Finite Group Databasebeta

← #14427810

Subgroups — #14427810

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4062C211yesmaximal, characteristic, complemented
2#11755270C211yesmaximal, characteristic, complemented
3#11755060C211yesmaximal, characteristic, complemented
4C2×D3×C8×D5C211yesmaximal, characteristic, complemented
5#11751272C211yesmaximal, characteristic, complemented
6C5×#5171C211yesmaximal, characteristic, complemented
7#11749299C211yesmaximal, characteristic, complemented
8#11749296C211yesmaximal, characteristic, complemented
9#11749207C211yesmaximal, characteristic, complemented
10#11749031C211yesmaximal, characteristic, complemented
11#11749028C211yesmaximal, characteristic, complemented
12#11748961C211yesmaximal, characteristic, complemented
13#11747930C211yesmaximal, characteristic, complemented
14#11747912C211yesmaximal, characteristic, complemented
15#11747671C211yesmaximal, characteristic, complemented
16#10612387—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C2×C3×C5×SD16C2211yescharacteristic, complemented
21#91835C2211yescharacteristic
22#91827C2211yescharacteristic
23C2×C8×D15C2211yescharacteristic
24C5×#946C2211yescharacteristic
25C5×#938C2211yescharacteristic
26C2×C5×D3×C8C2211yescharacteristic
27C2×C3×#689C2211yescharacteristic, complemented
28C2×C3×#686C2211yescharacteristic, complemented
29C3×#4062—24no—
30C2×C3×#677C2211yescharacteristic, complemented
31C2×C3×C8×D5C2211yescharacteristic
32#91577—21no—
33#91552—21no—
34Dic5×#67—21no—
35#91548—21no—
36#91474—21no—
37#91465C2211yescharacteristic
38#91456C2211yescharacteristic
39#91444—21no—
40#91440—21no—
41#91407—21no—
42#91390C2211yescharacteristic
43#91369C2211yescharacteristic
44#91358C2211yescharacteristic
45#91358C2211yescharacteristic
46C2×#6648C2211yescharacteristic
47C2×D3×#168C2211yescharacteristic
48C2×D5×C3⋊C8C2211yescharacteristic
49D3×C8×D5—24no—
50#91119C2211yescharacteristic, complemented
51#91116C2211yescharacteristic, complemented
52#91101C2211yescharacteristic, complemented
53C5×#835C2211yescharacteristic, complemented
54C5×#832C2211yescharacteristic, complemented
55C5×#817C2211yescharacteristic, complemented
56#90988C2211yescharacteristic, complemented
57#90988C2211yescharacteristic, complemented
58#90971C2211yescharacteristic, complemented
59#90970C2211yescharacteristic, complemented
60#90965C2211yescharacteristic, complemented
61#90964C2211yescharacteristic, complemented
62#83914—51nomaximal, Hall
63C2×#4062D311yescharacteristic, complemented
64C22×C8×D5—31no—
65#65961—31no—
66#65940—31no—
67C5×#465—31no—
68#65460—31no—
69#65403—31no—
70#65340—31no—
71#65327—31no—
72#65153—31no—
73#65149—31no—
74#65102—31no—
75#65093—31no—
76#65064—31no—
77#65061—31no—
78C22×D3×D5D411yescharacteristic
79C2×C3×C5×Q8C2311yescharacteristic
80C2×C3×C5×D4C2311yescharacteristic
81C2×#1220—21no—
82C2×C4×D15C2311yescharacteristic
83C2×C5×#67—21no—
84C2×C4×C5×D3C2311yescharacteristic
85C2×C3×C22⋊D5—21no—
86C22×C3×Dic5—21no—
87C3×#713—22no—
88C3×#713—22no—
89C3×#711—22no—
90C3×#711—22no—
91C2×C3×D20—21no—
92C2×C3×D20C2311yescharacteristic
