Finite Group Databasebeta

← #14453975

Subgroups — #14453975

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91797C211yesmaximal, characteristic, complemented
2C2×#91793C211yesmaximal, characteristic, complemented
3#11756310C211yesmaximal, characteristic, complemented
4#11756309C211yesmaximal, characteristic, complemented
5C3×C5×#435C211yesmaximal, characteristic, complemented
6#11751238C211yesmaximal, characteristic, complemented
7#11751215C211yesmaximal, characteristic, complemented
8#11750945C211yesmaximal, characteristic, complemented
9#11750942C211yesmaximal, characteristic, complemented
10#11750835C211yesmaximal, characteristic, complemented
11#11750834C211yesmaximal, characteristic, complemented
12#11750834C211yesmaximal, characteristic, complemented
13#11750832C211yesmaximal, characteristic, complemented
14#11750816C211yesmaximal, characteristic, complemented
15#11750812C211yesmaximal, characteristic, complemented
16#10611227—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C2×#6817C2211yescharacteristic
19C2×#6817C2211yescharacteristic, complemented
20C22×D60C2211yescharacteristic
21C2×C3×C5×M16C2211yescharacteristic
22C22×C3×C5×C8C2211yescharacteristic, complemented
23C3×C4×C5×D4C2211yescharacteristic
24#91827—21no—
25#91826—21no—
26#91819C2211yescharacteristic
27#91813C2211yescharacteristic
28#91813C2211yescharacteristic
29#91813C2211yescharacteristic, complemented
30#91797—24no—
31C2×Dic60C2211yescharacteristic, complemented
32C2×Dic60C2211yescharacteristic, complemented
33#91793—24no—
34C2×D120C2211yescharacteristic
35C2×D120C2211yescharacteristic
36C2×#6706C2211yescharacteristic
37C2×#6706C2211yescharacteristic
38C2×#6706C2211yescharacteristic
39C2×#6706C2211yescharacteristic
40C2×#6706C2211yescharacteristic, complemented
41#91783—21no—
42C4⋊C4×D15—21no—
43#91773—21no—
44#91772—21no—
45#91772—21no—
46C22⋊C4×D15—21no—
47#91764C2211yescharacteristic
48C4×D60C2211yescharacteristic
49C4×D60C2211yescharacteristic, complemented
50#91758C2211yescharacteristic, complemented
51C3×C5×C4⋊C8C2211yescharacteristic, complemented
52C3×C5×C22⋊C8C2211yescharacteristic
53C3×C5×C22⋊C8C2211yescharacteristic, complemented
54C3×C5×#97C2211yescharacteristic, complemented
55#91105C2211yescharacteristic
56#91105C2211yescharacteristic
57#91105C2211yescharacteristic, complemented
58#91101C2211yescharacteristic, complemented
59#91100C2211yescharacteristic, complemented
60#91100C2211yescharacteristic, complemented
61#91100C2211yescharacteristic, complemented
62#79496—51nomaximal, Hall
63C2×#4054—31no—
64C2×#4050—31no—
65#65885—31no—
66#65884—31no—
67C5×#435D311yescharacteristic, complemented
68#65426—31no—
69#65403—31no—
70#65133—31no—
71#65130—31no—
72#65023—31no—
73#65022—31no—
74#65022—31no—
75#65020—31no—
76#65004—31no—
77#65000—31no—
78C23×D15—21no—
79C2×C3×C5×D4D411yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×#1220—21no—
83C2×#1220—21no—
84C2×#1220—21no—
85C2×#1220—21no—
86#6817—22no—
87#6817—22no—
88#6817—22no—
89#6817—41no—
90#6817—41no—
91#6817—41no—
92C2×D60—22no—
93C2×D60—21no—
94C2×D60—41no—
95C2×D60C2311yescharacteristic
96C2×D60C2311yescharacteristic
97C2×D60C2311yescharacteristic
98C2×C4×D15—21no—
99C2×C4×D15—21no—
100C2×C4×D15—21no—
