomplemented
51Dic5×D12C2213yescomplemented
52D5×C4⋊Dic3C2213yescomplemented
53#91403C2211yescharacteristic
54#91403C2213yes—
55#91400C2216yescomplemented
56D3×#683C2213yescomplemented
57D3×#683C2213yescomplemented
58C4×D3×Dic5C2213yescomplemented
59#91393C2213yescomplemented
60#91393C2213yescomplemented
61C4×D5×Dic3C2216yescomplemented
62#91386C2213yes—
63#91357C2213yescomplemented
64#91347C2213yes—
65#91340C2213yescomplemented
66#91338C2213yescomplemented
67#91333C2213yescomplemented
68#85885—51nomaximal, Hall
69C2×D5×#41—31no—
70C4×C5×#41—31no—
71#41×Dic5—31no—
72#65908—31no—
73#65908D311yescharacteristic, complemented
74#65906—31no—
75#65906—31no—
76#65880—33no—
77#65880—33no—
78#65879—33no—
79#65879—33no—
80#65856—33no—
81D5×#117—33no—
82C4×#709—33no—
83C2×#4018—33no—
84C22×D3×D5C2313yes—
85C2×C3×C5×Q8C2311yescharacteristic
86Q8×D15C2×C418yescomplemented
87C2×C4×D15C2313yes—
88C2×Dic30C2313yes—
89C5×#239C2×C418yescomplemented
90C2×C5×D12C2313yes—
91C2×C4×C5×D3C2313yes—
92C2×C4×C5×D3C2313yes—
93C2×C4×C5×D3C2313yes—
94C3×#713C2×C418yescomplemented
95C2×C3×D20C2313yes—
96C2×C3×C4×D5C2316yes—
97C2×C3×C4×D5C2313yes—
98C2×#1201C2316yes—
99C2×#1200C2311yescharacteristic
100C2×D3×Dic5C2313yes—
101C2×D3×Dic5C2313yes—
102C2×D3×Dic5C2313yes—
103C2×D5×Dic3C2316yes—
104C2×D5×Dic3C2313yes—
105#6777C2×C4124yescomplemented
106C4×D3×D5C2×C4124yescomplemented
107#6772C2×C4124yescomplemented
108#6765C2×C4124yescomplemented
109C3×C5×C4⋊C4C2313yes—
110C3×C42×C5C2313yes—
111#6714C2313yes—
112#6714C2311yescharacteristic
113C4⋊Dic15C2313yes—
114#6712C2313yes—
115#6712C2313yes—
116C4×Dic15C2313yes—
117C4×Dic15C2316yes—
118C5×(C2×D3)⋊C4C2316yes—
119C5×C4⋊Dic3C2313yes—
120C4×C5×Dic3C2311yescharacteristic
121C4×C5×Dic3C2313yes—
122C4×C5×Dic3C2313yes—
123C3×#685C2313yes—
124C3×#685C2313yes—
125C3×C4⋊Dic5C2313yes—
126C3×#683C2311yescharacteristic
127C3×#683C2313yes—
128C3×C4×Dic5C2313yes—
129#6669C2313yes—
130#6669C2313yes—
131#6668C2311yescharacteristic
132#6668C2313yes—
133#6667C2313yes—
134#6667C2311yescharacteristic
135(C2×D3)⋊Dic5C2316yes—
136#6665C2313yes—
137#6665C2313yes—
138Dic3×Dic5C2311yescharacteristic
139Dic3×Dic5C2313yes—
140Dic3×Dic5C2316yes—
141C2×D3×#41—51no—
142C3×#520—51no—
143#5827—51no—
144C4×#239—51no—
145C4×#239D511yescharacteristic, complemented
146#5572—51no—
147#5572—51no—
148#5545—53no—
149#5545—53no—
150C4×#237—53no—
151C4×#237—53no—
152#5523—53no—
153D3×#117—53no—
154#5504—53no—
155C2×#892—53no—
156C2×C5×#41—31no—
157D5×#41—316no—
158C2×#713C2×D311yescharacteristic
159C2×Q8×D5—31no—
160C2×#711—33no—
161C2×D4×D5—33no—
162C2×#709—33no—
163C22×C4×D5—33no—
164C4×C5×Q8—31no—
165C4×C5×Q8C2×D311yescharacteristic, complemented
166C4×C5×D4—33no—