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5C2311yescharacteristic
95C2×C3×Dic10C2311yescharacteristic
96C2×#1202—21no—
97C2×#1201—21no—
98C2×#1200D411yescharacteristic
99C2×D3×Dic5D411yescharacteristic
100C2×D5×Dic3D411yescharacteristic
101C4×D3×D5—22no—
102C4×D3×D5—22no—
103C3×C5×SD16—22no—
104C2×C3×C5×C8C2311yescharacteristic
105#6719—21no—
106#6714—21no—
107C4⋊Dic15C2311yescharacteristic
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110C2×C3⋊#168C2311yescharacteristic
111C8×D15—22no—
112C5×#217—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×C4⋊Dic3C2311yescharacteristic
115C5×C4⋊Dic3C2311yescharacteristic
116C5×Dic3⋊C4—21no—
117C2×C5×C3⋊C8C2311yescharacteristic
118C5×D3×C8—22no—
119C3×#689—22no—
120C3×#686—22no—
121C2×C3×#168C2311yescharacteristic
122C3×#677—22no—
123C3×C8×D5D414yescomplemented
124Dic3⋊Dic5—21no—
125#6669—21no—
126#6667—21no—
127(C2×D3)⋊Dic5—21no—
128#6665—21no—
129#6665—21no—
130#6665—21no—
131#6665—21no—
132Dic3×Dic5—21no—
133Dic3×Dic5—21no—
134#6648—22no—
135D3×#168—22no—
136D5×C3⋊C8—22no—
137C2×C3×#135—51no—
138#5828—51no—
139#5828—51no—
140C22×D3×C8—51no—
141#5233—51no—
142#5233—51no—
143#5188—51no—
144#5188—51no—
145#5171—51no—
146#5171—51no—
147#5171—51no—
148#5171D511yescharacteristic, complemented
149#5157—51no—
150#5157—51no—
151#5106—51no—
152C2×#713C2×D311yescharacteristic
153C2×#711C2×D311yescharacteristic
154C22×C4×D5—31no—
155C2×C5×SD16C2×D311yescharacteristic, complemented
156C22×C5×C8—31no—
157C5×C22⋊Q8—31no—
158C5×#121—31no—
159#4092—31no—
160C2×#689C2×D311yescharacteristic, complemented
161#4084—31no—
162#4083—61no—
163D4×Dic5—61no—
164C2×#686C2×D311yescharacteristic, complemented
165#4076—31no—
166#4070—31no—
167C22×#168—31no—
168#4062—24no—
169C2×#677C2×D311yescharacteristic, complemented
170C2×C8×D5—31no—
171C2×C8×D5—31no—
172C2×C8×D5—31no—
173C2×C8×D5—64no—
174C2×C8×D5C2×D311yescharacteristic
175#4043—31no—
176#4041—31no—
177#4040—61no—
178#4039—61no—
179#4038—31no—
180#4038—31no—
181#4029—61no—
182#4028—61no—
183#4027—61no—
184#4027—61no—
185C5×#106—31no—
186C5×#103—31no—
187C5×#102—31no—
188#3967—31no—
189#3964—31no—
190#3953—31no—
191#3949—31no—
192#3948—31no—
193#3942—31no—
194#3941—31no—
195#3939—31no—
196#3939—31no—
197#3050—151noSylow
198C23×C3×C5—21no—
199C22×D15C2×D411yescharacteristic
200C22×C5×D3C2×D411yescharacteristic
201C22×C3×D5—21no—
202C22×C3×D5C2×D411yescharacteristic
203C2×D3×D5—22no—
204C2×D3×D5—22no—
205C2×D3×D5—22no—
206C3×C5×Q8—21no—
207C3×C5×Q8—21no—
208C3×C5×D4—21no—
209C3×C5×D4—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5C2411yescharacteristic
212#1220—42no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15C2×D411yescharacteristic
216C4×D15—21no—
217C4×D15—21no—
218C5×#67—42no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3C2×D411yescharacteristic
222C4×C5×D3—21no—
223C4×C5×D3—21no—
224C3×C22⋊D5—42no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—42no—
227C2×C3×Dic5C2×D411yescharacteristic
228C3×D20—21no—
229C3×D20—21no—
230C3×D20—42no—
231C3×C4×D5—42no—
232C3×C4×D5C2×D412yes—
