Finite Group Databasebeta

← #14427822

Subgroups — #14427822

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
1C22×C3×C8×D5C211yesmaximal, characteristic, complemented
2#11754527C211yesmaximal, characteristic, complemented
3#11754526C211yesmaximal, characteristic, complemented
4C2×#91269C211yesmaximal, characteristic, complemented
5#11751215C211yesmaximal, characteristic, complemented
6C5×#5114C211yesmaximal, characteristic, complemented
7#11748557C211yesmaximal, characteristic, complemented
8#11748514C211yesmaximal, characteristic, complemented
9#11748135C211yesmaximal, characteristic, complemented
10#11747939C211yesmaximal, characteristic, complemented
11#11747897C211yesmaximal, characteristic, complemented
12#11747896C211yesmaximal, characteristic, complemented
13#11747893C211yesmaximal, characteristic, complemented
14#11747671C211yesmaximal, characteristic, complemented
15#11747642C211yesmaximal, characteristic, complemented
16#10612387—31nomaximal, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C2×#6773C2211yescharacteristic
19C2×#6772C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic
21#91819C2211yescharacteristic
22#91813C2211yescharacteristic
23C2×#6706C2211yescharacteristic, complemented
24C5×#930C2211yescharacteristic
25C5×#924C2211yescharacteristic
26C2×C5×#204C2211yescharacteristic, complemented
27C22×C3×#168C2211yescharacteristic
28C2×C3×C8×D5—24no—
29C2×C3×C8×D5C2211yescharacteristic
30C2×C3×C8×D5C2211yescharacteristic
31C2×C3×C8×D5C2211yescharacteristic
32C2×C3×C8×D5C2211yescharacteristic
33#91564—21no—
34#91563—21no—
35#91552—21no—
36Dic5×#67—21no—
37#91450C2211yescharacteristic
38#91449C2211yescharacteristic
39#91447—21no—
40#91444—21no—
41#91440—21no—
42#91360C2211yescharacteristic
43#91359C2211yescharacteristic
44#91358C2211yescharacteristic
45#91358C2211yescharacteristic
46#91348—21no—
47C2×#6663C2211yescharacteristic, complemented
48C2×#6654C2211yescharacteristic, complemented
49#91269—24no—
50#91105C2211yescharacteristic, complemented
51#91101C2211yescharacteristic, complemented
52#91100C2211yescharacteristic, complemented
53C5×#821C2211yescharacteristic, complemented
54C5×#817C2211yescharacteristic, complemented
55C5×#816C2211yescharacteristic, complemented
56#90988C2211yescharacteristic, complemented
57#90988C2211yescharacteristic, complemented
58#90975C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60#90969C2211yescharacteristic, complemented
61#90967C2211yescharacteristic, complemented
62#83742—51nomaximal, Hall
63C2×#4062—31no—
64C22×C8×D5D311yescharacteristic, complemented
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—
78C23×C3×D5D411yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×D60C2311yescharacteristic
82C2×Dic30C2311yescharacteristic
83C2×C5×#67—21no—
84C2×C5×D12C2311yescharacteristic
85C2×C5×Dic6C2311yescharacteristic
86C22×C3×Dic5D411yescharacteristic
87C2×C3×C4×D5—22no—
88C2×C3×C4×D5—22no—
89C2×C3×C4×D5D411yescharacteristic
90C2×C3×C4×D5D411yescharacteristic
91C2×C3×C4×D5C2311yescharacteristic
92C2×C3×C4×D5C2311yescharacteristic
93C2×#1202—21no—
94C2×#1202—21no—
95C2×#1201—21no—
96C2×#1201—21no—
97C2×#1200—21no—
98C2×D3×Dic5—21no—
99#6773—22no—
100#6773—22no—
101#6772—22no—
102#6772—22no—
103C2×C3×C5×C8—22no—
104C2×C3×C5×C8C2311yescharacteristic