167C4×C5×D4—33no—
168C5×#117—33no—
169C2×C42×C5—33no—
170Q8×Dic5—31no—
171Q8×Dic5C2×D311yescharacteristic, complemented
172D4×Dic5—33no—
173D4×Dic5—33no—
174C4×C22⋊D5—36no—
175C4×C22⋊D5—36no—
176C2×#685—33no—
177C2×#685—33no—
178#4072—33no—
179C2×#683—33no—
180C2×#683—33no—
181C2×C4×Dic5—33no—
182#4039—33no—
183#4039C2×D313yescomplemented
184#4038—33no—
185#4038—33no—
186D5×C4⋊C4—33no—
187D5×C4⋊C4C2×D313yescomplemented
188#4033—33no—
189#4033—33no—
190#4027—36no—
191#4027—36no—
192D5×C22⋊C4—36no—
193#4023—36no—
194C4×D20—33no—
195C4×D20C2×D313yescomplemented
196#4018—33no—
197#4018—33no—
198#4018—33no—
199#4018—33no—
200#4018—31no—
201#4018—33no—
202#4018—33no—
203#4018C2×D313yescomplemented
204C42×D5—36no—
205C4×Dic10—33no—
206C4×Dic10—33no—
207#3428—151noSylow
208C22×D15C2411yescharacteristic
209C22×C5×D3C2413yes—
210C22×C3×D5C2413yes—
211C2×D3×D5—43no—
212C2×D3×D5—43no—
213C2×D3×D5C22×C4112yes—
214C3×C5×Q8C22×C414yes—
215C2×C3×C4×C5C2411yescharacteristic
216C2×C3×C4×C5C2413yes—
217C2×C3×C4×C5C2413yes—
218C2×Dic15C2411yescharacteristic
219C2×Dic15C2413yes—
220C2×Dic15C2413yes—
221C4×D15C22×C4112yes—
222Dic30C22×C4112yes—
223C2×C5×Dic3C2413yes—
224C2×C5×Dic3C2411yescharacteristic
225C2×C5×Dic3C2411yescharacteristic
226C5×D12C22×C4112yes—
227C4×C5×D3—43no—
228C4×C5×D3—43no—
229C4×C5×D3C22×C4112yes—
230C2×C3×Dic5C2413yes—
231C2×C3×Dic5C2411yescharacteristic
232C2×C3×Dic5C2411yescharacteristic
233C3×D20C22×C4112yes—
234C3×C4×D5—46no—
235C3×C4×D5C22×C4112yes—
236#1201C22×C4124yes—
237#1200C22×C414yes—
238D3×Dic5—43no—
239D3×Dic5—43no—
240D3×Dic5C22×C4112yes—
241D5×Dic3—46no—
242D5×Dic3C22×C4112yes—
243C2×C3×#41—51no—
244D3×#41—516no—
245C2×#239C2×D511yescharacteristic
246C2×D3×Q8—51no—
247C2×#237—53no—
248C2×D3×D4—53no—
249C2×#235—53no—
250C22×C4×D3—53no—
251C3×C4×Q8—51no—
252C3×C4×Q8C2×D511yescharacteristic, complemented
253C3×C4×D4—53no—
254C3×C4×D4—53no—
255C3×#117—53no—
256C2×C3×C4⋊C4—53no—
257Q8×Dic3—51no—
258Q8×Dic3C2×D511yescharacteristic, complemented
259D4×Dic3—53no—
260D4×Dic3—53no—
261C4×#67—56no—
262C4×#67—56no—
263C2×(C2×D3)⋊C4—56no—
264#926—53no—
265C2×C4⋊Dic3—53no—
266C2×C4×Dic3—56no—
267#893—53no—
268#893C2×D513yescomplemented
269#892—53no—
270#892—53no—
271#892—56no—
272#892—53no—
273#892—53no—
274#892—51no—
275#892C2×D513yescomplemented
276D3×C4⋊C4—53no—
277D3×C4⋊C4—53no—
278#887—53no—
279#887—53no—
280#67⋊C4—56no—
281#67⋊C4—56no—
282D3×C22⋊C4—53no—
283D3×C22⋊C4—53no—
284#877—53no—
285#877—53no—
286C4×D12—53no—
287C4×D12C2×D513yescomplemented
288#872—53no—
289#872—53no—
290C42×D3—53no—
291C42×D3C2×D513yescomplemented
292C4×Dic6—53no—
293C4×Dic6—53no—
294C23×D5—33no—
295C5×#41—38no—
296C2×C5×Q8C22×D311yescharacteristic
