Finite Group Databasebeta

← #14427824

Subgroups — #14427824

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×C5×D3×C8C211yesmaximal, characteristic, complemented
2#11754352C211yesmaximal, characteristic, complemented
3#11754341C211yesmaximal, characteristic, complemented
4C2×#91272C211yesmaximal, characteristic, complemented
5#11751215C211yesmaximal, characteristic, complemented
6C3×#65403C211yesmaximal, characteristic, complemented
7#11748560C211yesmaximal, characteristic, complemented
8#11748518C211yesmaximal, characteristic, complemented
9#11748137C211yesmaximal, characteristic, complemented
10#11747947C211yesmaximal, characteristic, complemented
11#11747914C211yesmaximal, characteristic, complemented
12#11747912C211yesmaximal, characteristic, complemented
13#11747909C211yesmaximal, characteristic, complemented
14#11747679C211yesmaximal, characteristic, complemented
15#11747643C211yesmaximal, characteristic, complemented
16#10615473—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C2×#6769C2211yescharacteristic
19C2×#6765C2211yescharacteristic
20C22×C3×C5×C8C2211yescharacteristic
21#91819C2211yescharacteristic
22#91813C2211yescharacteristic
23C2×#6706C2211yescharacteristic, complemented
24C22×C5×C3⋊C8C2211yescharacteristic
25C2×C5×D3×C8—24no—
26C2×C5×D3×C8C2211yescharacteristic
27C2×C5×D3×C8C2211yescharacteristic
28C2×C5×D3×C8C2211yescharacteristic
29C2×C5×D3×C8C2211yescharacteristic
30C3×#4076C2211yescharacteristic
31C3×#4070C2211yescharacteristic
32C2×C3×#677C2211yescharacteristic, complemented
33#91570—21no—
34#91568—21no—
35#91556—21no—
36Dic3×C22⋊D5—21no—
37#91460C2211yescharacteristic
38#91456C2211yescharacteristic
39#91452—21no—
40#91446—21no—
41#91441—21no—
42#91369C2211yescharacteristic
43#91365C2211yescharacteristic
44#91351—21no—
45#91338C2211yescharacteristic
46#91338C2211yescharacteristic
47C2×#6662C2211yescharacteristic, complemented
48C2×#6653C2211yescharacteristic, complemented
49#91272—24no—
50#91105C2211yescharacteristic, complemented
51#91101C2211yescharacteristic, complemented
52#91100C2211yescharacteristic, complemented
53C3×#3953C2211yescharacteristic, complemented
54C3×#3949C2211yescharacteristic, complemented
55C3×#3948C2211yescharacteristic, complemented
56#90990C2211yescharacteristic, complemented
57#90990C2211yescharacteristic, complemented
58#90974C2211yescharacteristic, complemented
59#90971C2211yescharacteristic, complemented
60#90968C2211yescharacteristic, complemented
61#90965C2211yescharacteristic, complemented
62#80656—51nomaximal, Hall
63C23×C5×C8—31no—
64#66125—31no—
65#66125—31no—
66C2×#4050—31no—
67#65405—31no—
68#65405—31no—
69#65404—31no—
70#65404—31no—
71#65403—31no—
72#65403—31no—
73#65403—31no—
74#65403D311yescharacteristic, complemented
75#65402—31no—
76#65402—31no—
77#65395—31no—
78C23×C5×D3D411yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×D60C2311yescharacteristic