105C2×C3×C5×C8C2311yescharacteristic
106#6719—21no—
107#6714—21no—
108C4⋊Dic15C2311yescharacteristic
109C4⋊Dic15C2311yescharacteristic
110#6712—21no—
111#6706—22no—
112C5×#217—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×C4⋊Dic3C2311yescharacteristic
115C5×C4⋊Dic3C2311yescharacteristic
116C5×Dic3⋊C4—21no—
117C5×#204—22no—
118C2×C3×#168—22no—
119C2×C3×#168C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C3×C8×D5—22no—
122C3×C8×D5—22no—
123C3×C8×D5—22no—
124C3×C8×D5D414yescomplemented
125Dic3⋊Dic5—21no—
126#6669—21no—
127#6667—21no—
128(C2×D3)⋊Dic5—21no—
129#6665—21no—
130#6665—21no—
131#6665—21no—
132#6665—21no—
133Dic3×Dic5—21no—
134Dic3×Dic5—21no—
135#6663—22no—
136#6654—22no—
137C23×C3×C8—51no—
138#5791—51no—
139#5791—51no—
140C2×#904—51no—
141#5116—51no—
142#5116—51no—
143#5115—51no—
144#5115—51no—
145#5114—51no—
146#5114—51no—
147#5114—51no—
148#5114D511yescharacteristic, complemented
149#5113—51no—
150#5113—51no—
151#5106—51no—
152C2×#713—31no—
153C2×#711—31no—
154C22×C4×D5C2×D311yescharacteristic
155C2×C5×SD16—31no—
156C22×C5×C8C2×D311yescharacteristic
157C5×C22⋊Q8—31no—
158C5×#121—31no—
159#4092—31no—
160C2×#689—31no—
161#4084—31no—
162#4083—61no—
163D4×Dic5—61no—
164C2×#686—31no—
165#4076—31no—
166#4070—31no—
167C22×#168C2×D311yescharacteristic
168#4062—64no—
169C2×#677—31no—
170C2×C8×D5—24no—
171C2×C8×D5C2×D311yescharacteristic
172C2×C8×D5C2×D311yescharacteristic
173C2×C8×D5C2×D311yescharacteristic
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×C5C2×D411yescharacteristic
199C22×D15—21no—
200C22×C5×D3—21no—
201C22×C3×D5—22no—
202C22×C3×D5—22no—
203C22×C3×D5—22no—
204C22×C3×D5C2×D411yescharacteristic
205C22×C3×D5C2×D411yescharacteristic
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C2×D411yescharacteristic
209C2×C3×C4×C5C2411yescharacteristic
210#1220—42no—
211C2×Dic15—21no—
212C2×Dic15—21no—
213C2×Dic15—21no—
214D60—21no—
215D60—21no—
216Dic30—21no—
217Dic30—21no—
218C5×#67—42no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C5×D12—21no—
223C5×D12—21no—
224C5×Dic6—21no—
225C5×Dic6—21no—
226C2×C3×Dic5—22no—
227C2×C3×Dic5C2×D411yescharacteristic
228C2×C3×Dic5C2×D411yescharacteristic
229C3×C4×D5—22no—
230C3×C4×D5—21no—
231C3×C4×D5—21no—
232C3×C4×D5—22no—
233C3×C4×D5C2×D412yes—
234C3×C4×D5#4112yes—
235#1202—42no—
236#1202—42no—
237#1201—42no—
238#1201—42no—
239#1200—42no—
240D3×Dic5—42no—
241C3×C5×C8—21no—
242C3×C5×C8C2×D412yes—
243C3×#168—21no—
244C3×#168C2×D412yes—
245C23×C3×C4—51no—
246C2×#235—51no—
247C2×#235—51no—
248C22×C3×C8—51no—
249C22×C3×C8—51no—
250C22×C3×C8—51no—
251C22×C3×C8—51no—
252C22×C3×C8—51no—
253C22×C3×C8—104no—
254C22×C3×C8C2×D511yescharacteristic
255#953—101no—
256#953—101no—
257#930—51no—
258#930—51no—
259#930—51no—
260#930C2×D511yescharacteristic
261#929—101no—
262#929—101no—
263C4×#67—101no—
264C4×#67—101no—
265C4×#67—101no—
266C4×#67—101no—
267#926—51no—
268#926—51no—
269#924—51no—
270#924—51no—
271#924—51no—
272#924C2×D511yescharacteristic
273C2×Dic12—51no—
274#904—104no—
275C2×D24—51no—
276C2×#204—51no—
277C2×#204C2×D511yescharacteristic, complemented
278#821—51no—
279#821—51no—
280#821—51no—
281#821C2×D511yescharacteristic, complemented
282#818—51no—
283#818—51no—
284#817—51no—
285#817C2×D511yescharacteristic, complemented
286#816—51no—
287#816—51no—