297C2×C5×D4—33no—
298C22×C4×C5—33no—
299C22×C4×C5—33no—
300C22×C4×C5—33no—
301C2×C22⋊D5—36no—
302C22×Dic5—33no—
303C22×Dic5—33no—
304C22×Dic5—33no—
305#713C4×D318yescomplemented
306Q8×D5—38no—
307#711—324no—
308D4×D5—324no—
309#709—324no—
310C2×D20C22×D313yes—
311C2×C4×D5—33no—
312C2×C4×D5—33no—
313C2×C4×D5—31no—
314C2×C4×D5—324no—
315C2×C4×D5—36no—
316C2×C4×D5C22×D316yes—
317C2×C4×D5C22×D313yes—
318C2×Dic10—33no—
319C5×C4⋊C4—33no—
320C5×C4⋊C4C22×D313yes—
321C5×C22⋊C4—36no—
322C42×C5—31no—
323C42×C5—33no—
324C42×C5—33no—
325C42×C5C22×D313yes—
326C22⋊Dic5—36no—
327#685—33no—
328#685—33no—
329#685—31no—
330#685—33no—
331#685—31no—
332#685—33no—
333#685C22×D313yes—
334#685C22×D313yes—
335C4⋊Dic5—33no—
336C4⋊Dic5C22×D313yes—
337#683—33no—
338#683—33no—
339#683—31no—
340#683—33no—
341#683—33no—
342#683—33no—
343#683C22×D311yescharacteristic
344#683C22×D313yes—
345C4×Dic5—36no—
346C4×Dic5—33no—
347C4×Dic5—36no—
348C4×Dic5—33no—
349C4×Dic5—31no—
350C4×Dic5C22×D313yes—
351C22×#41—151no—
352#520—51no—
353#520—153no—
354#520—153no—
355#520—151no—
356#519—151no—
357#519—151no—
358#518—153no—
359#518—153no—
360C4×#41—31no—
361C4×#41—153no—
362C4×#41—153no—
363C4×#41—151no—
364C2×#117—153no—
365C2×#117—153no—
366C22×C3×C5C2511yescharacteristic
367C2×D15—21no—
368C2×D15—21no—
369C2×D15C23×C412yes—
370C2×C5×D3—23no—
371C2×C5×D3—23no—
372C2×C5×D3C23×C416yes—
373C2×C3×D5—23no—
374C2×C3×D5—23no—
375C2×C3×D5C23×C416yes—
376D3×D5—412no—
377C3×C4×C5—23no—
378C3×C4×C5—21no—
379C3×C4×C5C23×C416yes—
380Dic15—23no—
381Dic15—21no—
382Dic15C23×C416yes—
383C3×Dic5—21no—
384C3×Dic5—23no—
385C3×Dic5C23×C412yes—
386C5×Dic3—23no—
387C5×Dic3—21no—
388C5×Dic3C23×C412yes—
389C23×D3—53no—
390C3×#41—58no—
391C2×C3×Q8C22×D511yescharacteristic
392C2×C3×D4—53no—
393C22×C3×C4—53no—
394C22×C3×C4—56no—
395C2×#67—56no—
396C22×Dic3—53no—
397C22×Dic3—56no—
398#239C4×D518yescomplemented
399D3×Q8—58no—
400#237—524no—
401D3×D4—524no—
402#235—524no—
403C2×D12C22×D513yes—
404C2×C4×D3—53no—
405C2×C4×D3—53no—
406C2×C4×D3—51no—
407C2×C4×D3—524no—
408C2×C4×D3—53no—
409C2×C4×D3—53no—
410C2×C4×D3C22×D513yes—
411C2×C4×D3C22×D513yes—
412C2×C4×D3C22×D513yes—
413C2×Dic6—53no—
414C3×C4⋊C4—51no—
415C3×C4⋊C4—53no—
416C3×C4⋊C4—53no—
417C3×C4⋊C4C22×D513yes—
418C3×C22⋊C4—53no—
419C3×C22⋊C4—53no—
420C3×C42—53no—
421C3×C42C22×D513yes—
422#217—53no—
423#217—53no—
424(C2×D3)⋊C4—56no—
425(C2×D3)⋊C4—51no—
426(C2×D3)⋊C4—53no—
427(C2×D3)⋊C4—51no—
428(C2×D3)⋊C4—53no—
429(C2×D3)⋊C4C22×D516yes—
430C4⋊Dic3—53no—
431C4⋊Dic3—51no—
432C4⋊Dic3—53no—
433C4⋊Dic3C22×D513yes—
434Dic3⋊C4—53no—
435Dic3⋊C4—53no—
436Dic3⋊C4—53no—
437Dic3⋊C4—53no—
438C4×Dic3—56no—
439C4×Dic3—53no—
440C4×Dic3—56no—
441C4×Dic3—51no—
442C4×Dic3—53no—
