Finite Group Databasebeta

← #14479172

Subgroups — #14479172

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×D3×#713C211yesmaximal, characteristic
2#11756333C211yesmaximal, characteristic, complemented
3C5×#5572C211yesmaximal, characteristic, complemented
4C3×C4×#713C211yesmaximal, characteristic, complemented
5Dic3×#713C211yesmaximal, characteristic, complemented
6#11755149C211yesmaximal, characteristic, complemented
7#11755144C211yesmaximal, characteristic, complemented
8#11753839C213yesmaximal, complemented
9#11753835C213yesmaximal, complemented
10#11753403C213yesmaximal, complemented
11#11753401C213yesmaximal, complemented
12#11752727C213yesmaximal, complemented
13D5×#872C213yesmaximal, complemented
14C4×#6773C213yesmaximal, complemented
15#11752520C213yesmaximal, complemented
16#10617773—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C3×#713C2211yescharacteristic
20D3×#713C4116yescomplemented
21C2×D3×D20C2213yes—
22C2×C4×D3×D5C2213yes—
23C2×#6773C2213yes—
24C2×#6766C2213yes—
25C3×C4×C5×Q8C2211yescharacteristic, complemented
26Q8×Dic15C2211yescharacteristic, complemented
27#91782C2213yescomplemented
28C4⋊C4×D15C2213yescomplemented
29C4×D60C2213yescomplemented
30#91761C2213yescomplemented
31C5×Q8×Dic3C2211yescharacteristic, complemented
32C5×#892C2213yes—
33C5×#887C2213yescomplemented
34C5×#872C2213yes—
35C4×C5×Dic6C2213yescomplemented
36C3×Q8×Dic5C2211yescharacteristic, complemented
37C3×#4039C2213yescomplemented
38C3×#4038C2213yescomplemented
39C3×C4×D20C2213yescomplemented
40C3×C42×D5C2213yescomplemented
41#91473C2216yes—
42D5×(C2×D3)⋊C4C2213yes—
43D5×(C2×D3)⋊C4C2213yes—
44#91444C2216yescomplemented
45C4×#1202C2216yescomplemented
46#91437C2213yescomplemented
47#91434C2213yescomplemented
48#91428C2213yescomplemented
49Dic3×D20C2213yescomplemented
50#91418C2213yescomplemented
51#91402C2213yescomplemented
52#91402C2213yescomplemented
53C4×#1200C2216yescomplemented
54#91398C2211yescharacteristic
55#91398C2213yes—
56#91396C2216yescomplemented
57#91395C2216yescomplemented
58#91393C2216yescomplemented
59D5×Dic3⋊C4C2213yescomplemented
60D5×Dic3⋊C4C2213yescomplemented
61C4×D5×Dic3C2213yescomplemented
62#91386C2213yescomplemented
63#91371C2213yes—
64#91358C2213yescomplemented
65#91344C2213yescomplemented
66#91338C2213yes—
67Dic5×Dic6C2213yescomplemented
68#85834—51nomaximal, Hall
69C22×#713—31no—
70C5×#519—31no—
71#66146—31no—
72#65908—31no—
73#65908—33no—
74#65908—33no—
75#65908—31no—
76C4×#713—33no—
77C4×#713—33no—
