Finite Group Databasebeta

← #14453720

Subgroups — #14453720

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91798C211yesmaximal, characteristic, complemented
2C22×#6706C211yesmaximal, characteristic, complemented
3#11756309C211yesmaximal, characteristic
4D4×Dic30C211yesmaximal, characteristic, complemented
5C3×C5×#435C211yesmaximal, characteristic, complemented
6#11751235C211yesmaximal, characteristic, complemented
7#11751217C211yesmaximal, characteristic, complemented
8#11750946C211yesmaximal, characteristic, complemented
9#11750942C211yesmaximal, characteristic, complemented
10#11750840C211yesmaximal, characteristic, complemented
11#11750839C211yesmaximal, characteristic, complemented
12#11750834C211yesmaximal, characteristic, complemented
13#11750832C211yesmaximal, characteristic, complemented
14#11750816C211yesmaximal, characteristic, complemented
15#11750811C211yesmaximal, characteristic, complemented
16#10611226—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×Dic30C2211yescharacteristic, complemented
21C2×C3×C5×M16C2211yescharacteristic, complemented
22C22×C3×C5×C8C2211yescharacteristic
23C3×C4×C5×D4C2211yescharacteristic
24#91826—21no—
25D4×Dic15—21no—
26#91819C2211yescharacteristic
27#91813C2211yescharacteristic
28#91813C2211yescharacteristic
29#91813C2211yescharacteristic, complemented
30#91798—24no—
31C2×Dic60C2211yescharacteristic, complemented
32C2×Dic60C2211yescharacteristic, complemented
33C2×Dic60C2211yescharacteristic, complemented
34C2×#6706—24no—
35C2×#6706C2211yescharacteristic
36C2×#6706C2211yescharacteristic
37C2×#6706C2211yescharacteristic
38C2×#6706C2211yescharacteristic
39C2×#6706C2211yescharacteristic
40C2×#6706C2211yescharacteristic
41#91783—21no—
42#91777—21no—
43#91773—21no—
44C22⋊C4×D15—21no—
45#91767—21no—
46#91767—21no—
47#91764C2211yescharacteristic
48C4×D60C2211yescharacteristic
49#91758C2211yescharacteristic, complemented
50C4×Dic30C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×C22⋊C8C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55#91105C2211yescharacteristic
56#91105C2211yescharacteristic
57#91102C2211yescharacteristic, complemented
58#91100C2211yescharacteristic, complemented
59#91100C2211yescharacteristic, complemented
60#91100C2211yescharacteristic, complemented
61#91100C2211yescharacteristic, complemented
62#79495—51nomaximal, Hall
63C2×#4055—31no—
64C22×#677—31no—
65#65884—31no—
66D4×Dic10—31no—
67C5×#435D311yescharacteristic, complemented
68#65423—31no—
69#65405—31no—
70#65134—31no—
71#65130—31no—
72#65028—31no—
73#65027—31no—
74#65022—31no—
75#65020—31no—
76#65004—31no—
77#64999—31no—
78C23×D15—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×#1220—21no—
84C22×Dic15—21no—
85C22×Dic15—21no—
86#6817—22no—
87#6817—41no—
88C2×D60—22no—
89C2×D60—21no—
90C2×D60—41no—
91C2×D60C2311yescharacteristic
92C2×D60C2311yescharacteristic
93C2×C4×D15—21no—
94C2×C4×D15—21no—
95C2×Dic30—22no—
96C2×Dic30—22no—
97C2×Dic30—21no—
98C2×Dic30—21no—
99C2×Dic30—41no—
100C2×Dic30—41no—
101C2×Dic30C2311yescharacteristic
102C2×Dic30C2311yescharacteristic
103C2×Dic30C2311yescharacteristic
104C2×Dic30C2311yescharacteristic
105C3×C5×M16—22no—
106C2×C3×C5×C8—22no—
107C2×C3×C5×C8C2311yescharacteristic
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C2×C3×C5×C8C2311yescharacteristic
111C3×C5×C4⋊C4D411yescharacteristic
112C3×C5×C22⋊C4D411yescharacteristic
113C3×C5×C22⋊C4D411yescharacteristic
114C3×C42×C5C2311yescharacteristic
115#6719—21no—
116#6719—21no—
117#6719—21no—
118#6714—21no—