443C4×Dic3C22×D511yescharacteristic
444C4×Dic3C22×D513yes—
445C4×Dic3C22×D513yes—
446C23×C5—33no—
447C22×D5—31no—
448C22×D5—312no—
449C22×D5—123no—
450C22×D5—123no—
451C22×D5C23×D313yes—
452C5×Q8C2×C4×D314yes—
453C5×D4—312no—
454C2×C4×C5—31no—
455C2×C4×C5—312no—
456C2×C4×C5—33no—
457C2×C4×C5—31no—
458C2×C4×C5—123no—
459C2×C4×C5—123no—
460C2×C4×C5C23×D313yes—
461C2×C4×C5C23×D311yescharacteristic
462C2×C4×C5C23×D313yes—
463C22⋊D5—324no—
464C2×Dic5—33no—
465C2×Dic5—312no—
466C2×Dic5—31no—
467C2×Dic5—33no—
468C2×Dic5—123no—
469C2×Dic5—123no—
470C2×Dic5C23×D313yes—
471C2×Dic5C23×D311yescharacteristic
472C2×Dic5C23×D311yescharacteristic
473D20C2×C4×D3112yes—
474C4×D5—312no—
475C4×D5—312no—
476C4×D5—34no—
477C4×D5—46no—
478C4×D5—126no—
479C4×D5C2×C4×D3112yes—
480Dic10—312no—
481C2×#41—31no—
482C2×#41—51no—
483C2×#41—153no—
484C2×#41—153no—
485C2×#41—1516no—
486C22×Q8—151no—
487C22×D4—153no—
488C23×C4—153no—
489C4×Q8—31no—
490C4×Q8—51no—
491C4×Q8—153no—
492C4×Q8—153no—
493C4×Q8—151no—
494C4×Q8—153no—
495C4×Q8—153no—
496C4×Q8D3×D511yescharacteristic, complemented
497C4×D4—33no—
498C4×D4—33no—
499C4×D4—53no—
500C4×D4—53no—
501C4×D4—153no—
502C4×D4—153no—
503C4×D4—156no—
504C4×D4—156no—
505C4×D4—156no—
506C4×D4—153no—
507C4×D4—153no—
508C4×D4—156no—
509#117—33no—
510#117—53no—
511#117—153no—
512#117—153no—
513#117—153no—
514#117—151no—
515#117—153no—
516#117—153no—
517#117—156no—
518#117—153no—
519#117—153no—
520#117—153no—
521#117—153no—
522C2×C4⋊C4—53no—
523C2×C4⋊C4—153no—
524C2×C4⋊C4—153no—
525C2×C4⋊C4—153no—
526C2×C22⋊C4—156no—
527C2×C22⋊C4—153no—
528C2×C22⋊C4—153no—
529C2×C42—33no—
530C2×C42—156no—
531C2×C42—153no—
532C2×C3×C5C24×C411yescharacteristic
533C2×C3×C5#58511yescharacteristic
534C2×C3×C5#58511yescharacteristic
535D15—22no—
536C3×D5—26no—
537C5×D3—26no—
538C23×C3—53no—
539C22×D3—51no—
540C22×D3—512no—
541C22×D3—203no—
542C22×D3—203no—
543C22×D3C23×D513yes—
544C3×Q8C2×C4×D514yes—
545C3×D4—512no—
546C2×C3×C4—51no—
547C2×C3×C4—512no—
548C2×C3×C4—53no—
549C2×C3×C4—51no—
550C2×C3×C4—206no—
551C2×C3×C4C23×D513yes—
552C2×C3×C4C23×D511yescharacteristic
553C2×C3×C4C23×D513yes—
554#67—524no—
555C2×Dic3—53no—
556C2×Dic3—512no—
557C2×Dic3—51no—
558C2×Dic3—53no—
559C2×Dic3—206no—
560C2×Dic3C23×D513yes—
561C2×Dic3C23×D511yescharacteristic
562C2×Dic3C23×D511yescharacteristic
563D12C2×C4×D5112yes—
564C4×D3—43no—
565C4×D3—43no—
566C4×D3—512no—
567C4×D3—512no—
568C4×D3—54no—
569C4×D3—203no—
570C4×D3—203no—
571C4×D3C2×C4×D5112yes—
572Dic6—512no—
573C22×C5—36no—
574C22×C5—63no—
575C22×C5—63no—
576C22×C5C24×D311yescharacteristic
577C2×D5—23no—
578C2×D5—23no—
579C2×D5—32no—
580C2×D5—61no—
581C2×D5—61no—
582C2×D5—1212no—
583C2×D5C22×C4×D316yes—
584C4×C5—23no—