78C4×#713—31no—
79C4×#713D311yescharacteristic, complemented
80#65855—33no—
81#65855—33no—
82D5×#117—33no—
83D5×#117—33no—
84C22×D3×D5C2313yes—
85C2×C3×C5×Q8C2311yescharacteristic
86#6821C2×C418yescomplemented
87C2×D60C2313yes—
88C2×C4×D15C2316yes—
89C2×C4×D15C2313yes—
90C5×D3×Q8C2×C418yescomplemented
91C2×C4×C5×D3C2313yes—
92C2×C5×Dic6C2313yes—
93C3×#713C2×C418yescomplemented
94C2×C3×D20C2313yes—
95C2×C3×C4×D5C2313yes—
96C2×C3×C4×D5C2313yes—
97C2×C3×C4×D5C2313yes—
98C2×#1202C2316yes—
99C2×#1200C2316yes—
100C2×#1200C2313yes—
101C2×D3×Dic5C2311yescharacteristic
102C2×D5×Dic3C2313yes—
103C2×D5×Dic3C2313yes—
104C2×D5×Dic3C2313yes—
105D3×D20C2×C4124yescomplemented
106C4×D3×D5C2×C4124yescomplemented
107#6773C2×C4124yescomplemented
108#6766C2×C4124yescomplemented
109C3×C5×C4⋊C4C2313yes—
110C3×C42×C5C2313yes—
111#6714C2313yes—
112#6714C2313yes—
113C4⋊Dic15C2313yes—
114#6712C2311yescharacteristic
115#6712C2313yes—
116C4×Dic15C2313yes—
117C5×(C2×D3)⋊C4C2311yescharacteristic
118C5×(C2×D3)⋊C4C2313yes—
119C5×C4⋊Dic3C2313yes—
120C5×Dic3⋊C4C2313yes—
121C5×Dic3⋊C4C2313yes—
122C4×C5×Dic3C2316yes—
123C4×C5×Dic3C2313yes—
124C3×#685C2316yes—
125C3×C4⋊Dic5C2313yes—
126C3×C4×Dic5C2313yes—
127C3×C4×Dic5C2311yescharacteristic
128C3×C4×Dic5C2313yes—
129Dic3⋊Dic5C2313yes—
130Dic3⋊Dic5C2313yes—
131#6669C2311yescharacteristic
132#6669C2313yes—
133#6667C2313yes—
134#6667C2313yes—
135(C2×D3)⋊Dic5C2311yescharacteristic
136(C2×D3)⋊Dic5C2313yes—
137#6665C2316yes—
138Dic3×Dic5C2316yes—
139Dic3×Dic5C2313yes—
140Dic3×Dic5C2311yescharacteristic
141C2×D3×#41—51no—
142C3×C4×#41—51no—
143Dic3×#41—51no—
144#5574—51no—
145#5574—51no—
146#5572—51no—
147#5572D511yescharacteristic, complemented
148#5546—53no—
149#5546—53no—
150#5545—53no—
151#5545—53no—
152#5522—53no—
153D3×#117—53no—
154C4×#235—53no—
155C2×#872—53no—
156C22×C5×Q8—31no—
157C2×#713—31no—
158C2×#713—316no—
159C2×#713—33no—
160C2×#713—33no—
161C2×#713C2×D311yescharacteristic
162C22×D20—33no—
163C22×C4×D5—33no—
164C4×C5×Q8—31no—
165C4×C5×Q8—33no—
166C4×C5×Q8—33no—
167C4×C5×Q8C2×D311yescharacteristic, complemented
168C5×#117—33no—
169C5×#117—33no—
170Q8×Dic5—31no—
171Q8×Dic5—33no—
172Q8×Dic5—33no—
173Q8×Dic5C2×D311yescharacteristic, complemented
174#4072—33no—
175#4072—33no—
176#4039—33no—
177#4039—36no—
178#4039—33no—
179#4039—36no—
180#4039—33no—
181#4039C2×D313yescomplemented
182#4038—33no—
183#4038—33no—
184#4038—33no—
185#4038C2×D313yescomplemented
186D5×C4⋊C4—33no—
187D5×C4⋊C4—33no—
188D5×C4⋊C4—33no—
