Finite Group Databasebeta

← #14426284

Subgroups — #14426284

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91839C211yesmaximal, characteristic, complemented
2C5×#5832C211yesmaximal, characteristic, complemented
3#11754436C211yesmaximal, characteristic, complemented
4C2×#91303C211yesmaximal, characteristic, complemented
5C3×#65522C211yesmaximal, characteristic, complemented
6#11749259C211yesmaximal, characteristic, complemented
7#11749258C211yesmaximal, characteristic, complemented
8#11749236C211yesmaximal, characteristic, complemented
9#11749233C211yesmaximal, characteristic, complemented
10#11749013C211yesmaximal, characteristic, complemented
11#11749012C211yesmaximal, characteristic, complemented
12#11748990C211yesmaximal, characteristic, complemented
13#11748987C211yesmaximal, characteristic, complemented
14C2×Dic3⋊#168C211yesmaximal, characteristic, complemented
15#11748382C211yesmaximal, characteristic, complemented
16#10615027—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×#6817C2211yescharacteristic
19C2×C5×#235C2211yescharacteristic
20#91839—24no—
21C2×#6718C2211yescharacteristic
22C2×#6717C2211yescharacteristic
23C2×#6716C2211yescharacteristic
24C2×#6715C2211yescharacteristic
25C22×C3⋊#168C2211yescharacteristic
26C5×#947C2211yescharacteristic
27C5×#944C2211yescharacteristic
28C5×#940C2211yescharacteristic
29C5×#939—21no—
30C5×#939—21no—
31C5×#936C2211yescharacteristic
32C4×C5×#67—21no—
33C4×C5×#67—21no—
34C2×C4×C5×Dic3C2211yescharacteristic
35C3×#4072C2211yescharacteristic
36C22×C3×#168C2211yescharacteristic
37#91556—21no—
38#91556—21no—
39#91428C2211yescharacteristic
40#91428C2211yescharacteristic
41C4×#1200—21no—
42#91386—21no—
43#91340C2211yescharacteristic
44#91340C2211yescharacteristic
45C2×#6663C2211yescharacteristic
46C2×#6660C2211yescharacteristic
47C2×#6659C2211yescharacteristic
48#91303—24no—
49C2×#6654C2211yescharacteristic
50C3×#3967C2211yescharacteristic
51C3×#3967C2211yescharacteristic
52C3×#3964C2211yescharacteristic
53C3×#3964C2211yescharacteristic
54Dic3⋊#168C2211yescharacteristic
55Dic3⋊#168C2211yescharacteristic
56Dic3⋊#168C2211yescharacteristic
57Dic3⋊#168C2211yescharacteristic
58#90972C2211yescharacteristic
59#90972C2211yescharacteristic
60#90966C2211yescharacteristic
61#90966C2211yescharacteristic
62#78861—51nomaximal, Hall
63C5×#532—31no—
64C2×#4096—31no—
65C2×#4096—31no—
66C4×#709—31no—
67#65522—31no—
68#65522D311yescharacteristic, complemented
69#65379—31no—
70#65372—31no—
71#65364—31no—
72#65361—31no—
73#65346—31no—
74#65346—31no—
75#65343—31no—
76#65343—31no—
77C2×C4⋊#168—31no—
78C3×C5×#41—22no—
79C3×C5×#41—22no—
80C2×C3×C5×Q8C2311yescharacteristic
81C2×C3×C5×D4—21no—
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5C2311yescharacteristic
85C2×#1220—21no—
86#6817—22no—
87#6817D414yescomplemented
88C2×D60C2311yescharacteristic