82C2×Dic30C2311yescharacteristic
83C22×C5×Dic3D411yescharacteristic
84C2×C4×C5×D3—22no—
85C2×C4×C5×D3—22no—
86C2×C4×C5×D3D411yescharacteristic
87C2×C4×C5×D3D411yescharacteristic
88C2×C4×C5×D3C2311yescharacteristic
89C2×C4×C5×D3C2311yescharacteristic
90C2×C3×C22⋊D5—21no—
91C2×C3×D20C2311yescharacteristic
92C2×C3×Dic10C2311yescharacteristic
93C2×#1203—21no—
94C2×#1203—21no—
95C2×#1201—21no—
96C2×#1201—21no—
97C2×#1200—21no—
98C2×D5×Dic3—21no—
99#6769—22no—
100#6769—22no—
101#6765—22no—
102#6765—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—
112C2×C5×C3⋊C8—22no—
113C2×C5×C3⋊C8C2311yescharacteristic
114C2×C5×C3⋊C8C2311yescharacteristic
115C5×D3×C8—22no—
116C5×D3×C8—22no—
117C5×D3×C8—22no—
118C5×D3×C8D414yescomplemented
119C3×C22⋊Dic5—21no—
120C3×#685—21no—
121C3×C4⋊Dic5C2311yescharacteristic
122C3×C4⋊Dic5C2311yescharacteristic
123C3×#683—21no—
124C3×#677—22no—
125#6669—21no—
126#6668—21no—
127#6667—21no—
128(C2×D3)⋊Dic5—21no—
129(C2×D3)⋊Dic5—21no—
130(C2×D3)⋊Dic5—21no—
131(C2×D3)⋊Dic5—21no—
132#6665—21no—
133Dic3×Dic5—21no—
134Dic3×Dic5—21no—
135#6662—22no—
136#6653—22no—
137C2×#916—51no—
138C22×D3×C8D511yescharacteristic, complemented
139#5627—51no—
140#5606—51no—
141C3×#465—51no—
142#5171—51no—
143#5114—51no—
144#5051—51no—
145#5038—51no—
146#4864—51no—
147#4860—51no—
148#4813—51no—
149#4804—51no—
150#4775—51no—
151#4772—51no—
152C23×C4×C5—31no—
153C2×#709—31no—
154C2×#709—31no—
155C22×C5×C8—31no—
156C22×C5×C8—31no—
157C22×C5×C8—31no—
158C22×C5×C8—31no—
159C22×C5×C8—31no—
160C22×C5×C8—64no—
161C22×C5×C8C2×D311yescharacteristic
162#4099—61no—
163#4099—61no—
164#4076—31no—
165#4076—31no—
166#4076—31no—
167#4076C2×D311yescharacteristic
168#4075—61no—
169#4075—61no—
170C4×C22⋊D5—61no—
171C4×C22⋊D5—61no—
172C4×C22⋊D5—61no—
173C4×C22⋊D5—61no—
174#4072—31no—
175#4072—31no—
176#4070—31no—
177#4070—31no—
178#4070—31no—
179#4070C2×D311yescharacteristic
180C2×Dic20—31no—
181#4050—64no—
182C2×D40—31no—
183C2×#677—31no—
184C2×#677C2×D311yescharacteristic, complemented
185#3953—31no—
186#3953—31no—
187#3953—31no—
188#3953C2×D311yescharacteristic, complemented
189#3950—31no—
190#3950—31no—
191#3949—31no—
192#3949C2×D311yescharacteristic, complemented
193#3948—31no—
194#3948—31no—
195#3948—31no—
196#3948C2×D311yescharacteristic, complemented
197#3050—151noSylow
198C23×C3×C5C2×D411yescharacteristic
199C22×D15—21no—
200C22×C5×D3—22no—
201C22×C5×D3—22no—
202C22×C5×D3—22no—
203C22×C5×D3C2×D411yescharacteristic
204C22×C5×D3C2×D411yescharacteristic
205C22×C3×D5—21no—
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—
218C2×C5×Dic3—22no—
219C2×C5×Dic3C2×D411yescharacteristic
220C2×C5×Dic3C2×D411yescharacteristic
221C4×C5×D3—22no—
222C4×C5×D3—21no—
223C4×C5×D3—21no—
224C4×C5×D3—22no—
225C4×C5×D3C2×D412yes—
226C4×C5×D3#4112yes—
227C3×C22⋊D5—42no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—21no—