189D5×C4⋊C4—33no—
190D5×C22⋊C4—33no—
191D5×C22⋊C4—33no—
192D5×C22⋊C4—36no—
193#4023—33no—
194#4023—31no—
195C4×D20—33no—
196C4×D20—36no—
197C4×D20—33no—
198C4×D20—36no—
199C4×D20—33no—
200C4×D20C2×D313yescomplemented
201#4018—33no—
202#4018—36no—
203#4018—33no—
204C42×D5—33no—
205C42×D5—36no—
206C42×D5C2×D313yescomplemented
207#3428—151noSylow
208C22×D15C2413yes—
209C22×C5×D3C2411yescharacteristic
210C22×C3×D5C2413yes—
211C2×D3×D5—43no—
212C2×D3×D5—43no—
213C2×D3×D5C22×C4112yes—
214C3×C5×Q8C22×C414yes—
215C2×C3×C4×C5C2413yes—
216C2×C3×C4×C5C2411yescharacteristic
217C2×C3×C4×C5C2413yes—
218C2×Dic15C2413yes—
219C2×Dic15C2411yescharacteristic
220C2×Dic15C2411yescharacteristic
221D60C22×C4112yes—
222C4×D15—46no—
223C4×D15C22×C4112yes—
224C2×C5×Dic3C2413yes—
225C2×C5×Dic3C2411yescharacteristic
226C2×C5×Dic3C2413yes—
227C4×C5×D3C22×C4112yes—
228C5×Dic6C22×C4112yes—
229C2×C3×Dic5C2413yes—
230C2×C3×Dic5C2411yescharacteristic
231C2×C3×Dic5C2411yescharacteristic
232C3×D20C22×C4112yes—
233C3×C4×D5—43no—
234C3×C4×D5—43no—
235C3×C4×D5C22×C4112yes—
236#1202C22×C4124yes—
237#1200—46no—
238#1200C22×C4112yes—
239D3×Dic5C22×C414yes—
240D5×Dic3—43no—
241D5×Dic3—43no—
242D5×Dic3C22×C4112yes—
243C2×C3×#41—51no—
244D3×#41—516no—
245C2×#239—51no—
246C2×D3×Q8C2×D511yescharacteristic
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×C42—53no—
257Q8×Dic3—51no—
258Q8×Dic3C2×D511yescharacteristic, complemented
259D4×Dic3—53no—
260D4×Dic3—53no—
261C4×#67—56no—
262C4×#67—56no—
263C2×(C2×D3)⋊C4—53no—
264C2×(C2×D3)⋊C4—53no—
265#926—53no—
266C2×Dic3⋊C4—53no—
267C2×Dic3⋊C4—53no—
268C2×C4×Dic3—53no—
269#893—53no—
270#893—53no—
271#892—53no—
272#892C2×D513yes—
273D3×C4⋊C4—53no—
274D3×C4⋊C4—53no—
275#887—53no—
276#887C2×D513yescomplemented
277#67⋊C4—56no—
278#67⋊C4—56no—
279D3×C22⋊C4—56no—
280#877—56no—
281C4×D12—53no—
282C4×D12—53no—
283#872—53no—
284#872—53no—
285#872—51no—
286#872—53no—
287#872—53no—
288#872—53no—
289#872—53no—
290#872C2×D513yes—
291C42×D3—56no—
292C4×Dic6—53no—
293C4×Dic6C2×D513yescomplemented
294C23×D5—33no—
295C2×C5×Q8—38no—
296C2×C5×Q8—33no—
297C2×C5×Q8C22×D311yescharacteristic
298C22×C4×C5—33no—
299C22×Dic5—31no—
300#713—38no—
301#713—324no—
302#713—324no—
303#713C4×D318yescomplemented
304C2×D20—36no—
305C2×D20—33no—
306C2×D20—324no—
307C2×D20C22×D313yes—
308C2×C4×D5—33no—
309C2×C4×D5—33no—
310C2×C4×D5—33no—
311C2×C4×D5—324no—
312C2×C4×D5—33no—
313C2×C4×D5—33no—
314C2×C4×D5—36no—
315C2×C4×D5—36no—
316C2×C4×D5C22×D313yes—