233C3×C4×D5#4112yes—
234C3×Dic10—21no—
235C3×Dic10—21no—
236#1202—42no—
237#1201—42no—
238#1200—22no—
239D3×Dic5—22no—
240D5×Dic3—22no—
241C3×C5×C8C2×D412yes—
242C3⋊#168—21no—
243C3×#168C2×D412yes—
244C5×C3⋊C8—21no—
245C2×C3×#41—51no—
246C2×C3×#41—51no—
247C22×C4×D3—51no—
248C3×#135—104no—
249C2×C3×Q16—51no—
250C2×C3×SD16—51no—
251C2×C3×SD16C2×D511yescharacteristic, complemented
252C2×C3×D8—51no—
253C22×C3×C8—51no—
254#946—51no—
255#946—51no—
256#946—51no—
257#946C2×D511yescharacteristic
258#938—51no—
259#938—51no—
260#938—51no—
261#938C2×D511yescharacteristic
262#937—101no—
263#937—101no—
264#935—101no—
265#935—101no—
266C4×#67—101no—
267C4×#67—101no—
268C4×#67—101no—
269C4×#67—101no—
270#926—51no—
271#926—51no—
272C22×C3⋊C8—51no—
273C2×D3×C8—51no—
274C2×D3×C8—51no—
275C2×D3×C8—51no—
276C2×D3×C8—104no—
277C2×D3×C8C2×D511yescharacteristic
278#835—51no—
279#835—51no—
280#835—51no—
281#835C2×D511yescharacteristic, complemented
282#832—51no—
283#832—51no—
284#832—51no—
285#832C2×D511yescharacteristic, complemented
286#818—51no—
287#818—51no—
288#817—51no—
289#817C2×D511yescharacteristic, complemented
290C23×D5—31no—
291C2×C5×Q8C22×D311yescharacteristic
292C2×C5×D4—61no—
293C2×C5×D4C22×D311yescharacteristic
294C22×C4×C5—31no—
295C2×C22⋊D5—21no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C22×Dic5—21no—
299C22×Dic5—31no—
300#713—22no—
301#713—22no—
302#711—22no—
303#711—22no—
304C2×D20—21no—
305C2×D20—61no—
306C2×D20C22×D311yescharacteristic
307C2×C4×D5—21no—
308C2×C4×D5—31no—
309C2×C4×D5—31no—
310C2×C4×D5—31no—
311C2×C4×D5—62no—
312C2×C4×D5—62no—
313C2×C4×D5C22×D311yescharacteristic
314C2×Dic10C22×D311yescharacteristic
315C5×SD16—22no—
316C2×C5×C8—31no—
317C2×C5×C8—62no—
318C2×C5×C8C22×D311yescharacteristic
319C5×C4⋊C4—31no—
320C5×C4⋊C4—31no—
321C5×C4⋊C4—61no—
322C5×C22⋊C4—61no—
323C5×C22⋊C4—61no—
324C22⋊Dic5—61no—
325C22⋊Dic5—61no—
326#689—22no—
327#686—22no—
328#685—61no—
329#685—61no—
330#685—61no—
331#685—61no—
332#685—61no—
333#685—61no—
334C4⋊Dic5—31no—
335C4⋊Dic5—31no—
336C4⋊Dic5—61no—
337#683—61no—
338#683—61no—
339C4×Dic5—61no—
340C4×Dic5—61no—
341C2×#168—31no—
342C2×#168—62no—
343C2×#168C22×D311yescharacteristic
344#677—22no—
345C8×D5—62no—
346C8×D5—62no—
347C8×D5—62no—
348C8×D5#6714yescomplemented
349C2×#135—51no—
350C23×C8—151no—
351#525—151no—
352#525—151no—
353#467—151no—
354#467—151no—
355#466—151no—
356#466—151no—
357#465—31no—
358#465—151no—
359#465—151no—
360#465—151no—
361#427—151no—
362#416—151no—
363#416—151no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5C22×D411yescharacteristic
368C2×D15—21no—
369C2×D15—21no—
370C2×D15#13512yescomplemented
371C2×C5×D3—21no—
372C2×C5×D3—21no—
373C2×C5×D3#13512yescomplemented
374C2×C3×D5—21no—
375C2×C3×D5—21no—
376C2×C3×D5—41no—
377C2×C3×D5—41no—
378C2×C3×D5—41no—
379C2×C3×D5#12112yes—
380D3×D5—28no—
381C3×C4×C5—41no—
382C3×C4×C5C22×D411yescharacteristic
383C3×C4×C5C2×#4111yescharacteristic
384Dic15—21no—
385Dic15—41no—
386Dic15—41no—
387C3×Dic5—41no—
388C3×Dic5#12112yes—
389C5×Dic3—21no—
390C5×Dic3—41no—
391C5×Dic3—41no—
392C23×D3—51no—