288#816—51no—
289#816C2×D511yescharacteristic, complemented
290C23×D5D1211yescharacteristic
291C2×C5×Q8—31no—
292C2×C5×D4—31no—
293C2×C5×D4—61no—
294C22×C4×C5C22×D311yescharacteristic
295C2×C22⋊D5—61no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C22×Dic5—61no—
299C22×Dic5D1211yescharacteristic
300#713—62no—
301#713—62no—
302#711—62no—
303#711—62no—
304C2×D20—31no—
305C2×D20—61no—
306C2×D20—61no—
307C2×C4×D5—22no—
308C2×C4×D5—22no—
309C2×C4×D5—61no—
310C2×C4×D5D1211yescharacteristic
311C2×C4×D5D1211yescharacteristic
312C2×C4×D5C22×D311yescharacteristic
313C2×C4×D5C22×D311yescharacteristic
314C2×Dic10—31no—
315C5×SD16—62no—
316C2×C5×C8—22no—
317C2×C5×C8C22×D311yescharacteristic
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—62no—
327#686—62no—
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—22no—
342C2×#168C22×D311yescharacteristic
343C2×#168C22×D311yescharacteristic
344#677—62no—
345C8×D5—22no—
346C8×D5—22no—
347C8×D5—22no—
348C8×D5#6714yescomplemented
349C2×#135—151no—
350C23×C8—51no—
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—21no—
365C22×C3×C5—21no—
366C22×C3×C5#13512yescomplemented
367C22×C3×C5C22×D411yescharacteristic
368C2×D15—41no—
369C2×D15—41no—
370C2×D15—41no—
371C2×C5×D3—41no—
372C2×C5×D3—41no—
373C2×C5×D3—41no—
374C2×C3×D5—28no—
375C2×C3×D5—21no—
376C2×C3×D5—21no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5#12112yes—
380C2×C3×D5#13512yescomplemented
381C3×C4×C5—21no—
382C3×C4×C5C22×D411yescharacteristic
383C3×C4×C5C2×#4111yescharacteristic
384Dic15—41no—
385Dic15—41no—
386Dic15—41no—
387C3×Dic5—21no—
388C3×Dic5#12112yes—
389C5×Dic3—41no—
390C5×Dic3—41no—
391C5×Dic3—41no—
392C24×C3—51no—
393C22×C3×C4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—102no—
399C22×C3×C4—102no—
400C22×C3×C4C22×D511yescharacteristic
401C2×#67—21no—
402C2×#67—101no—
403C2×#67—101no—
404C2×#67—101no—
405C2×#67—101no—
406C2×#67—101no—
407#235—102no—
408#235—102no—
409#235—102no—
410#235—102no—
411C2×D12—51no—
412C2×D12C22×D511yescharacteristic
413C2×C4×D3—101no—
414C2×C4×D3—101no—
415C2×Dic6—51no—
416C2×Dic6C22×D511yescharacteristic
417C2×C3×C8—22no—
418C2×C3×C8—51no—
419C2×C3×C8—54no—
420C2×C3×C8—51no—
421C2×C3×C8—102no—
422C2×C3×C8—102no—
423C2×C3×C8—102no—
424C2×C3×C8—102no—
425C2×C3×C8C22×D511yescharacteristic
426C2×C3×C8C22×D511yescharacteristic
427#217—21no—
428#217—101no—
429#217—101no—
430#217—101no—
431#217—101no—
432#217—101no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—101no—
435(C2×D3)⋊C4—101no—
436(C2×D3)⋊C4—101no—
437C4⋊Dic3—51no—
438C4⋊Dic3—51no—
439C4⋊Dic3C22×D511yescharacteristic
440C4⋊Dic3C22×D511yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—101no—
443Dic3⋊C4—101no—
444Dic3⋊C4—101no—
445C4×Dic3—101no—
446C4×Dic3—101no—
447Dic12—102no—
448D24—102no—
449#204—22no—
450#204—102no—
451C23×C5—61no—
452C23×C5C2×D1211yescharacteristic
453C22×D5—22no—
454C22×D5—22no—
455C22×D5—22no—
456C22×D5—61no—
457C22×D5C2×D1211yescharacteristic
458C22×D5C2×D1211yescharacteristic
459C5×Q8—61no—
460C5×Q8—61no—
461C5×D4—61no—
462C5×D4—61no—
463C5×D4—122no—
464C2×C4×C5—21no—
465C2×C4×C5—21no—
466C2×C4×C5—61no—
467C2×C4×C5—61no—
468C2×C4×C5—61no—
469C2×C4×C5C2×D1211yescharacteristic
470C2×C4×C5C23×D311yescharacteristic
471C22⋊D5—122no—
472C22⋊D5—122no—
473C22⋊D5—122no—