89C2×C4×D15—21no—
90C2×Dic30C2311yescharacteristic
91C2×C5×#67—21no—
92C2×C5×#67—21no—
93C2×C5×#67—21no—
94C22×C5×Dic3D411yescharacteristic
95C22×C5×Dic3D411yescharacteristic
96C5×#235—22no—
97C5×#235—22no—
98C2×C5×D12C2311yescharacteristic
99C2×C4×C5×D3—21no—
100C2×C5×Dic6C2311yescharacteristic
101C2×#1200—21no—
102C2×#1200—21no—
103#6718—22no—
104#6717—22no—
105#6716—22no—
106#6715—22no—
107C2×C3⋊#168—22no—
108C2×C3⋊#168C2311yescharacteristic
109C2×C3⋊#168C2311yescharacteristic
110C5×#217—21no—
111C5×#217—21no—
112C5×(C2×D3)⋊C4—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×Dic3⋊C4—21no—
115C5×Dic3⋊C4—21no—
116C4×C5×Dic3D411yescharacteristic
117C4×C5×Dic3D411yescharacteristic
118C4×C5×Dic3C2311yescharacteristic
119C4×C5×Dic3C2311yescharacteristic
120C3×C22⋊Dic5—21no—
121C3×C4⋊Dic5C2311yescharacteristic
122C3×C4⋊Dic5C2311yescharacteristic
123C3×C4×Dic5—21no—
124C2×C3×#168—22no—
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127#6669—21no—
128#6669—21no—
129#6667—21no—
130#6667—21no—
131Dic3×Dic5—21no—
132Dic3×Dic5—21no—
133#6663—22no—
134#6660—22no—
135#6659—22no—
136#6654—22no—
137#5832D511yescharacteristic, complemented
138C2×#950—51no—
139C2×#904—51no—
140#5522—51no—
141C3×#416—51no—
142C2×Dic3⋊C8—51no—
143#5002—51no—
144#4819—51no—
145#4818—51no—
146#4798—51no—
147#4795—51no—
148#4787—51no—
149#4786—51no—
150#4767—51no—
151#4762—51no—
152C2×C5×#41—31no—
153C2×C5×#41C2×D311yescharacteristic
154C2×#709—31no—
155C5×C4⋊Q8—31no—
156C5×#127—31no—
157C5×#124—31no—
158C5×#124—31no—
159C5×#121—61no—
160C5×#121—61no—
161C4×C5×D4—61no—
162C4×C5×D4—61no—
163C2×C42×C5—31no—
164#4096—64no—
165#4096—64no—
166C2×#689—31no—
167C2×#689—31no—
168C2×#688—31no—
169C2×#688—31no—
170C2×#687—31no—
171C2×#687—31no—
172C2×#686—31no—
173C2×#686—31no—
174C4×C22⋊D5—61no—
175C4×C22⋊D5—61no—
176#4072C2×D311yescharacteristic
177C22×#168—31no—
178C22×#168C2×D311yescharacteristic
179C4×D20—31no—
180C4×D20—31no—
181#4018—61no—
182C42×D5—61no—
183C4×Dic10—31no—
184C4×Dic10—31no—
185#3967—31no—
186#3967—31no—
187#3967C2×D311yescharacteristic
188#3967C2×D311yescharacteristic
189#3964—31no—
190#3964—31no—
191#3964C2×D311yescharacteristic
192#3964C2×D311yescharacteristic
193C4⋊#168—31no—
194C4⋊#168—31no—
195C4⋊#168—31no—
196C4⋊#168—31no—
197#3035—151noSylow
198C23×C3×C5—21no—
199C23×C3×C5C2×D411yescharacteristic
200C22×D15—21no—
201C22×C5×D3—21no—
202C3×C5×Q8—21no—
203C3×C5×Q8—21no—
204C3×C5×D4—21no—
205C3×C5×D4—21no—
206C3×C5×D4—42no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—42no—
209C2×C3×C4×C5C2×D411yescharacteristic
210C2×C3×C4×C5C2×D412yes—
211C2×C3×C4×C5#4112yes—
212C2×C3×C4×C5C2411yescharacteristic
213#1220—24no—
214C2×Dic15—21no—
215D60—21no—
216D60C2×D412yes—
217C4×D15—24no—
218Dic30—21no—
219Dic30C2×D412yes—
220C5×#67—42no—
221C5×#67—42no—
222C5×#67—42no—