585C4×C5—21no—
586C4×C5—32no—
587C4×C5—61no—
588C4×C5—63no—
589C4×C5C22×C4×D316yes—
590Dic5—23no—
591Dic5—21no—
592Dic5—36no—
593Dic5—61no—
594Dic5—63no—
595Dic5C22×C4×D312yes—
596C24—153no—
597#41—38no—
598#41—58no—
599#41—1524no—
600#41—1524no—
601C2×Q8—158no—
602C2×Q8—153no—
603C2×Q8C2×D3×D511yescharacteristic
604C2×D4—33no—
605C2×D4—53no—
606C2×D4—1524no—
607C2×D4—156no—
608C22×C4—33no—
609C22×C4—33no—
610C22×C4—33no—
611C22×C4—53no—
612C22×C4—56no—
613C22×C4—151no—
614C22×C4—1524no—
615C22×C4—153no—
616C22×C4—156no—
617C22×C4—153no—
618C22×C4—153no—
619C22×C4—153no—
620C22×C4—153no—
621C4⋊C4—33no—
622C4⋊C4—53no—
623C4⋊C4—53no—
624C4⋊C4—51no—
625C4⋊C4—151no—
626C4⋊C4—153no—
627C4⋊C4—153no—
628C4⋊C4—153no—
629C4⋊C4—153no—
630C4⋊C4—153no—
631C4⋊C4—153no—
632C4⋊C4C2×D3×D513yes—
633C22⋊C4—36no—
634C22⋊C4—53no—
635C22⋊C4—53no—
636C22⋊C4—151no—
637C22⋊C4—153no—
638C22⋊C4—153no—
639C22⋊C4—153no—
640C22⋊C4—156no—
641C22⋊C4—153no—
642C22⋊C4—151no—
643C42—31no—
644C42—33no—
645C42—33no—
646C42—53no—
647C42—151no—
648C42—153no—
649C42—156no—
650C42—156no—
651C42—153no—
652C42C2×D3×D513yes—
653C3×C5#342811yescharacteristic, complemented, Hall
654C22×C3—56no—
655C22×C3—103no—
656C22×C3—103no—
657C22×C3C24×D511yescharacteristic
658C2×D3—23no—
659C2×D3—23no—
660C2×D3—52no—
661C2×D3—101no—
662C2×D3—101no—
663C2×D3—2012no—
664C2×D3C22×C4×D516yes—
665C3×C4—21no—
666C3×C4—23no—
667C3×C4—52no—
668C3×C4—101no—
669C3×C4—103no—
670C3×C4C22×C4×D516yes—
671Dic3—21no—
672Dic3—23no—
673Dic3—56no—
674Dic3—101no—
675Dic3—103no—
676Dic3C22×C4×D512yes—
677C2×C5—66no—
678C2×C5C23×C4×D311yescharacteristic
679C2×C5#596611yescharacteristic
680C2×C5#596811yescharacteristic
681D5—26no—
682D5—62no—
683C23—33no—
684C23—53no—
685C23—1512no—
686C23—151no—
687C23—603no—
688C23—603no—
689Q8—1512no—
690Q8C4×D3×D514yes—
691D4—312no—
692D4—512no—
693D4—1524no—
694C2×C4—31no—
695C2×C4—312no—
696C2×C4—31no—
697C2×C4—33no—
698C2×C4—51no—
699C2×C4—512no—
700C2×C4—51no—
701C2×C4—53no—
702C2×C4—123no—
703C2×C4—123no—
704C2×C4—154no—
705C2×C4—1512no—
706C2×C4—1512no—
707C2×C4—153no—
708C2×C4—1512no—
709C2×C4—151no—
710C2×C4—153no—
711C2×C4—206no—
712C2×C4—606no—
713C2×C4—603no—
714C2×C4—603no—
715C2×C4C22×D3×D513yes—
716C2×C4C22×D3×D511yescharacteristic
717C2×C4C22×D3×D513yes—
718C2×C3—106no—
719C2×C3C23×C4×D511yescharacteristic
720C2×C3#6628311yescharacteristic
721C2×C3#6628311yescharacteristic
722D3—26no—
723D3—102no—
724C5#8588511yescharacteristic, complemented, Sylow
725C22—36no—
726C22—56no—
727C22—63no—
728C22—63no—
729C22—103no—
730C22—103no—
731C22—152no—
732C22—301no—
733C22—301no—
734C22—6012no—
735C22C23×D3×D511yescharacteristic
736C4—23no—
737C4—21no—
738C4—32no—
739C4—52no—
740C4—61no—