393C3×#41—102no—
394C3×#41—102no—
395C3×#41—102no—
396C3×#41—102no—
397C2×C3×Q8—51no—
398C2×C3×Q8C22×D511yescharacteristic
399C2×C3×D4—51no—
400C2×C3×D4—101no—
401C2×C3×D4—101no—
402C2×C3×D4C22×D511yescharacteristic
403C22×C3×C4—51no—
404C22×C3×C4—101no—
405C22×C3×C4—101no—
406C2×#67—21no—
407C2×#67—101no—
408C2×#67—101no—
409C2×#67—101no—
410C22×Dic3—51no—
411C2×C4×D3—51no—
412C2×C4×D3—51no—
413C2×C4×D3—51no—
414C2×C4×D3—102no—
415C2×C4×D3—102no—
416C2×C4×D3C22×D511yescharacteristic
417C3×Q16—102no—
418C3×SD16—22no—
419C3×SD16—102no—
420C3×D8—102no—
421C2×C3×C8—51no—
422C2×C3×C8—54no—
423C2×C3×C8C22×D511yescharacteristic
424#217—21no—
425#217—101no—
426#217—101no—
427#217—101no—
428#217—101no—
429#217—101no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—101no—
432(C2×D3)⋊C4—101no—
433(C2×D3)⋊C4—101no—
434C4⋊Dic3—51no—
435C4⋊Dic3—51no—
436C4⋊Dic3C22×D511yescharacteristic
437C4⋊Dic3C22×D511yescharacteristic
438Dic3⋊C4—21no—
439Dic3⋊C4—101no—
440Dic3⋊C4—101no—
441Dic3⋊C4—101no—
442C4×Dic3—101no—
443C4×Dic3—101no—
444C2×C3⋊C8—51no—
445C2×C3⋊C8—102no—
446C2×C3⋊C8C22×D511yescharacteristic
447D3×C8—22no—
448D3×C8—102no—
449D3×C8—102no—
450D3×C8—102no—
451C23×C5—21no—
452C23×C5—31no—
453C22×D5—21no—
454C22×D5—31no—
455C22×D5—62no—
456C22×D5—62no—
457C22×D5—62no—
458C22×D5D3×D411yescharacteristic
459C5×Q8—21no—
460C5×Q8—21no—
461C5×D4—21no—
462C5×D4—21no—
463C5×D4—122no—
464C2×C4×C5—21no—
465C2×C4×C5—31no—
466C2×C4×C5—61no—
467C2×C4×C5—61no—
468C2×C4×C5—61no—
469C2×C4×C5—61no—
470C2×C4×C5C23×D311yescharacteristic
471C22⋊D5—42no—
472C22⋊D5—122no—
473C22⋊D5—122no—
474C2×Dic5—21no—
475C2×Dic5—31no—
476C2×Dic5—42no—
477C2×Dic5—62no—
478C2×Dic5—61no—
479C2×Dic5—61no—
480C2×Dic5D3×D411yescharacteristic
481D20—21no—
482D20—21no—
483D20—42no—
484D20—122no—
485C4×D5—42no—
486C4×D5—62no—
487C4×D5—61no—
488C4×D5—61no—
489C4×D5—62no—
490C4×D5#23712yes—
491C4×D5C2×#6712yes—
492Dic10—21no—
493Dic10—21no—
494C5×C8—61no—
495C5×C8C2×#6712yes—
496#168—61no—
497#168C2×#6712yes—
498C2×#41—51no—
499C2×#41—51no—
500C23×C4—151no—
501#135—104no—
502C2×Q16—51no—
503C2×SD16—51no—
504C2×SD16D3×D511yescharacteristic, complemented
505C2×D8—51no—
506C22×C8—31no—
507C22×C8—51no—
508C22×C8—151no—
509C22×C8—151no—
510C22×C8—151no—
511C22×C8—151no—
512C22×C8—304no—
513#123—301no—
514#123—301no—
515C22⋊Q8—31no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518C22⋊Q8—151no—
519#121—31no—
520#121—151no—
521#121—151no—
522#121—151no—
523#120—301no—
524#120—301no—
525C4×D4—301no—
526C4×D4—301no—
527C4×D4—301no—
528C4×D4—301no—
529#117—151no—
530#117—151no—
531#107—151no—
532#107—151no—
533#106—31no—
534#106—151no—
535#103—31no—
536#103—151no—
537#103—151no—
538#103—151no—
539#102—31no—
540#102—151no—
541#102—151no—
542#102—151no—
543C2×C3×C5—81no—
544C2×C3×C5C2×#12111yescharacteristic
545C2×C3×C5C2×#13511yescharacteristic
546C2×C3×C5C2×#13511yescharacteristic
547D15—22no—
548C3×D5—22no—
549C3×D5—81no—
550C5×D3—22no—
551C23×C3—21no—
552C23×C3—51no—
553C23×C3—101no—
554C22×D3—51no—
555C22×D3—102no—
556C22×D3—102no—
557C22×D3—102no—