223C2×C5×Dic3—22no—
224C2×C5×Dic3—21no—
225C2×C5×Dic3—41no—
226C2×C5×Dic3C2×D411yescharacteristic
227C2×C5×Dic3C2×D411yescharacteristic
228C2×C5×Dic3C2×D411yescharacteristic
229C2×C5×Dic3C2×D411yescharacteristic
230C5×D12—21no—
231C5×D12—21no—
232C4×C5×D3—42no—
233C5×Dic6—21no—
234C5×Dic6—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237#1200—42no—
238#1200—42no—
239C3⋊#168—21no—
240C3⋊#168—21no—
241C3×#168—21no—
242C3×#168—21no—
243C2×C3×#41C2×D511yescharacteristic
244C2×#235—51no—
245C2×#235C2×D511yescharacteristic
246C22×C3×C8—51no—
247C3×#117—51no—
248#950—104no—
249#947C2×D511yescharacteristic
250#944C2×D511yescharacteristic
251C2×#216—51no—
252C2×#215—51no—
253#940C2×D511yescharacteristic
254#939—21no—
255#939—21no—
256#936C2×D511yescharacteristic
257C2×#214—51no—
258C2×#213—51no—
259C4×#67—21no—
260C4×#67—21no—
261C2×C4×Dic3C2×D511yescharacteristic
262C22×C3⋊C8—51no—
263C2×Dic12—51no—
264#904—104no—
265C2×D24—51no—
266C2×#204—51no—
267C2×#204—51no—
268#893—51no—
269#893—51no—
270#887—51no—
271#887—51no—
272#67⋊C4—101no—
273#67⋊C4—101no—
274#872—101no—
275C42×D3—101no—
276C3×#103—51no—
277C3×#103—51no—
278C3×#102—51no—
279C3×#102—51no—
280Dic3⋊C8—51no—
281Dic3⋊C8—51no—
282Dic3⋊C8—51no—
283Dic3⋊C8—51no—
284#810—51no—
285#810—51no—
286#809—51no—
287#809—51no—
288C5×#41—22no—
289C5×#41—22no—
290C5×#41—62no—
291C5×#41—62no—
292C2×C5×Q8—31no—
293C2×C5×Q8C22×D311yescharacteristic
294C2×C5×D4—21no—
295C2×C5×D4—31no—
296C2×C5×D4—61no—
297C2×C5×D4—61no—
298C2×C5×D4—61no—
299C2×C5×D4C22×D311yescharacteristic
300C22×C4×C5—21no—
301C22×C4×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—61no—
304C22×C4×C5C22×D311yescharacteristic
305C2×C22⋊D5—61no—
306#709—34no—
307#709—62no—
308C2×D20—31no—
309C2×C4×D5—61no—
310C2×C4×D5—61no—
311C2×C4×D5—61no—
312C2×Dic10—31no—
313C5×C4⋊C4—61no—
314C5×C4⋊C4—61no—
315C5×C22⋊C4—61no—
316C5×C22⋊C4—61no—
317C5×C22⋊C4—61no—
318C5×C22⋊C4—61no—
319C42×C5—31no—
320C42×C5—31no—
321C42×C5—31no—
322C42×C5—31no—
323C22⋊Dic5—21no—
324#689—62no—
325#689—62no—
326#688—62no—
327#688—62no—
328#687—62no—
329#687—62no—
330#686—62no—
331#686—62no—
332#685—61no—
333#685—61no—
334C4⋊Dic5C22×D311yescharacteristic
335C4⋊Dic5C22×D311yescharacteristic
336#683—61no—
337#683—61no—
338C4×Dic5—21no—
339C4×Dic5—61no—
340C4×Dic5—61no—
341C2×#168—22no—
342C2×#168—31no—
343C2×#168—31no—
344C2×#168—62no—
345C2×#168C22×D311yescharacteristic
346C2×#168C22×D311yescharacteristic
347C2×#135—151no—
348C2×#135—151no—
349#532—31no—
350C4×#41—151no—
351#464—151no—
352#464—151no—
353#463—151no—
354#463—151no—
355#462—151no—
356#461—151no—
357#460—151no—
358#459—151no—
359C2×C4⋊C8—151no—
360#416—51no—
361#416—151no—
362C22×C3×C5—21no—
363C22×C3×C5—21no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5#12112yes—
368C22×C3×C5C22×D411yescharacteristic
369C2×D15—22no—