317C2×C4×D5C22×D313yes—
318C2×C4×D5C22×D313yes—
319C5×C4⋊C4—33no—
320C5×C4⋊C4—33no—
321C5×C4⋊C4—33no—
322C5×C4⋊C4C22×D313yes—
323C5×C22⋊C4—31no—
324C5×C22⋊C4—33no—
325C42×C5—36no—
326C42×C5—33no—
327C42×C5C22×D313yes—
328C22⋊Dic5—33no—
329C22⋊Dic5—31no—
330#685—36no—
331#685—33no—
332#685—33no—
333#685—33no—
334#685—33no—
335#685C22×D316yes—
336C4⋊Dic5—33no—
337C4⋊Dic5—33no—
338C4⋊Dic5—33no—
339C4⋊Dic5C22×D313yes—
340#683—31no—
341#683—33no—
342#683—33no—
343#683—31no—
344C4×Dic5—33no—
345C4×Dic5—33no—
346C4×Dic5—31no—
347C4×Dic5—36no—
348C4×Dic5C22×D313yes—
349C4×Dic5C22×D311yescharacteristic
350C4×Dic5C22×D313yes—
351C22×#41—151no—
352#520—153no—
353#520—153no—
354#520—151no—
355#520—151no—
356#519—31no—
357#519—151no—
358#518—153no—
359#518—153no—
360C4×#41—51no—
361C4×#41—153no—
362C4×#41—153no—
363C4×#41—151no—
364C2×#117—153no—
365C2×#117—153no—
366C22×C3×C5C2511yescharacteristic
367C2×D15—23no—
368C2×D15—23no—
369C2×D15C23×C416yes—
370C2×C5×D3—21no—
371C2×C5×D3—21no—
372C2×C5×D3C23×C412yes—
373C2×C3×D5—23no—
374C2×C3×D5—23no—
375C2×C3×D5C23×C416yes—
376D3×D5—412no—
377C3×C4×C5—21no—
378C3×C4×C5—23no—
379C3×C4×C5C23×C416yes—
380Dic15—21no—
381Dic15—23no—
382Dic15C23×C412yes—
383C3×Dic5—23no—
384C3×Dic5—21no—
385C3×Dic5C23×C412yes—
386C5×Dic3—21no—
387C5×Dic3—23no—
388C5×Dic3C23×C416yes—
389C23×D3—53no—
390C3×#41—58no—
391C2×C3×Q8C22×D511yescharacteristic
392C2×C3×D4—53no—
393C22×C3×C4—53no—
394C22×C3×C4—53no—
395C22×C3×C4—53no—
396C2×#67—56no—
397C22×Dic3—53no—
398C22×Dic3—53no—
399C22×Dic3—53no—
400#239—58no—
401D3×Q8C4×D518yescomplemented
402#237—524no—
403D3×D4—524no—
404#235—524no—
405C2×D12—53no—
406C2×C4×D3—51no—
407C2×C4×D3—53no—
408C2×C4×D3—53no—
409C2×C4×D3—524no—
410C2×C4×D3—56no—
411C2×C4×D3—56no—
412C2×C4×D3C22×D513yes—
413C2×Dic6C22×D513yes—
414C3×C4⋊C4—53no—
415C3×C4⋊C4C22×D513yes—
416C3×C22⋊C4—56no—
417C3×C42—53no—
418C3×C42—53no—
419C3×C42—51no—
420C3×C42C22×D513yes—
421#217—56no—
422(C2×D3)⋊C4—51no—
423(C2×D3)⋊C4—53no—
424(C2×D3)⋊C4—53no—
425(C2×D3)⋊C4—53no—
426(C2×D3)⋊C4—53no—
427(C2×D3)⋊C4—53no—
428(C2×D3)⋊C4C22×D511yescharacteristic
429(C2×D3)⋊C4C22×D513yes—
430C4⋊Dic3—53no—
431C4⋊Dic3C22×D513yes—
432Dic3⋊C4—51no—
433Dic3⋊C4—53no—
434Dic3⋊C4—51no—
435Dic3⋊C4—53no—
436Dic3⋊C4—53no—
437Dic3⋊C4—53no—
438Dic3⋊C4C22×D513yes—
439Dic3⋊C4C22×D513yes—
440C4×Dic3—53no—
441C4×Dic3—56no—
442C4×Dic3—53no—
443C4×Dic3—51no—
444C4×Dic3C22×D516yes—
445C4×Dic3C22×D513yes—
446C23×C5—31no—
447C22×D5—33no—
448C22×D5—312no—