558C22×D3D4×D511yescharacteristic
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—101no—
562C3×Q8—101no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—101no—
566C3×D4—101no—
567C3×D4—202no—
568C3×D4—202no—
569C2×C3×C4—21no—
570C2×C3×C4—51no—
571C2×C3×C4—52no—
572C2×C3×C4—52no—
573C2×C3×C4—101no—
574C2×C3×C4—202no—
575C2×C3×C4—202no—
576C2×C3×C4C23×D511yescharacteristic
577#67—42no—
578#67—202no—
579#67—202no—
580#67—202no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—51no—
584C2×Dic3—102no—
585C2×Dic3—101no—
586C2×Dic3—101no—
587C2×Dic3D4×D511yescharacteristic
588C4×D3—21no—
589C4×D3—21no—
590C4×D3—102no—
591C4×D3—102no—
592C4×D3—101no—
593C4×D3—101no—
594C3×C8—52no—
595C3×C8D4×D512yes—
596C3⋊C8—21no—
597C3⋊C8—101no—
598C22×C5—32no—
599C22×C5—41no—
600C22×C5—41no—
601C22×C5—41no—
602C22×C5—61no—
603C22×C5—61no—
604C22×C5C2×D3×D411yescharacteristic
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—32no—
608C2×D5—41no—
609C2×D5—41no—
610C2×D5—41no—
611C2×D5—68no—
612C2×D5—61no—
613C2×D5—61no—
614C2×D5#93812yes—
615C4×C5—41no—
616C4×C5—61no—
617C4×C5—121no—
618C4×C5—121no—
619C4×C5C2×#23711yescharacteristic
620C4×C5C22×#6711yescharacteristic
621Dic5—41no—
622Dic5—61no—
623Dic5—121no—
624Dic5—121no—
625Dic5#93812yes—
626C24—151no—
627#41—102no—
628#41—102no—
629#41—102no—
630#41—102no—
631C2×Q8—51no—
632C2×Q8C2×D3×D511yescharacteristic
633C2×D4—51no—
634C2×D4—61no—
635C2×D4—101no—
636C2×D4—101no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4C2×D3×D511yescharacteristic
641C22×C4—31no—
642C22×C4—51no—
643C22×C4—101no—
644C22×C4—101no—
645C22×C4—151no—
646C22×C4—151no—
647C22×C4—151no—
648C22×C4—151no—
649C22×C4—302no—
650C22×C4—302no—
651Q16—102no—
652SD16—22no—
653SD16—102no—
654D8—102no—
655C2×C8—31no—
656C2×C8—51no—
657C2×C8—54no—
658C2×C8—62no—
659C2×C8—151no—
660C2×C8—302no—
661C2×C8—302no—
662C2×C8—302no—
663C2×C8—302no—
664C2×C8C2×D3×D511yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—61no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—301no—
671C4⋊C4—301no—
672C4⋊C4—301no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—301no—
676C22⋊C4—301no—
677C22⋊C4—301no—
678C22⋊C4—301no—
679C22⋊C4—301no—
680C22⋊C4—301no—
681C22⋊C4—301no—
682C22⋊C4—301no—
683C42—301no—
684C42—301no—
685C3×C5#305011yescharacteristic, complemented, Hall
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—52no—
690C22×C3—101no—
691C22×C3—101no—
692C22×C3—201no—
693C22×C3—201no—
694C22×C3—201no—
695C22×C3C2×D4×D511yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—52no—
699C2×D3—108no—
700C2×D3—101no—
701C2×D3—101no—
702C2×D3#406212yescomplemented
703C3×C4—41no—
704C3×C4—52no—
705C3×C4—201no—
706C3×C4C2×D4×D511yescharacteristic
707C3×C4D5×#4111yescharacteristic
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—101no—
712Dic3—201no—
713Dic3—201no—
714C2×C5—62no—
715C2×C5—81no—
716C2×C5D3×#13511yescharacteristic
717C2×C5D3×#13511yescharacteristic
718C2×C5C2×#93811yescharacteristic
719D5—22no—
720D5—62no—
721D5—81no—
722C23—21no—
723C23—31no—
724C23—51no—
725C23—101no—
726C23—151no—
727C23—302no—