119#6714—21no—
120#6714—21no—
121#6714—21no—
122C4⋊Dic15—21no—
123C4⋊Dic15—21no—
124C4⋊Dic15C2311yescharacteristic
125C4⋊Dic15C2311yescharacteristic
126#6712—21no—
127#6712—21no—
128#6712—21no—
129#6712—21no—
130C4×Dic15—21no—
131Dic60—22no—
132Dic60—22no—
133Dic60—41no—
134#6706—22no—
135#6706—22no—
136#6706—22no—
137#6706—22no—
138#6706—41no—
139#6706D414yescomplemented
140C2×#909—51no—
141C22×#204—51no—
142#5550—51no—
143D4×Dic6—51no—
144C3×#435D511yescharacteristic, complemented
145#5134—51no—
146#5116—51no—
147#4845—51no—
148#4841—51no—
149#4739—51no—
150#4738—51no—
151#4733—51no—
152#4731—51no—
153#4715—51no—
154#4710—51no—
155C2×#709—31no—
156C22×D20—31no—
157C22×Dic10—31no—
158C22×Dic10—31no—
159C2×C5×M16C2×D311yescharacteristic, complemented
160C22×C5×C8C2×D311yescharacteristic
161C4×C5×D4C2×D311yescharacteristic
162#4083—61no—
163D4×Dic5—61no—
164#4076—31no—
165#4070—31no—
166#4070—31no—
167#4070—31no—
168#4055—64no—
169C2×Dic20—31no—
170C2×Dic20—31no—
171C2×Dic20—31no—
172C2×#677—31no—
173C2×#677—31no—
174C2×#677—31no—
175C2×#677—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—64no—
179#4040—61no—
180#4034—61no—
181#4030—61no—
182D5×C22⋊C4—61no—
183#4024—61no—
184#4024—61no—
185#4021—31no—
186C4×D20—31no—
187#4015—31no—
188C4×Dic10—31no—
189C5×C4⋊C8C2×D311yescharacteristic, complemented
190C5×C22⋊C8C2×D311yescharacteristic
191C5×C22⋊C8C2×D311yescharacteristic, complemented
192C5×#97C2×D311yescharacteristic, complemented
193#3953—31no—
194#3953—31no—
195#3950—31no—
196#3948—31no—
197#3948—31no—
198#3948—31no—
199#3948—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—42no—
206C22×D15—42no—
207C22×D15—81no—
208C3×C5×D4—22no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5C2×D411yescharacteristic
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2411yescharacteristic
218#1220—42no—
219#1220—81no—
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—21no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—42no—
227C2×Dic15—42no—
228D60—21no—
229D60—21no—
230D60—21no—
231D60—42no—
232D60C2×D412yes—
233C4×D15—42no—
234C4×D15—81no—
235Dic30—21no—
236Dic30—21no—
237Dic30—21no—
238Dic30—21no—
239Dic30—21no—
240Dic30—21no—
241Dic30—21no—
242Dic30—42no—
243Dic30—42no—
244Dic30C2×D412yes—
245C3×C5×C8—21no—
246C3×C5×C8—21no—
247C3×C5×C8—21no—
248C3×C5×C8C2×D412yes—
249C2×#235—51no—
250C22×D12—51no—
251C22×Dic6—51no—
252C22×Dic6—51no—
253C2×C3×M16C2×D511yescharacteristic, complemented
254C22×C3×C8C2×D511yescharacteristic
255C3×C4×D4C2×D511yescharacteristic
256#937—101no—
257D4×Dic3—101no—
258#930—51no—
259#924—51no—
260#924—51no—
261#924—51no—
262#909—104no—
263C2×Dic12—51no—
264C2×Dic12—51no—
265C2×Dic12—51no—
266C2×#204—51no—
267C2×#204—51no—
268C2×#204—51no—
269C2×#204—51no—
270C2×#204—51no—
271C2×#204—51no—
272C2×#204—104no—
273#894—101no—
274#888—101no—
275#884—101no—
276D3×C22⋊C4—101no—
277#878—101no—
278#878—101no—
279#875—51no—
280C4×D12—51no—
281#869—51no—
282C4×Dic6—51no—
283C3×C4⋊C8C2×D511yescharacteristic, complemented
284C3×C22⋊C8C2×D511yescharacteristic
285C3×C22⋊C8C2×D511yescharacteristic, complemented
286C3×#97C2×D511yescharacteristic, complemented
287#821—51no—
288#821—51no—
289#818—51no—
290#816—51no—
291#816—51no—
292#816—51no—
293#816—51no—
294C23×D5—61no—
295C2×C5×D4D1211yescharacteristic
296C22×C4×C5C22×D311yescharacteristic
297C22×C4×C5C22×D311yescharacteristic
298C2×C22⋊D5—61no—
299C2×C22⋊D5—61no—
300C22×Dic5—61no—
301C22×Dic5—61no—
302#709—62no—
303#709—121no—
304C2×D20—31no—