449C22×D5—123no—
450C22×D5—123no—
451C22×D5C23×D313yes—
452C5×Q8—312no—
453C5×Q8C2×C4×D314yes—
454C2×C4×C5—33no—
455C2×C4×C5—312no—
456C2×C4×C5—33no—
457C2×C4×C5—31no—
458C2×C4×C5C23×D311yescharacteristic
459C2×C4×C5C23×D313yes—
460C2×C4×C5C23×D313yes—
461C2×Dic5—31no—
462C2×Dic5—34no—
463C2×Dic5—31no—
464C2×Dic5—33no—
465C2×Dic5C23×D313yes—
466C2×Dic5C23×D311yescharacteristic
467C2×Dic5C23×D311yescharacteristic
468D20—324no—
469D20—312no—
470D20C2×C4×D3112yes—
471C4×D5—312no—
472C4×D5—312no—
473C4×D5—312no—
474C4×D5—43no—
475C4×D5—43no—
476C4×D5—126no—
477C4×D5—126no—
478C4×D5—123no—
479C4×D5—123no—
480C4×D5C2×C4×D3112yes—
481C2×#41—51no—
482C2×#41—153no—
483C2×#41—153no—
484C2×#41—1516no—
485C2×#41—151no—
486C22×Q8—31no—
487C22×D4—153no—
488C23×C4—153no—
489C4×Q8—31no—
490C4×Q8—33no—
491C4×Q8—33no—
492C4×Q8—51no—
493C4×Q8—153no—
494C4×Q8—153no—
495C4×Q8—151no—
496C4×Q8D3×D511yescharacteristic, complemented
497C4×D4—53no—
498C4×D4—53no—
499C4×D4—156no—
500C4×D4—153no—
501C4×D4—156no—
502C4×D4—153no—
503C4×D4—153no—
504C4×D4—156no—
505C4×D4—156no—
506C4×D4—153no—
507C4×D4—153no—
508C4×D4—153no—
509#117—33no—
510#117—33no—
511#117—53no—
512#117—153no—
513#117—156no—
514#117—151no—
515#117—153no—
516#117—153no—
517#117—153no—
518#117—153no—
519#117—153no—
520#117—153no—
521#117—153no—
522C2×C4⋊C4—153no—
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—53no—
530C2×C42—156no—
531C2×C42—153no—
532C2×C3×C5C24×C411yescharacteristic
533C2×C3×C5#58511yescharacteristic
534C2×C3×C5#58511yescharacteristic
535D15—26no—
536C3×D5—26no—
537C5×D3—22no—
538C23×C3—53no—
539C22×D3—53no—
540C22×D3—512no—
541C22×D3—203no—
542C22×D3—203no—
543C22×D3C23×D511yescharacteristic
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—203no—
551C2×C3×C4—203no—
552C2×C3×C4C23×D513yes—
553C2×C3×C4C23×D511yescharacteristic
554C2×C3×C4C23×D513yes—
555#67—524no—
556C2×Dic3—51no—
557C2×Dic3—512no—
558C2×Dic3—51no—
559C2×Dic3—53no—
560C2×Dic3—203no—
561C2×Dic3—203no—
562C2×Dic3C23×D511yescharacteristic
563C2×Dic3C23×D513yes—
564C2×Dic3C23×D513yes—
565D12—512no—
566C4×D3—54no—
567C4×D3—512no—
568C4×D3—512no—
569C4×D3—206no—
570C4×D3—206no—
571C4×D3C2×C4×D5112yes—
572Dic6C2×C4×D5112yes—
573C22×C5—32no—
574C22×C5—61no—
575C22×C5—61no—
576C22×C5C24×D311yescharacteristic
577C2×D5—23no—
578C2×D5—23no—
579C2×D5—36no—
580C2×D5—63no—
581C2×D5—63no—
582C2×D5—1212no—
583C2×D5C22×C4×D316yes—
584C4×C5—21no—
585C4×C5—23no—
586C4×C5—36no—
587C4×C5—61no—
588C4×C5—63no—