741C4—63no—
742C4—103no—
743C4—101no—
744C4—156no—
745C4—301no—
746C4—303no—
747C4C2×C4×D3×D516yes—
748C3#1061773511yescharacteristic, complemented, Sylow
749C2—66no—
750C2—106no—
751C2—302no—
752C2C22×C4×D3×D511yescharacteristic
753C2#1175704911yescharacteristic
754C2#1175706111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC3×C4×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC2×#92034C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #11756331C2semidirect
3. C4×C5×#239C2semidirect
4. C3×#65908C2semidirect
5. #11755217C2semidirect
6. Dic5×#239C2semidirect
7. #11755124C2semidirect
8. #11753841C2semidirect
9. D5×#892C2semidirect
10. #11753671C2semidirect
11. #11753398C2semidirect
12. #11752729C2semidirect
13. D3×#4018C2semidirect
14. #11752669C2semidirect
15. C4×#6765C2semidirect
20. #92034C4semidirect
25. C3×C4×C5×Q8C22semidirect
26. Q8×Dic15C22semidirect
28. #91776C22semidirect
30. C4×Dic30C22semidirect
31. C5×Q8×Dic3C22semidirect
32. C5×#893C22semidirect
33. C5×#892C22semidirect
34. C4×C5×D12C22semidirect
35. C42×C5×D3C22semidirect
36. C3×Q8×Dic5C22semidirect
37. C3×#4039C22semidirect
38. C3×D5×C4⋊C4C22semidirect
39. C3×C4×D20C22semidirect
40. C3×#4018C22semidirect
44. #91442C22semidirect
45. #91441C22semidirect
46. #91440C22semidirect
47. C4×#1201C22semidirect
48. #91435C22semidirect
49. #91434C22semidirect
50. Dic3×D20C22semidirect
51. Dic5×D12C22semidirect
52. D5×C4⋊Dic3C22semidirect
55. #91400C22semidirect
56. D3×#683C22semidirect
57. D3×#683C22semidirect
58. C4×D3×Dic5C22semidirect
59. #91393C22semidirect
60. #91393C22semidirect
61. C4×D5×Dic3C22semidirect
63. #91357C22semidirect
65. #91340C22semidirect
66. #91338C22semidirect
67. #91333C22semidirect
73. #65908D3semidirect
86. Q8×D15C2×C4semidirect
89. C5×#239C2×C4semidirect
94. C3×#713C2×C4semidirect
105. #6777C2×C4semidirect
106. C4×D3×D5C2×C4semidirect
107. #6772C2×C4semidirect
108. #6765C2×C4semidirect
145. C4×#239D5semidirect
165. C4×C5×Q8C2×D3semidirect
171. Q8×Dic5C2×D3semidirect
183. #4039C2×D3semidirect
187. D5×C4⋊C4C2×D3semidirect
195. C4×D20C2×D3semidirect
203. #4018C2×D3semidirect
252. C3×C4×Q8C2×D5semidirect
258. Q8×Dic3C2×D5semidirect
268. #893C2×D5semidirect
275. #892C2×D5semidirect
287. C4×D12C2×D5semidirect
291. C42×D3C2×D5semidirect
305. #713C4×D3semidirect
398. #239C4×D5semidirect
496. C4×Q8D3×D5semidirect
653. C3×C5#3428semidirect
724. C5#85885semidirect
748. C3#10617735semidirect

Maximal subgroups

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

subgroupindex
C2×#920342
#117563312
C4×C5×#2392
C3×#659082
#117552172
Dic5×#2392
#117551242
#117538412
D5×#8922
#117536712
#117533982
#117527292
D3×#40182
#117526692
C4×#67652
#106177353
#858855