305C2×D20—31no—
306C2×D20—62no—
307C2×D20—61no—
308C2×D20—121no—
309C2×C4×D5—61no—
310C2×C4×D5—61no—
311C2×Dic10—31no—
312C2×Dic10—31no—
313C2×Dic10—31no—
314C2×Dic10—31no—
315C2×Dic10—62no—
316C2×Dic10—62no—
317C2×Dic10—61no—
318C2×Dic10—61no—
319C2×Dic10—121no—
320C2×Dic10—121no—
321C5×M16—22no—
322C2×C5×C8—22no—
323C2×C5×C8C22×D311yescharacteristic
324C2×C5×C8C22×D311yescharacteristic
325C2×C5×C8C22×D311yescharacteristic
326C2×C5×C8C22×D311yescharacteristic
327C5×C4⋊C4D1211yescharacteristic
328C5×C22⋊C4D1211yescharacteristic
329C5×C22⋊C4D1211yescharacteristic
330C42×C5C22×D311yescharacteristic
331C22⋊Dic5—61no—
332C22⋊Dic5—61no—
333C22⋊Dic5—61no—
334#685—61no—
335#685—61no—
336#685—61no—
337#685—61no—
338C4⋊Dic5—31no—
339C4⋊Dic5—31no—
340C4⋊Dic5—61no—
341C4⋊Dic5—61no—
342#683—61no—
343#683—61no—
344#683—61no—
345#683—61no—
346C4×Dic5—61no—
347Dic20—62no—
348Dic20—62no—
349Dic20—121no—
350#677—34no—
351#677—62no—
352#677—62no—
353#677—62no—
354#677—62no—
355#677—121no—
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8—151no—
359#546—151no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435D1511yescharacteristic, complemented
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5#13712yescomplemented
377C22×C3×C5C22×D411yescharacteristic
378C2×D15—22no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—84no—
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5H(5,𝔽2)11yescharacteristic
391Dic15—22no—
392Dic15—41no—
393Dic15—41no—
394Dic15—41no—
395Dic15—41no—
396Dic15—41no—
397C23×D3—101no—
398C2×C3×D4D2011yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C2×#67—101no—
402C2×#67—101no—
403C22×Dic3—101no—
404C22×Dic3—101no—
405#235—102no—
406#235—201no—
407C2×D12—51no—
408C2×D12—51no—
409C2×D12—102no—
410C2×D12—101no—
411C2×D12—201no—
412C2×C4×D3—101no—
413C2×C4×D3—101no—
414C2×Dic6—51no—
415C2×Dic6—51no—
416C2×Dic6—51no—
417C2×Dic6—51no—
418C2×Dic6—102no—
419C2×Dic6—102no—
420C2×Dic6—101no—
421C2×Dic6—101no—
422C2×Dic6—201no—
423C2×Dic6—201no—
424C3×M16—22no—
425C2×C3×C8—22no—
426C2×C3×C8C22×D511yescharacteristic
427C2×C3×C8C22×D511yescharacteristic
428C2×C3×C8C22×D511yescharacteristic
429C2×C3×C8C22×D511yescharacteristic
430C3×C4⋊C4D2011yescharacteristic
431C3×C22⋊C4D2011yescharacteristic
432C3×C22⋊C4D2011yescharacteristic
433C3×C42C22×D511yescharacteristic
434#217—101no—
435#217—101no—
436#217—101no—
437(C2×D3)⋊C4—101no—
438(C2×D3)⋊C4—101no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441C4⋊Dic3—51no—
442C4⋊Dic3—51no—
443C4⋊Dic3—101no—
444C4⋊Dic3—101no—
445Dic3⋊C4—101no—
446Dic3⋊C4—101no—
447Dic3⋊C4—101no—
448Dic3⋊C4—101no—
449C4×Dic3—101no—
450Dic12—102no—
451Dic12—102no—
452Dic12—201no—
453#204—54no—
454#204—102no—
455#204—102no—
456#204—102no—
457#204—102no—
458#204—201no—
459C23×C5C2×D1211yescharacteristic
460C23×C5C2×D1211yescharacteristic
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×D4—22no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5C2×D1211yescharacteristic
472C2×C4×C5C2×D1211yescharacteristic
473C2×C4×C5C2×D1211yescharacteristic
474C2×C4×C5C2×D1211yescharacteristic
475C2×C4×C5C23×D311yescharacteristic
476C22⋊D5—122no—
477C22⋊D5—241no—
478C2×Dic5—61no—
479C2×Dic5—61no—
480C2×Dic5—61no—
481C2×Dic5—61no—
482C2×Dic5—61no—
483C2×Dic5—61no—
484C2×Dic5—122no—
485C2×Dic5—122no—
486D20—32no—
487D20—61no—
488D20—61no—
489D20—61no—
490D20—122no—
491C4×D5—122no—
492C4×D5—241no—
493Dic10—32no—
494Dic10—61no—
495Dic10—61no—
496Dic10—61no—
497Dic10—61no—
498Dic10—61no—
499Dic10—61no—