101C2×C4×D15—21no—
102C2×C4×D15—21no—
103C2×Dic30C2311yescharacteristic
104C2×Dic30C2311yescharacteristic
105C2×Dic30C2311yescharacteristic
106C3×C5×M16—22no—
107C2×C3×C5×C8—22no—
108C2×C3×C5×C8C2311yescharacteristic
109C2×C3×C5×C8C2311yescharacteristic
110C2×C3×C5×C8C2311yescharacteristic
111C2×C3×C5×C8C2311yescharacteristic
112C3×C5×C4⋊C4D411yescharacteristic
113C3×C5×C22⋊C4D411yescharacteristic
114C3×C5×C22⋊C4D411yescharacteristic
115C3×C42×C5C2311yescharacteristic
116#6719—21no—
117#6719—21no—
118#6719—21no—
119#6714—21no—
120#6714—21no—
121#6714—21no—
122#6714—21no—
123#6714—21no—
124C4⋊Dic15—21no—
125C4⋊Dic15—21no—
126C4⋊Dic15C2311yescharacteristic
127C4⋊Dic15C2311yescharacteristic
128#6712—21no—
129#6712—21no—
130#6712—21no—
131Dic60—22no—
132Dic60—41no—
133D120—22no—
134D120D414yescomplemented
135#6706—22no—
136#6706—22no—
137#6706—22no—
138#6706—22no—
139#6706—41no—
140C2×#908—51no—
141C2×#904—51no—
142#5551—51no—
143#5550—51no—
144C3×#435D511yescharacteristic, complemented
145#5137—51no—
146#5114—51no—
147#4844—51no—
148#4841—51no—
149#4734—51no—
150#4733—51no—
151#4733—51no—
152#4731—51no—
153#4715—51no—
154#4711—51no—
155C2×#709—31no—
156C2×#709—31no—
157C2×#709—31no—
158C22×D20—31no—
159C2×C5×M16C2×D311yescharacteristic
160C22×C5×C8C2×D311yescharacteristic, complemented
161C4×C5×D4C2×D311yescharacteristic
162#4084—61no—
163#4083—61no—
164#4076—31no—
165#4070—31no—
166#4070—31no—
167#4070—31no—
168#4054—64no—
169C2×Dic20—31no—
170C2×Dic20—31no—
171#4050—64no—
172C2×D40—31no—
173C2×D40—31no—
174C2×#677—31no—
175C2×#677—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—31no—
179#4040—61no—
180D5×C4⋊C4—61no—
181#4030—61no—
182#4029—61no—
183#4029—61no—
184D5×C22⋊C4—61no—
185#4021—31no—
186C4×D20—31no—
187C4×D20—31no—
188#4015—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#3953—31no—
196#3949—31no—
197#3948—31no—
198#3948—31no—
199#3948—31no—
200#3267—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—42no—
207C22×D15—42no—
208C22×D15—81no—
209C3×C5×D4—41no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5C2×D411yescharacteristic
215C2×C3×C4×C5C2×D411yescharacteristic
216C2×C3×C4×C5C2×D411yescharacteristic
217C2×C3×C4×C5C2×D411yescharacteristic
218C2×C3×C4×C5C2411yescharacteristic
219#1220—42no—
220#1220—42no—
221#1220—42no—
222#1220—81no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228D60—21no—
229D60—21no—
230D60—21no—
231D60—21no—
232D60—42no—
233D60C2×D412yes—
234D60C2×D412yes—
235C4×D15—42no—
236C4×D15—42no—
237C4×D15—42no—
238C4×D15—42no—
239C4×D15—81no—
240Dic30—21no—
241Dic30—21no—
242Dic30—21no—
243Dic30—21no—
244Dic30—21no—
245Dic30—21no—
246C3×C5×C8—21no—
247C3×C5×C8—21no—
248C3×C5×C8—21no—
249C3×C5×C8C2×D412yes—
250C2×#235—51no—
251C2×#235—51no—
252C2×#235—51no—
253C22×D12—51no—
254C2×C3×M16C2×D511yescharacteristic
255C22×C3×C8C2×D511yescharacteristic, complemented
256C3×C4×D4C2×D511yescharacteristic
257#938—101no—
258#937—101no—
259#930—51no—
260#924—51no—
261#924—51no—
262#924—51no—
263#908—104no—
264C2×Dic12—51no—
265C2×Dic12—51no—
266#904—104no—
267C2×D24—51no—
268C2×D24—51no—
269C2×#204—51no—
270C2×#204—51no—
271C2×#204—51no—
272C2×#204—51no—
273C2×#204—51no—
274#894—101no—
275D3×C4⋊C4—101no—
276#884—101no—
277#883—101no—