728C23—302no—
729C23—302no—
730Q8—21no—
731Q8—21no—
732Q8—101no—
733Q8—101no—
734D4—21no—
735D4—21no—
736D4—101no—
737D4—101no—
738D4—122no—
739D4—202no—
740D4—202no—
741D4—602no—
742D4—602no—
743D4—602no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—51no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—101no—
754C2×C4—151no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4—302no—
758C2×C4—302no—
759C2×C4—302no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4C22×D3×D511yescharacteristic
765C8—52no—
766C8—61no—
767C8—301no—
768C8D5×#6712yes—
769C2×C3—81no—
770C2×C3—102no—
771C2×C3—401no—
772C2×C3D5×#12111yescharacteristic
773C2×C3C2×#406211yescharacteristic
774C2×C3D5×#13511yescharacteristic
775D3—22no—
776D3—102no—
777C5#8391411yescharacteristic, complemented, Sylow
778C22—32no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—52no—
783C22—61no—
784C22—61no—
785C22—101no—
786C22—101no—
787C22—152no—
788C22—201no—
789C22—201no—
790C22—201no—
791C22—308no—
792C22—301no—
793C22—301no—
794C22D3×D4×D511yescharacteristic
795C4—41no—
796C4—52no—
797C4—61no—
798C4—121no—
799C4—121no—
800C4—201no—
801C4—301no—
802C4—601no—
803C4—601no—
804C4D5×#23711yescharacteristic
805C4C2×D5×#6711yescharacteristic
806C3#1061238711yescharacteristic, complemented, Sylow
807C2—62no—
808C2—81no—
809C2—102no—
810C2—302no—
811C2—401no—
812C2D3×#406211yescharacteristic
813C2#1175407911yescharacteristic
814C2D5×#93811yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
hypercenterC2×SD16D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4062C2semidirect
2. #11755270C2semidirect
3. #11755060C2semidirect
4. C2×D3×C8×D5C2semidirect
5. #11751272C2semidirect
6. C5×#5171C2semidirect
7. #11749299C2semidirect
8. #11749296C2semidirect
9. #11749207C2semidirect
10. #11749031C2semidirect
11. #11749028C2semidirect
12. #11748961C2semidirect
13. #11747930C2semidirect
14. #11747912C2semidirect
15. #11747671C2semidirect
20. C2×C3×C5×SD16C22semidirect
27. C2×C3×#689C22semidirect
28. C2×C3×#686C22semidirect
30. C2×C3×#677C22semidirect
50. #91119C22semidirect
51. #91116C22semidirect
52. #91101C22semidirect
53. C5×#835C22semidirect
54. C5×#832C22semidirect
55. C5×#817C22semidirect
56. #90988C22semidirect
57. #90988C22semidirect
58. #90971C22semidirect
59. #90970C22semidirect
60. #90965C22semidirect
61. #90964C22semidirect
63. C2×#4062D3semidirect
123. C3×C8×D5D4semidirect
148. #5171D5semidirect
155. C2×C5×SD16C2×D3semidirect
160. C2×#689C2×D3semidirect
164. C2×#686C2×D3semidirect
169. C2×#677C2×D3semidirect
251. C2×C3×SD16C2×D5semidirect
281. #835C2×D5semidirect
285. #832C2×D5semidirect
289. #817C2×D5semidirect
348. C8×D5#67semidirect
370. C2×D15#135semidirect
373. C2×C5×D3#135semidirect
504. C2×SD16D3×D5semidirect
685. C3×C5#3050semidirect
702. C2×D3#4062semidirect
777. C5#83914semidirect
806. C3#10612387semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40622
#117552702
#117550602
C2×D3×C8×D52
#117512722
C5×#51712
#117492992
#117492962
#117492072
#117490312
#117490282
#117489612
#117479302
#117479122
#117476712
#106123873
#839145