500Dic10—61no—
501Dic10—122no—
502Dic10—122no—
503C5×C8—21no—
504C5×C8—21no—
505C5×C8—21no—
506C5×C8D3×D412yes—
507C2×#41—151no—
508C22×Q8—151no—
509C22×Q8—151no—
510C22×D4—151no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16C2×D1511yescharacteristic, complemented
523C22×C8C2×D1511yescharacteristic
524C4⋊Q8—151no—
525C4⋊Q8—301no—
526#124—151no—
527#123—301no—
528C22⋊Q8—151no—
529C22⋊Q8—151no—
530C22⋊Q8—151no—
531C22⋊Q8—301no—
532C22⋊Q8—301no—
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8—151no—
537C4×D4—151no—
538C4×D4—301no—
539C4×D4C2×D1511yescharacteristic
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8C2×D1511yescharacteristic, complemented
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8C2×D1511yescharacteristic
550C22⋊C8C2×D1511yescharacteristic, complemented
551#97C2×D1511yescharacteristic, complemented
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557D15—42no—
558D15—81no—
559C23×C3C2×D2011yescharacteristic
560C23×C3C2×D2011yescharacteristic
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—202no—
564C22×D3—202no—
565C22×D3—401no—
566C3×D4—22no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4C2×D2011yescharacteristic
572C2×C3×C4C2×D2011yescharacteristic
573C2×C3×C4C2×D2011yescharacteristic
574C2×C3×C4C2×D2011yescharacteristic
575C2×C3×C4C23×D511yescharacteristic
576#67—202no—
577#67—401no—
578C2×Dic3—101no—
579C2×Dic3—101no—
580C2×Dic3—101no—
581C2×Dic3—101no—
582C2×Dic3—101no—
583C2×Dic3—101no—
584C2×Dic3—202no—
585C2×Dic3—202no—
586D12—52no—
587D12—101no—
588D12—101no—
589D12—101no—
590D12—202no—
591C4×D3—202no—
592C4×D3—401no—
593Dic6—52no—
594Dic6—101no—
595Dic6—101no—
596Dic6—101no—
597Dic6—101no—
598Dic6—101no—
599Dic6—101no—
600Dic6—101no—
601Dic6—202no—
602Dic6—202no—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8D4×D512yes—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5#90912yescomplemented
613C22×C5C22×D1211yescharacteristic
614C2×D5—62no—
615C2×D5—121no—
616C2×D5—121no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5C2×D3×D411yescharacteristic
626C4×C5#100911yescharacteristic
627Dic5—62no—
628Dic5—121no—
629Dic5—121no—
630Dic5—121no—
631Dic5—121no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—151no—
637C2×Q8—151no—
638C2×Q8—151no—
639C2×Q8—151no—
640C2×Q8—302no—
641C2×Q8—302no—
642C2×Q8—301no—
643C2×Q8—301no—
644C2×Q8—601no—
645C2×Q8—601no—
646C2×D4—151no—
647C2×D4—151no—
648C2×D4—302no—
649C2×D4—301no—
650C2×D4—301no—
651C2×D4—301no—
652C2×D4—601no—
653C2×D4D6011yescharacteristic
654C22×C4—301no—
655C22×C4—301no—
656C22×C4—301no—
657C22×C4—301no—
658C22×C4C22×D1511yescharacteristic
659C22×C4C22×D1511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—22no—
670C2×C8—22no—
671C2×C8C22×D1511yescharacteristic
672C2×C8C22×D1511yescharacteristic
673C2×C8C22×D1511yescharacteristic
674C2×C8C22×D1511yescharacteristic
675C4⋊C4—151no—
676C4⋊C4—151no—
677C4⋊C4—301no—
678C4⋊C4—301no—
679C4⋊C4—301no—
680C4⋊C4—301no—
681C4⋊C4—301no—
682C4⋊C4—301no—
683C4⋊C4D6011yescharacteristic
684C22⋊C4—301no—
685C22⋊C4—301no—
686C22⋊C4—301no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4D6011yescharacteristic
692C22⋊C4D6011yescharacteristic
693C42—301no—
694C42C22×D1511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3#405512yescomplemented
702C22×C3C22×D2011yescharacteristic
703C2×D3—102no—
704C2×D3—201no—
705C2×D3—201no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4C2×D4×D511yescharacteristic
715C3×C4#414911yescharacteristic
716Dic3—102no—