370C2×D15—41no—
371C2×D15—41no—
372C2×C5×D3—41no—
373C2×C5×D3—41no—
374C2×C5×D3—41no—
375C3×C4×C5—41no—
376C3×C4×C5#12112yes—
377C3×C4×C5C22×D411yescharacteristic
378C3×C4×C5C2×#4111yescharacteristic
379Dic15—22no—
380C3×Dic5—41no—
381C3×Dic5—41no—
382C5×Dic3—21no—
383C5×Dic3—21no—
384C5×Dic3—21no—
385C5×Dic3—41no—
386C5×Dic3#13512yescomplemented
387C3×#41—22no—
388C3×#41—22no—
389C2×C3×Q8C22×D511yescharacteristic
390C2×C3×D4—21no—
391C2×C3×D4C22×D511yescharacteristic
392C22×C3×C4—21no—
393C22×C3×C4C22×D511yescharacteristic
394C2×#67—21no—
395C2×#67—21no—
396C2×#67—21no—
397C2×#67—101no—
398C22×Dic3C22⋊D511yescharacteristic
399C22×Dic3C22⋊D511yescharacteristic
400#235—22no—
401#235—22no—
402#235—54no—
403#235—102no—
404C2×D12—51no—
405C2×D12C22×D511yescharacteristic
406C2×C4×D3—21no—
407C2×C4×D3—101no—
408C2×C4×D3—101no—
409C2×C4×D3—101no—
410C2×Dic6—51no—
411C2×Dic6C22×D511yescharacteristic
412C2×C3×C8—51no—
413C2×C3×C8—51no—
414C2×C3×C8—102no—
415C3×C4⋊C4—51no—
416C3×C4⋊C4—51no—
417C3×C22⋊C4—101no—
418C3×C42—101no—
419#217—21no—
420#217—21no—
421#216—102no—
422#215—102no—
423#214—102no—
424#213—102no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—101no—
428(C2×D3)⋊C4—101no—
429Dic3⋊C4—21no—
430Dic3⋊C4—21no—
431Dic3⋊C4—101no—
432Dic3⋊C4—101no—
433C4×Dic3—101no—
434C4×Dic3—101no—
435C4×Dic3C22⋊D511yescharacteristic
436C4×Dic3C22⋊D511yescharacteristic
437C4×Dic3C22×D511yescharacteristic
438C4×Dic3C22×D511yescharacteristic
439C2×C3⋊C8—51no—
440C2×C3⋊C8—51no—
441C2×C3⋊C8—102no—
442Dic12—102no—
443D24—102no—
444#204—102no—
445#204—102no—
446C23×C5—21no—
447C23×C5—61no—
448C23×C5D3×D411yescharacteristic
449C22×D5—61no—
450C5×Q8—21no—
451C5×Q8—21no—
452C5×Q8—61no—
453C5×Q8—61no—
454C5×D4—21no—
455C5×D4—21no—
456C5×D4—42no—
457C5×D4—61no—
458C5×D4—61no—
459C5×D4—122no—
460C5×D4—122no—
461C5×D4—122no—
462C2×C4×C5—21no—
463C2×C4×C5—31no—
464C2×C4×C5—31no—
465C2×C4×C5—31no—
466C2×C4×C5—31no—
467C2×C4×C5—42no—
468C2×C4×C5—62no—
469C2×C4×C5—61no—
470C2×C4×C5—121no—
471C2×C4×C5—122no—
472C2×C4×C5#23512yes—
473C2×C4×C5D3×D411yescharacteristic
474C2×C4×C5D3×D412yes—
475C2×C4×C5C23×D311yescharacteristic
476C22⋊D5—64no—
477C2×Dic5—21no—
478C2×Dic5—21no—
479C2×Dic5—61no—
480D20—32no—
481D20—61no—
482C4×D5—64no—
483C4×D5—122no—
484C4×D5—122no—
485Dic10—32no—
486Dic10—61no—
487#168—21no—
488#168—21no—
489#168—61no—
490#168—61no—
491C2×#41—31no—
492C2×#41—151no—
493C2×#41D3×D511yescharacteristic
494#135—304no—
495#135—304no—
496C2×Q16—151no—
497C2×Q16—151no—
498C2×SD16—151no—
499C2×SD16—151no—
500C2×SD16—151no—
501C2×SD16—151no—
502C2×D8—151no—
503C2×D8—151no—
504C22×C8—51no—
505C22×C8—151no—
506C4⋊Q8—31no—
507#127—31no—
508#124—31no—
509#124—31no—
510#121—61no—
511#121—61no—
512C4×Q8—151no—
513C4×Q8—151no—
514C4×D4—61no—
515C4×D4—61no—
516C4×D4—151no—
517C4×D4—151no—
518C4×D4—301no—