474C2×Dic5—22no—
475C2×Dic5—61no—
476C2×Dic5—61no—
477C2×Dic5—61no—
478C2×Dic5—122no—
479C2×Dic5C2×D1211yescharacteristic
480C2×Dic5C2×D1211yescharacteristic
481D20—61no—
482D20—61no—
483D20—122no—
484D20—122no—
485C4×D5—22no—
486C4×D5—21no—
487C4×D5—21no—
488C4×D5—22no—
489C4×D5—122no—
490C4×D5#23512yes—
491C4×D5C2×#6712yes—
492Dic10—61no—
493Dic10—61no—
494C5×C8—21no—
495C5×C8C2×#6712yes—
496#168—21no—
497#168C2×#6712yes—
498C2×#41—151no—
499C2×#41—151no—
500C23×C4—51no—
501#135—304no—
502C2×Q16—151no—
503C2×SD16—31no—
504C2×SD16—151no—
505C2×D8—151no—
506C22×C8—51no—
507C22×C8—51no—
508C22×C8—51no—
509C22×C8—51no—
510C22×C8—51no—
511C22×C8—104no—
512C22×C8D3×D511yescharacteristic
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—22no—
544C2×C3×C5C2×#12111yescharacteristic
545C2×C3×C5C2×#13511yescharacteristic
546C2×C3×C5C2×#13511yescharacteristic
547D15—81no—
548C3×D5—22no—
549C3×D5—22no—
550C5×D3—81no—
551C23×C3—51no—
552C23×C3—51no—
553C23×C3—102no—
554C23×C3—102no—
555C23×C3—102no—
556C23×C3D4×D511yescharacteristic
557C22×D3—21no—
558C22×D3—101no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—51no—
562C2×C3×C4—52no—
563C2×C3×C4—52no—
564C2×C3×C4—51no—
565C2×C3×C4—102no—
566C2×C3×C4—102no—
567C2×C3×C4—102no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4D4×D511yescharacteristic
571C2×C3×C4C23×D511yescharacteristic
572#67—42no—
573#67—202no—
574#67—202no—
575#67—202no—
576#67—202no—
577#67—202no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583C2×Dic3—101no—
584D12—21no—
585D12—21no—
586D12—101no—
587D12—101no—
588C4×D3—202no—
589C4×D3—202no—
590Dic6—21no—
591Dic6—21no—
592Dic6—101no—
593Dic6—101no—
594C3×C8—21no—
595C3×C8—52no—
596C3×C8—101no—
597C3×C8D4×D512yes—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—121no—
601C22×C5—121no—
602C22×C5—121no—
603C22×C5#90412yescomplemented
604C22×C5C22×D1211yescharacteristic
605C2×D5—28no—
606C2×D5—21no—
607C2×D5—21no—
608C2×D5—21no—
609C2×D5—21no—
610C2×D5—121no—
611C2×D5—121no—
612C2×D5—121no—
613C2×D5#90412yescomplemented
614C2×D5#93012yes—
615C4×C5—21no—
616C4×C5—121no—
617C4×C5—121no—
618C4×C5—121no—
619C4×C5C2×#23511yescharacteristic
620C4×C5C22×#6711yescharacteristic
621Dic5—21no—
622Dic5—121no—
623Dic5—121no—
624Dic5—121no—
625Dic5#93012yes—
626C24—51no—
627#41—302no—
628#41—302no—
629#41—302no—
630#41—302no—
631C2×Q8—31no—
632C2×Q8—151no—
633C2×D4—31no—
634C2×D4—61no—
635C2×D4—151no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4—301no—
641C22×C4—51no—
642C22×C4—51no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—51no—
646C22×C4—102no—
647C22×C4—102no—
648C22×C4—301no—
649C22×C4—301no—
650C22×C4C2×D3×D511yescharacteristic
651Q16—302no—
652SD16—62no—
653SD16—302no—
654D8—302no—
655C2×C8—22no—
656C2×C8—51no—
657C2×C8—54no—
658C2×C8—51no—
659C2×C8—102no—
660C2×C8—102no—
661C2×C8—102no—
662C2×C8—102no—
663C2×C8C2×D3×D511yescharacteristic
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—21no—
687C22×C3—21no—
688C22×C3—52no—
689C22×C3—52no—
690C22×C3—108no—
691C22×C3—101no—
692C22×C3—101no—
693C22×C3—101no—
694C22×C3—101no—
695C22×C3#406212yescomplemented
696C22×C3C2×D4×D511yescharacteristic
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—201no—
701C2×D3—201no—
702C2×D3—201no—
703C3×C4—21no—
704C3×C4—52no—
705C3×C4—101no—