589C4×C5C22×C4×D316yes—
590Dic5—21no—
591Dic5—23no—
592Dic5—32no—
593Dic5—63no—
594Dic5—61no—
595Dic5C22×C4×D312yes—
596C24—153no—
597#41—58no—
598#41—1524no—
599#41—1524no—
600#41—158no—
601C2×Q8—38no—
602C2×Q8—33no—
603C2×Q8C2×D3×D511yescharacteristic
604C2×D4—53no—
605C2×D4—1524no—
606C2×D4—156no—
607C2×D4—153no—
608C22×C4—33no—
609C22×C4—53no—
610C22×C4—53no—
611C22×C4—53no—
612C22×C4—153no—
613C22×C4—1524no—
614C22×C4—156no—
615C22×C4—153no—
616C22×C4—153no—
617C22×C4—153no—
618C22×C4—151no—
619C22×C4—153no—
620C22×C4—156no—
621C4⋊C4—33no—
622C4⋊C4—33no—
623C4⋊C4—33no—
624C4⋊C4—53no—
625C4⋊C4—151no—
626C4⋊C4—153no—
627C4⋊C4—153no—
628C4⋊C4—153no—
629C4⋊C4—153no—
630C4⋊C4—151no—
631C4⋊C4—153no—
632C4⋊C4C2×D3×D513yes—
633C22⋊C4—33no—
634C22⋊C4—31no—
635C22⋊C4—56no—
636C22⋊C4—153no—
637C22⋊C4—153no—
638C22⋊C4—156no—
639C22⋊C4—151no—
640C22⋊C4—153no—
641C22⋊C4—153no—
642C22⋊C4—153no—
643C42—36no—
644C42—33no—
645C42—51no—
646C42—53no—
647C42—53no—
648C42—153no—
649C42—151no—
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—21no—
659C2×D3—21no—
660C2×D3—56no—
661C2×D3—103no—
662C2×D3—103no—
663C2×D3—2012no—
664C2×D3C22×C4×D512yes—
665C3×C4—23no—
666C3×C4—21no—
667C3×C4—52no—
668C3×C4—103no—
669C3×C4—101no—
670C3×C4C22×C4×D516yes—
671Dic3—23no—
672Dic3—21no—
673Dic3—52no—
674Dic3—103no—
675Dic3—101no—
676Dic3C22×C4×D516yes—
677C2×C5—62no—
678C2×C5C23×C4×D311yescharacteristic
679C2×C5#596411yescharacteristic
680C2×C5#596411yescharacteristic
681D5—26no—
682D5—66no—
683C23—31no—
684C23—53no—
685C23—1512no—
686C23—153no—
687C23—603no—
688C23—603no—
689Q8—312no—
690Q8C4×D3×D514yes—
691D4—512no—
692D4—1524no—
693D4—1512no—
694C2×C4—33no—
695C2×C4—312no—
696C2×C4—31no—
697C2×C4—33no—
698C2×C4—51no—
699C2×C4—512no—
700C2×C4—51no—
701C2×C4—53no—
702C2×C4—1512no—
703C2×C4—1512no—
704C2×C4—154no—
705C2×C4—151no—
706C2×C4—1512no—
707C2×C4—153no—
708C2×C4—151no—
709C2×C4—203no—
710C2×C4—203no—
711C2×C4—606no—
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#6628711yescharacteristic
721C2×C3#6628711yescharacteristic
722D3—22no—
723D3—106no—
724C5#8583411yescharacteristic, complemented, Sylow
725C22—32no—
726C22—56no—
727C22—61no—
728C22—61no—
729C22—103no—
730C22—103no—
731C22—156no—
732C22—303no—
733C22—303no—
734C22—6012no—
735C22C23×D3×D511yescharacteristic
736C4—23no—
737C4—21no—
738C4—36no—
739C4—52no—
740C4—61no—
741C4—63no—
742C4—101no—
743C4—103no—
744C4—152no—
745C4—303no—
746C4—301no—
747C4C2×C4×D3×D516yes—