519C4×D4—301no—
520#117—51no—
521#117—301no—
522C2×C42—31no—
523C2×C42—301no—
524C4⋊C8—151no—
525C4⋊C8—151no—
526C4⋊C8—151no—
527C4⋊C8—151no—
528#103—51no—
529#103—51no—
530#103—151no—
531#103—151no—
532#102—51no—
533#102—51no—
534#102—151no—
535#102—151no—
536C2×C3×C5—22no—
537C2×C3×C5—81no—
538C2×C3×C5C2×#12111yescharacteristic
539C2×C3×C5C2×#13511yescharacteristic
540C2×C3×C5#57511yescharacteristic
541D15—42no—
542C5×D3—81no—
543C23×C3—21no—
544C23×C3C2×C22⋊D511yescharacteristic
545C22×D3—21no—
546C22×D3—101no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—42no—
552C2×C3×C4—21no—
553C2×C3×C4—42no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4D4×D512yes—
557C2×C3×C4#71112yes—
558C2×C3×C4C2×C22⋊D511yescharacteristic
559C2×C3×C4C23×D511yescharacteristic
560#67—42no—
561#67—42no—
562#67—42no—
563#67—104no—
564C2×Dic3—22no—
565C2×Dic3—21no—
566C2×Dic3—41no—
567C2×Dic3—101no—
568C2×Dic3C2×C22⋊D511yescharacteristic
569C2×Dic3C2×C22⋊D511yescharacteristic
570C2×Dic3C2×C22⋊D511yescharacteristic
571C2×Dic3C2×C22⋊D511yescharacteristic
572D12—21no—
573D12—21no—
574D12—52no—
575D12—101no—
576C4×D3—42no—
577C4×D3—104no—
578C4×D3—202no—
579C4×D3—202no—
580Dic6—21no—
581Dic6—21no—
582Dic6—52no—
583Dic6—101no—
584C3×C8—101no—
585C3×C8—101no—
586C3⋊C8—101no—
587C3⋊C8—101no—
588C22×C5—21no—
589C22×C5—21no—
590C22×C5—41no—
591C22×C5—41no—
592C22×C5—41no—
593C22×C5—121no—
594C22×C5—121no—
595C22×C5—121no—
596C22×C5#88412yes—
597C22×C5C2×D3×D411yescharacteristic
598C2×D5—62no—
599C2×D5—121no—
600C2×D5—121no—
601C4×C5—32no—
602C4×C5—41no—
603C4×C5—61no—
604C4×C5—61no—
605C4×C5—61no—
606C4×C5—121no—
607C4×C5#88412yes—
608C4×C5C2×#23511yescharacteristic
609C4×C5C2×D3×D411yescharacteristic
610Dic5—41no—
611Dic5—41no—
612Dic5—62no—
613#41—22no—
614#41—22no—
615#41—62no—
616#41—62no—
617#41—154no—
618#41—302no—
619C2×Q8—31no—
620C2×Q8—151no—
621C2×Q8C2×D3×D511yescharacteristic
622C2×D4—21no—
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—151no—
628C2×D4—301no—
629C2×D4C2×D3×D511yescharacteristic
630C22×C4—21no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—301no—
635C22×C4—301no—
636C22×C4—301no—
637C22×C4C2×D3×D511yescharacteristic
638Q16—302no—
639Q16—302no—
640SD16—302no—
641SD16—302no—
642SD16—302no—
643SD16—302no—
644D8—302no—
645D8—302no—
646C2×C8—51no—
647C2×C8—51no—
648C2×C8—102no—
649C2×C8—151no—
650C2×C8—151no—
651C2×C8—302no—
652C4⋊C4—51no—
653C4⋊C4—51no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4—301no—
657C4⋊C4—301no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—101no—
663C22⋊C4—301no—
664C22⋊C4—301no—
665C42—31no—
666C42—31no—
667C42—31no—
668C42—31no—
669C42—101no—
670C42—301no—
671C42—301no—
672C3×C5#303511yescharacteristic, complemented, Hall
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3#408412yes—
679C22×C3C22×C22⋊D511yescharacteristic