230C2×C3×Dic5—21no—
231C3×D20—21no—
232C3×D20—21no—
233C3×Dic10—21no—
234C3×Dic10—21no—
235#1203—42no—
236#1203—42no—
237#1201—42no—
238#1201—42no—
239#1200—42no—
240D5×Dic3—42no—
241C3×C5×C8—21no—
242C3×C5×C8C2×D412yes—
243C5×C3⋊C8—21no—
244C5×C3⋊C8C2×D412yes—
245C2×#239—51no—
246C2×#237—51no—
247C22×C4×D3C2×D511yescharacteristic
248C2×C3×SD16—51no—
249C22×C3×C8C2×D511yescharacteristic
250C3×C22⋊Q8—51no—
251C3×#121—51no—
252#946—51no—
253C2×#216—51no—
254#938—51no—
255#937—101no—
256D4×Dic3—101no—
257C2×#213—51no—
258#930—51no—
259#924—51no—
260C22×C3⋊C8C2×D511yescharacteristic
261#916—104no—
262C2×#204—51no—
263C2×D3×C8—24no—
264C2×D3×C8C2×D511yescharacteristic
265C2×D3×C8C2×D511yescharacteristic
266C2×D3×C8C2×D511yescharacteristic
267C2×D3×C8C2×D511yescharacteristic
268#897—51no—
269#895—51no—
270#894—101no—
271#893—101no—
272#892—51no—
273#892—51no—
274#883—101no—
275#882—101no—
276#67⋊C4—101no—
277#67⋊C4—101no—
278C3×#106—51no—
279C3×#103—51no—
280C3×#102—51no—
281#835—51no—
282#832—51no—
283#821—51no—
284#817—51no—
285#816—51no—
286#810—51no—
287#809—51no—
288#807—51no—
289#807—51no—
290C24×C5—31no—
291C22×C4×C5—31no—
292C22×C4×C5—31no—
293C22×C4×C5—31no—
294C22×C4×C5—31no—
295C22×C4×C5—31no—
296C22×C4×C5—62no—
297C22×C4×C5—62no—
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5—21no—
300C2×C22⋊D5—61no—
301C2×C22⋊D5—61no—
302C2×C22⋊D5—61no—
303C2×C22⋊D5—61no—
304C2×C22⋊D5—61no—
305#709—62no—
306#709—62no—
307#709—62no—
308#709—62no—
309C2×D20—31no—
310C2×D20C22×D311yescharacteristic
311C2×C4×D5—61no—
312C2×C4×D5—61no—
313C2×Dic10—31no—
314C2×Dic10C22×D311yescharacteristic
315C2×C5×C8—22no—
316C2×C5×C8—31no—
317C2×C5×C8—34no—
318C2×C5×C8—31no—
319C2×C5×C8—62no—
320C2×C5×C8—62no—
321C2×C5×C8—62no—
322C2×C5×C8—62no—
323C2×C5×C8C22×D311yescharacteristic
324C2×C5×C8C22×D311yescharacteristic
325C22⋊Dic5—21no—
326C22⋊Dic5—61no—
327C22⋊Dic5—61no—
328C22⋊Dic5—61no—
329C22⋊Dic5—61no—
330C22⋊Dic5—61no—
331#685—21no—
332#685—61no—
333#685—61no—
334#685—61no—
335C4⋊Dic5—31no—
336C4⋊Dic5—31no—
337C4⋊Dic5C22×D311yescharacteristic
338C4⋊Dic5C22×D311yescharacteristic
339#683—21no—
340#683—61no—
341#683—61no—
342#683—61no—
343C4×Dic5—61no—
344C4×Dic5—61no—
345Dic20—62no—
346D40—62no—
347#677—22no—
348#677—62no—
349C2×#135—151no—
350C23×C8—31no—
351#525—151no—
352#525—151no—
353#467—151no—
354#467—151no—
355#466—151no—
356#466—151no—
357#465—51no—
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—28no—
372C2×C5×D3—21no—
373C2×C5×D3—21no—
374C2×C5×D3—21no—
375C2×C5×D3—21no—
376C2×C5×D3#12112yes—
377C2×C5×D3#13512yescomplemented
378C2×C3×D5—41no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C3×C4×C5—21no—
382C3×C4×C5C22×D411yescharacteristic
383C3×C4×C5C2×#4111yescharacteristic
384Dic15—41no—
385Dic15—41no—
386Dic15—41no—
387C3×Dic5—41no—
388C3×Dic5—41no—
389C3×Dic5—41no—
390C5×Dic3—21no—
391C5×Dic3#12112yes—