717Dic3—201no—
718Dic3—201no—
719Dic3—201no—
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5D4×D1211yescharacteristic
725C2×C5C2×#90911yescharacteristic
726C2×C5#575111yescharacteristic
727D5—122no—
728D5—241no—
729C23—301no—
730C23—301no—
731C23—602no—
732C23—602no—
733C23—1201no—
734C23C2×D6011yescharacteristic
735C23C2×D6011yescharacteristic
736Q8—152no—
737Q8—301no—
738Q8—301no—
739Q8—301no—
740Q8—301no—
741Q8—301no—
742Q8—301no—
743Q8—301no—
744Q8—602no—
745Q8—602no—
746D4—22no—
747D4—152no—
748D4—301no—
749D4—301no—
750D4—301no—
751D4—602no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—301no—
759C2×C4—301no—
760C2×C4—301no—
761C2×C4—301no—
762C2×C4—301no—
763C2×C4—301no—
764C2×C4—602no—
765C2×C4—602no—
766C2×C4—602no—
767C2×C4—1201no—
768C2×C4C2×D6011yescharacteristic
769C2×C4C2×D6011yescharacteristic
770C2×C4C2×D6011yescharacteristic
771C2×C4C2×D6011yescharacteristic
772C2×C4C23×D1511yescharacteristic
773C8—21no—
774C8—21no—
775C8—21no—
776C8D4×D1512yes—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3D4×D2011yescharacteristic
780C2×C3C2×#405511yescharacteristic
781C2×C3#6608511yescharacteristic
782D3—202no—
783D3—401no—
784C5#7949511yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—302no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22#9179812yescomplemented
798C22C22×D6011yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—302no—
804C4—601no—
805C4—601no—
806C4—601no—
807C4—601no—
808C4—601no—
809C4C2×D4×D1511yescharacteristic
810C4#9210011yescharacteristic
811C3#1061122611yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—602no—
815C2—1201no—
816C2D4×D6011yescharacteristic
817C2C2×#9179811yescharacteristic
818C2#1175651011yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#435C2
socleC22×C3×C5C22×D4
prime radical#11756309C2
hypercenter#435D15
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#91798C2semidirect
2. C22×#6706C2semidirect
4. D4×Dic30C2semidirect
5. C3×C5×#435C2semidirect
6. #11751235C2semidirect
7. #11751217C2semidirect
8. #11750946C2semidirect
9. #11750942C2semidirect
10. #11750840C2semidirect
11. #11750839C2semidirect
12. #11750834C2semidirect
13. #11750832C2semidirect
14. #11750816C2semidirect
15. #11750811C2semidirect
20. C22×Dic30C22semidirect
21. C2×C3×C5×M16C22semidirect
29. #91813C22semidirect
31. C2×Dic60C22semidirect
32. C2×Dic60C22semidirect
33. C2×Dic60C22semidirect
49. #91758C22semidirect
50. C4×Dic30C22semidirect
51. C3×C5×C4⋊C8C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×C5×#97C22semidirect
57. #91102C22semidirect
58. #91100C22semidirect
59. #91100C22semidirect
60. #91100C22semidirect
61. #91100C22semidirect
67. C5×#435D3semidirect
139. #6706D4semidirect
144. C3×#435D5semidirect
159. C2×C5×M16C2×D3semidirect
189. C5×C4⋊C8C2×D3semidirect
191. C5×C22⋊C8C2×D3semidirect
192. C5×#97C2×D3semidirect
253. C2×C3×M16C2×D5semidirect
283. C3×C4⋊C8C2×D5semidirect
285. C3×C22⋊C8C2×D5semidirect
286. C3×#97C2×D5semidirect
370. #435D15semidirect
376. C22×C3×C5#137semidirect
522. C2×M16C2×D15semidirect
542. C4⋊C8C2×D15semidirect
550. C22⋊C8C2×D15semidirect
551. #97C2×D15semidirect
612. C22×C5#909semidirect
695. C3×C5#3266semidirect
701. C22×C3#4055semidirect
784. C5#79495semidirect
797. C22#91798semidirect
811. C3#10611226semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
C22×#67062
#117563092
D4×Dic302
C3×C5×#4352
#117512352
#117512172
#117509462
#117509422
#117508402
#117508392
#117508342
#117508322
#117508162
#117508112
#106112263
#794955