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—102no—
684C2×D3—201no—
685C2×D3—201no—
686C3×C4—41no—
687C3×C4—201no—
688C3×C4—201no—
689C3×C4#408412yes—
690C3×C4C2×D4×D511yescharacteristic
691C3×C4C2×#71111yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—102no—
697Dic3#409612yescomplemented
698C2×C5—22no—
699C2×C5—81no—
700C2×C5—241no—
701C2×C5C2×#88411yescharacteristic
702C2×C5D3×#13511yescharacteristic
703C2×C5#576811yescharacteristic
704D5—122no—
705C23—21no—
706C23—61no—
707C23—301no—
708C23D3×C22⋊D511yescharacteristic
709Q8—21no—
710Q8—21no—
711Q8—61no—
712Q8—61no—
713Q8—152no—
714Q8—301no—
715D4—21no—
716D4—21no—
717D4—42no—
718D4—61no—
719D4—61no—
720D4—122no—
721D4—122no—
722D4—122no—
723D4—152no—
724D4—304no—
725D4—301no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—42no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—101no—
735C2×C4—101no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—301no—
739C2×C4—304no—
740C2×C4—602no—
741C2×C4—602no—
742C2×C4#678212yes—
743C2×C4D3×C22⋊D511yescharacteristic
744C2×C4#679012yes—
745C2×C4C22×D3×D511yescharacteristic
746C8—101no—
747C8—101no—
748C8—301no—
749C8—301no—
750C2×C3—22no—
751C2×C3—81no—
752C2×C3C2×#408411yescharacteristic
753C2×C3C2×#409611yescharacteristic
754C2×C3#6615611yescharacteristic
755D3—81no—
756D3—202no—
757C5#7886111yescharacteristic, complemented, Sylow
758C22—21no—
759C22—21no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—302no—
767C22—601no—
768C22—601no—
769C22#9155712yes—
770C22C2×D3×C22⋊D511yescharacteristic
771C4—32no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—201no—
778C4—201no—
779C4—302no—
780C4#9155712yes—
781C4C2×#678211yescharacteristic
782C4C2×#679011yescharacteristic
783C3#1061502711yescharacteristic, complemented, Sylow
784C2—22no—
785C2—81no—
786C2—241no—
787C2—602no—
788C2D3×#409611yescharacteristic
789C2#1175532211yescharacteristic
790C2C2×#9155711yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3035
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91839C2semidirect
2. C5×#5832C2semidirect
3. #11754436C2semidirect
4. C2×#91303C2semidirect
5. C3×#65522C2semidirect
6. #11749259C2semidirect
7. #11749258C2semidirect
8. #11749236C2semidirect
9. #11749233C2semidirect
10. #11749013C2semidirect
11. #11749012C2semidirect
12. #11748990C2semidirect
13. #11748987C2semidirect
14. C2×Dic3⋊#168C2semidirect
15. #11748382C2semidirect
68. #65522D3semidirect
87. #6817D4semidirect
137. #5832D5semidirect
386. C5×Dic3#135semidirect
672. C3×C5#3035semidirect
697. Dic3#4096semidirect
757. C5#78861semidirect
783. C3#10615027semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C5×#58322
#117544362
C2×#913032
C3×#655222
#117492592
#117492582
#117492362
#117492332
#117490132
#117490122
#117489902
#117489872
C2×Dic3⋊#1682
#117483822
#106150273
#788615