392C23×D3D2011yescharacteristic
393C2×C3×Q8—51no—
394C2×C3×D4—51no—
395C2×C3×D4—101no—
396C22×C3×C4C22×D511yescharacteristic
397C2×#67—101no—
398C2×#67—101no—
399C2×#67—101no—
400C22×Dic3—101no—
401C22×Dic3D2011yescharacteristic
402#239—102no—
403#239—102no—
404#237—102no—
405#237—102no—
406C2×D12—51no—
407C2×D12—101no—
408C2×D12—101no—
409C2×C4×D3—22no—
410C2×C4×D3—22no—
411C2×C4×D3—101no—
412C2×C4×D3D2011yescharacteristic
413C2×C4×D3D2011yescharacteristic
414C2×C4×D3C22×D511yescharacteristic
415C2×C4×D3C22×D511yescharacteristic
416C2×Dic6—51no—
417C3×SD16—102no—
418C2×C3×C8—22no—
419C2×C3×C8C22×D511yescharacteristic
420C2×C3×C8C22×D511yescharacteristic
421C3×C4⋊C4—51no—
422C3×C4⋊C4—51no—
423C3×C4⋊C4—101no—
424C3×C22⋊C4—101no—
425C3×C22⋊C4—101no—
426#217—101no—
427#217—101no—
428#216—102no—
429#213—102no—
430(C2×D3)⋊C4—101no—
431(C2×D3)⋊C4—101no—
432(C2×D3)⋊C4—101no—
433(C2×D3)⋊C4—101no—
434(C2×D3)⋊C4—101no—
435(C2×D3)⋊C4—101no—
436C4⋊Dic3—51no—
437C4⋊Dic3—51no—
438C4⋊Dic3—101no—
439Dic3⋊C4—101no—
440Dic3⋊C4—101no—
441C4×Dic3—101no—
442C4×Dic3—101no—
443C2×C3⋊C8—22no—
444C2×C3⋊C8C22×D511yescharacteristic
445C2×C3⋊C8C22×D511yescharacteristic
446#204—102no—
447D3×C8—22no—
448D3×C8—22no—
449D3×C8—22no—
450D3×C8C22⋊D514yescomplemented
451C23×C5—31no—
452C23×C5—31no—
453C23×C5—62no—
454C23×C5—62no—
455C23×C5—62no—
456C23×C5D3×D411yescharacteristic
457C22×D5—21no—
458C22×D5—61no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—31no—
462C2×C4×C5—32no—
463C2×C4×C5—32no—
464C2×C4×C5—31no—
465C2×C4×C5—62no—
466C2×C4×C5—62no—
467C2×C4×C5—62no—
468C2×C4×C5—61no—
469C2×C4×C5—61no—
470C2×C4×C5D3×D411yescharacteristic
471C2×C4×C5C23×D311yescharacteristic
472C22⋊D5—42no—
473C22⋊D5—122no—
474C22⋊D5—122no—
475C22⋊D5—122no—
476C22⋊D5—122no—
477C22⋊D5—122no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—21no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484D20—21no—
485D20—21no—
486D20—61no—
487D20—61no—
488C4×D5—122no—
489C4×D5—122no—
490Dic10—21no—
491Dic10—21no—
492Dic10—61no—
493Dic10—61no—
494C5×C8—21no—
495C5×C8—32no—
496C5×C8—61no—
497C5×C8D3×D412yes—
498C2×#41—151no—
499C2×#41—151no—
500C23×C4—31no—
501#135—304no—
502C2×Q16—151no—
503C2×SD16—51no—
504C2×SD16—151no—
505C2×D8—151no—
506C22×C8—31no—
507C22×C8—31no—
508C22×C8—31no—
509C22×C8—31no—
510C22×C8—31no—
511C22×C8—64no—
512C22×C8D3×D511yescharacteristic
513#123—301no—
514#123—301no—
515C22⋊Q8—51no—
516C22⋊Q8—151no—
517C22⋊Q8—151no—
518C22⋊Q8—151no—
519#121—51no—
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—51no—
534#106—151no—
535#103—51no—
536#103—151no—
537#103—151no—
538#103—151no—
539#102—51no—
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—81no—
549C5×D3—22no—
550C5×D3—22no—
551C23×C3—101no—
552C23×C3C2×D2011yescharacteristic
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—101no—
557C22×D3C2×D2011yescharacteristic
558C22×D3C2×D2011yescharacteristic