748C3#1061777311yescharacteristic, complemented, Sylow
749C2—62no—
750C2—106no—
751C2—306no—
752C2C22×C4×D3×D511yescharacteristic
753C2#1175704811yescharacteristic
754C2#1175706011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC3×C4×C5×Q8C22
socle, cosocleC22×C3×C5C25
prime radicalC2×D3×#713C2
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. #11756333C2semidirect
3. C5×#5572C2semidirect
4. C3×C4×#713C2semidirect
5. Dic3×#713C2semidirect
6. #11755149C2semidirect
7. #11755144C2semidirect
8. #11753839C2semidirect
9. #11753835C2semidirect
10. #11753403C2semidirect
11. #11753401C2semidirect
12. #11752727C2semidirect
13. D5×#872C2semidirect
14. C4×#6773C2semidirect
15. #11752520C2semidirect
20. D3×#713C4semidirect
25. C3×C4×C5×Q8C22semidirect
26. Q8×Dic15C22semidirect
27. #91782C22semidirect
28. C4⋊C4×D15C22semidirect
29. C4×D60C22semidirect
30. #91761C22semidirect
31. C5×Q8×Dic3C22semidirect
33. C5×#887C22semidirect
35. C4×C5×Dic6C22semidirect
36. C3×Q8×Dic5C22semidirect
37. C3×#4039C22semidirect
38. C3×#4038C22semidirect
39. C3×C4×D20C22semidirect
40. C3×C42×D5C22semidirect
44. #91444C22semidirect
45. C4×#1202C22semidirect
46. #91437C22semidirect
47. #91434C22semidirect
48. #91428C22semidirect
49. Dic3×D20C22semidirect
50. #91418C22semidirect
51. #91402C22semidirect
52. #91402C22semidirect
53. C4×#1200C22semidirect
56. #91396C22semidirect
57. #91395C22semidirect
58. #91393C22semidirect
59. D5×Dic3⋊C4C22semidirect
60. D5×Dic3⋊C4C22semidirect
61. C4×D5×Dic3C22semidirect
62. #91386C22semidirect
64. #91358C22semidirect
65. #91344C22semidirect
67. Dic5×Dic6C22semidirect
79. C4×#713D3semidirect
86. #6821C2×C4semidirect
90. C5×D3×Q8C2×C4semidirect
93. C3×#713C2×C4semidirect
105. D3×D20C2×C4semidirect
106. C4×D3×D5C2×C4semidirect
107. #6773C2×C4semidirect
108. #6766C2×C4semidirect
147. #5572D5semidirect
167. C4×C5×Q8C2×D3semidirect
173. Q8×Dic5C2×D3semidirect
181. #4039C2×D3semidirect
185. #4038C2×D3semidirect
200. C4×D20C2×D3semidirect
206. C42×D5C2×D3semidirect
252. C3×C4×Q8C2×D5semidirect
258. Q8×Dic3C2×D5semidirect
276. #887C2×D5semidirect
293. C4×Dic6C2×D5semidirect
303. #713C4×D3semidirect
401. D3×Q8C4×D5semidirect
496. C4×Q8D3×D5semidirect
653. C3×C5#3428semidirect
724. C5#85834semidirect
748. C3#10617773semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7132
#117563332
C5×#55722
C3×C4×#7132
Dic3×#7132
#117551492
#117551442
#117538392
#117538352
#117534032
#117534012
#117527272
D5×#8722
C4×#67732
#117525202
#106177733
#858345