706C3×C4C2×D4×D511yescharacteristic
707C3×C4D5×#4111yescharacteristic
708Dic3—41no—
709Dic3—41no—
710Dic3—41no—
711Dic3—201no—
712Dic3—201no—
713Dic3—201no—
714C2×C5—22no—
715C2×C5—241no—
716C2×C5C2×#90411yescharacteristic
717C2×C5C2×#90411yescharacteristic
718C2×C5C2×#93011yescharacteristic
719D5—22no—
720D5—22no—
721D5—241no—
722C23—51no—
723C23—51no—
724C23—61no—
725C23—102no—
726C23—102no—
727C23—102no—
728C23—301no—
729C23D5×D1211yescharacteristic
730Q8—61no—
731Q8—61no—
732Q8—301no—
733Q8—301no—
734D4—61no—
735D4—61no—
736D4—122no—
737D4—301no—
738D4—301no—
739D4—602no—
740D4—602no—
741D4—602no—
742D4—602no—
743D4—602no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—51no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—51no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—602no—
762C2×C4—602no—
763C2×C4D5×D1211yescharacteristic
764C2×C4C22×D3×D511yescharacteristic
765C8—21no—
766C8—52no—
767C8—101no—
768C8D5×#6712yes—
769C2×C3—22no—
770C2×C3—102no—
771C2×C3—102no—
772C2×C3D5×#12111yescharacteristic
773C2×C3C2×#406211yescharacteristic
774C2×C3D5×#13511yescharacteristic
775D3—81no—
776D3—401no—
777C5#8374211yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—52no—
781C22—52no—
782C22—108no—
783C22—101no—
784C22—101no—
785C22—101no—
786C22—101no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22#9126912yescomplemented
794C22C2×D5×D1211yescharacteristic
795C4—21no—
796C4—52no—
797C4—101no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—601no—
802C4—601no—
803C4—601no—
804C4D5×#23511yescharacteristic
805C4C2×D5×#6711yescharacteristic
806C3#1061238711yescharacteristic, complemented, Sylow
807C2—22no—
808C2—102no—
809C2—102no—
810C2—241no—
811C2—1201no—
812C2D5×#90411yescharacteristic
813C2C2×#9126911yescharacteristic
814C2D5×#93011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C8×D5C2semidirect
2. #11754527C2semidirect
3. #11754526C2semidirect
4. C2×#91269C2semidirect
5. #11751215C2semidirect
6. C5×#5114C2semidirect
7. #11748557C2semidirect
8. #11748514C2semidirect
9. #11748135C2semidirect
10. #11747939C2semidirect
11. #11747897C2semidirect
12. #11747896C2semidirect
13. #11747893C2semidirect
14. #11747671C2semidirect
15. #11747642C2semidirect
23. C2×#6706C22semidirect
26. C2×C5×#204C22semidirect
47. C2×#6663C22semidirect
48. C2×#6654C22semidirect
50. #91105C22semidirect
51. #91101C22semidirect
52. #91100C22semidirect
53. C5×#821C22semidirect
54. C5×#817C22semidirect
55. C5×#816C22semidirect
56. #90988C22semidirect
57. #90988C22semidirect
58. #90975C22semidirect
59. #90973C22semidirect
60. #90969C22semidirect
61. #90967C22semidirect
64. C22×C8×D5D3semidirect
124. C3×C8×D5D4semidirect
148. #5114D5semidirect
277. C2×#204C2×D5semidirect
281. #821C2×D5semidirect
285. #817C2×D5semidirect
289. #816C2×D5semidirect
348. C8×D5#67semidirect
366. C22×C3×C5#135semidirect
380. C2×C3×D5#135semidirect
603. C22×C5#904semidirect
613. C2×D5#904semidirect
685. C3×C5#3050semidirect
695. C22×C3#4062semidirect
777. C5#83742semidirect
793. C22#91269semidirect
806. C3#10612387semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C8×D52
#117545272
#117545262
C2×#912692
#117512152
C5×#51142
#117485572
#117485142
#117481352
#117479392
#117478972
#117478962
#117478932
#117476712
#117476422
#106123873
#837425