559C3×Q8—101no—
560C3×Q8—101no—
561C3×D4—101no—
562C3×D4—101no—
563C3×D4—202no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4C2×D2011yescharacteristic
570C2×C3×C4C23×D511yescharacteristic
571#67—202no—
572#67—202no—
573#67—202no—
574C2×Dic3—22no—
575C2×Dic3—101no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—202no—
579C2×Dic3C2×D2011yescharacteristic
580C2×Dic3C2×D2011yescharacteristic
581D12—101no—
582D12—101no—
583D12—202no—
584D12—202no—
585C4×D3—22no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—22no—
589C4×D3—202no—
590C4×D3#70912yes—
591C4×D3C2×C22⋊D512yes—
592Dic6—101no—
593Dic6—101no—
594C3×C8—21no—
595C3×C8C2×C22⋊D512yes—
596C3⋊C8—21no—
597C3⋊C8C2×C22⋊D512yes—
598C22×C5—21no—
599C22×C5—21no—
600C22×C5—32no—
601C22×C5—32no—
602C22×C5—68no—
603C22×C5—61no—
604C22×C5—61no—
605C22×C5—61no—
606C22×C5—61no—
607C22×C5#91612yescomplemented
608C22×C5C2×D3×D411yescharacteristic
609C2×D5—41no—
610C2×D5—41no—
611C2×D5—41no—
612C2×D5—121no—
613C2×D5—121no—
614C2×D5—121no—
615C4×C5—21no—
616C4×C5—32no—
617C4×C5—61no—
618C4×C5C2×D3×D411yescharacteristic
619C4×C5D3×#4111yescharacteristic
620Dic5—41no—
621Dic5—41no—
622Dic5—41no—
623Dic5—121no—
624Dic5—121no—
625Dic5—121no—
626C24—31no—
627#41—302no—
628#41—302no—
629#41—302no—
630#41—302no—
631C2×Q8—51no—
632C2×Q8—151no—
633C2×D4—51no—
634C2×D4—101no—
635C2×D4—151no—
636C2×D4—301no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4—301no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—62no—
647C22×C4—62no—
648C22×C4—301no—
649C22×C4—301no—
650C22×C4C2×D3×D511yescharacteristic
651Q16—302no—
652SD16—102no—
653SD16—302no—
654D8—302no—
655C2×C8—22no—
656C2×C8—31no—
657C2×C8—34no—
658C2×C8—31no—
659C2×C8—62no—
660C2×C8—62no—
661C2×C8—62no—
662C2×C8—62no—
663C2×C8C2×D3×D511yescharacteristic
664C2×C8C2×D3×D511yescharacteristic
665C4⋊C4—51no—
666C4⋊C4—51no—
667C4⋊C4—101no—
668C4⋊C4—151no—
669C4⋊C4—151no—
670C4⋊C4—301no—
671C4⋊C4—301no—
672C4⋊C4—301no—
673C22⋊C4—101no—
674C22⋊C4—101no—
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—201no—
689C22×C3—201no—
690C22×C3—201no—
691C22×C3#405012yescomplemented
692C22×C3C22×D2011yescharacteristic
693C2×D3—28no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—201no—
699C2×D3—201no—
700C2×D3—201no—
701C2×D3#405012yescomplemented
702C2×D3#407612yes—
703C3×C4—21no—
704C3×C4—201no—
705C3×C4—201no—
706C3×C4—201no—
707C3×C4C2×#70911yescharacteristic
708C3×C4C22×C22⋊D511yescharacteristic
709Dic3—21no—
710Dic3—201no—
711Dic3—201no—
712Dic3—201no—
713Dic3#407612yes—
714C2×C5—22no—
715C2×C5—62no—
716C2×C5—62no—
717C2×C5D3×#12111yescharacteristic
718C2×C5C2×#91611yescharacteristic
719C2×C5D3×#13511yescharacteristic
720D5—81no—
721D5—241no—
722C23—31no—
723C23—31no—
724C23—62no—
725C23—62no—
726C23—62no—
727C23—101no—
728C23—301no—
729C23D3×D2011yescharacteristic
730Q8—101no—
731Q8—101no—
732Q8—301no—
733Q8—301no—
734D4—101no—
735D4—101no—
736D4—202no—
737D4—301no—
738D4—301no—
739D4—602no—
740D4—602no—
741D4—602no—
742D4—602no—
743D4—602no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—31no—
747C2×C4—32no—
748C2×C4—32no—
749C2×C4—31no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—602no—
762C2×C4—602no—
763C2×C4D3×D2011yescharacteristic
764C2×C4C22×D3×D511yescharacteristic
765C8—21no—
766C8—32no—
767C8—61no—
768C8D3×C22⋊D512yes—
769C2×C3—22no—
770C2×C3—401no—
771C2×C3C2×#405011yescharacteristic
772C2×C3C2×#405011yescharacteristic
773C2×C3C2×#407611yescharacteristic
774D3—22no—
775D3—22no—
776D3—401no—
777C5#8065611yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—32no—
781C22—32no—
782C22—68no—
783C22—61no—
784C22—61no—
785C22—61no—
786C22—61no—
787C22—201no—
788C22—201no—
789C22—201no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22#9127212yescomplemented
794C22C2×D3×D2011yescharacteristic
795C4—21no—
796C4—32no—
797C4—61no—
798C4—201no—
799C4—201no—
800C4—201no—
801C4—601no—
802C4—601no—
803C4—601no—
804C4D3×#70911yescharacteristic
805C4C2×D3×C22⋊D511yescharacteristic
806C3#1061547311yescharacteristic, complemented, Sylow
807C2—22no—
808C2—62no—
809C2—62no—
810C2—401no—
811C2—1201no—
812C2D3×#405011yescharacteristic
813C2C2×#9127211yescharacteristic
814C2D3×#407611yescharacteristic
subgroupG/H
centerC22C2×D3×D20
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×C5×D3×C8C2semidirect
2. #11754352C2semidirect
3. #11754341C2semidirect
4. C2×#91272C2semidirect
5. #11751215C2semidirect
6. C3×#65403C2semidirect
7. #11748560C2semidirect
8. #11748518C2semidirect
9. #11748137C2semidirect
10. #11747947C2semidirect
11. #11747914C2semidirect
12. #11747912C2semidirect
13. #11747909C2semidirect
14. #11747679C2semidirect
15. #11747643C2semidirect
23. C2×#6706C22semidirect
32. C2×C3×#677C22semidirect
47. C2×#6662C22semidirect
48. C2×#6653C22semidirect
50. #91105C22semidirect
51. #91101C22semidirect
52. #91100C22semidirect
53. C3×#3953C22semidirect
54. C3×#3949C22semidirect
55. C3×#3948C22semidirect
56. #90990C22semidirect
57. #90990C22semidirect
58. #90974C22semidirect
59. #90971C22semidirect
60. #90968C22semidirect
61. #90965C22semidirect
74. #65403D3semidirect
118. C5×D3×C8D4semidirect
138. C22×D3×C8D5semidirect
184. C2×#677C2×D3semidirect
188. #3953C2×D3semidirect
192. #3949C2×D3semidirect
196. #3948C2×D3semidirect
366. C22×C3×C5#135semidirect
377. C2×C5×D3#135semidirect
450. D3×C8C22⋊D5semidirect
607. C22×C5#916semidirect
685. C3×C5#3050semidirect
691. C22×C3#4050semidirect
701. C2×D3#4050semidirect
777. C5#80656semidirect
793. C22#91272semidirect
806. C3#10615473semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×C82
#117543522
#117543412
C2×#912722
#117512152
C3×#654032
#117485602
#117485182
#117481372
#117479472
#117479142
#117479122
#117479092
#117476792
#117476432
#106154733
#806565