278#883—101no—
279D3×C22⋊C4—101no—
280#875—51no—
281C4×D12—51no—
282C4×D12—51no—
283#869—51no—
284C3×C4⋊C8C2×D511yescharacteristic, complemented
285C3×C22⋊C8C2×D511yescharacteristic
286C3×C22⋊C8C2×D511yescharacteristic, complemented
287C3×#97C2×D511yescharacteristic, complemented
288#821—51no—
289#821—51no—
290#821—51no—
291#817—51no—
292#816—51no—
293#816—51no—
294#816—51no—
295C23×D5—61no—
296C2×C5×D4D1211yescharacteristic
297C22×C4×C5C22×D311yescharacteristic
298C22×C4×C5C22×D311yescharacteristic
299C2×C22⋊D5—61no—
300C2×C22⋊D5—61no—
301C2×C22⋊D5—61no—
302C2×C22⋊D5—61no—
303#709—62no—
304#709—62no—
305#709—62no—
306#709—121no—
307#709—121no—
308#709—121no—
309C2×D20—31no—
310C2×D20—31no—
311C2×D20—31no—
312C2×D20—62no—
313C2×D20—61no—
314C2×D20—121no—
315C2×C4×D5—61no—
316C2×C4×D5—61no—
317C2×C4×D5—61no—
318C2×C4×D5—61no—
319C2×C4×D5—61no—
320C2×Dic10—31no—
321C2×Dic10—31no—
322C2×Dic10—31no—
323C5×M16—22no—
324C2×C5×C8—22no—
325C2×C5×C8C22×D311yescharacteristic
326C2×C5×C8C22×D311yescharacteristic
327C2×C5×C8C22×D311yescharacteristic
328C2×C5×C8C22×D311yescharacteristic
329C5×C4⋊C4D1211yescharacteristic
330C5×C22⋊C4D1211yescharacteristic
331C5×C22⋊C4D1211yescharacteristic
332C42×C5C22×D311yescharacteristic
333C22⋊Dic5—61no—
334C22⋊Dic5—61no—
335C22⋊Dic5—61no—
336#685—61no—
337#685—61no—
338#685—61no—
339#685—61no—
340#685—61no—
341C4⋊Dic5—31no—
342C4⋊Dic5—31no—
343C4⋊Dic5—61no—
344C4⋊Dic5—61no—
345#683—61no—
346#683—61no—
347#683—61no—
348Dic20—62no—
349Dic20—121no—
350D40—34no—
351D40—62no—
352#677—62no—
353#677—62no—
354#677—62no—
355#677—62no—
356#677—121no—
357C2×AGL(1,ℤ/8)—151no—
358C2×#135—151no—
359#547—151no—
360#546—151no—
361#497—151no—
362#470—151no—
363#465—151no—
364#463—151no—
365#461—151no—
366#452—151no—
367#452—151no—
368#450—151no—
369#449—151no—
370#442—151no—
371#435D1511yescharacteristic, complemented
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5—21no—
377C22×C3×C5—21no—
378C22×C3×C5C22×D411yescharacteristic
379C2×D15—22no—
380C2×D15—22no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—41no—
385C2×D15—41no—
386C2×D15—41no—
387C2×D15—41no—
388C2×D15—84no—
389C3×C4×C5—21no—
390C3×C4×C5—21no—
391C3×C4×C5—21no—
392C3×C4×C5—21no—
393C3×C4×C5C22×D411yescharacteristic
394C3×C4×C5H(5,𝔽2)11yescharacteristic
395Dic15—41no—
396Dic15—41no—
397Dic15—41no—
398Dic15—41no—
399Dic15—41no—
400C23×D3—101no—
401C2×C3×D4D2011yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C22×C3×C4C22×D511yescharacteristic
404C2×#67—101no—
405C2×#67—101no—
406C2×#67—101no—
407C2×#67—101no—
408#235—102no—
409#235—102no—
410#235—102no—
411#235—201no—
412#235—201no—
413#235—201no—
414C2×D12—51no—
415C2×D12—51no—
416C2×D12—51no—
417C2×D12—102no—
418C2×D12—101no—
419C2×D12—201no—
420C2×C4×D3—101no—
421C2×C4×D3—101no—
422C2×C4×D3—101no—
423C2×C4×D3—101no—
424C2×C4×D3—101no—
425C2×Dic6—51no—
426C2×Dic6—51no—
427C2×Dic6—51no—
428C3×M16—22no—
429C2×C3×C8—22no—
430C2×C3×C8C22×D511yescharacteristic
431C2×C3×C8C22×D511yescharacteristic
432C2×C3×C8C22×D511yescharacteristic
433C2×C3×C8C22×D511yescharacteristic
434C3×C4⋊C4D2011yescharacteristic
435C3×C22⋊C4D2011yescharacteristic
436C3×C22⋊C4D2011yescharacteristic
437C3×C42C22×D511yescharacteristic
438#217—101no—
439#217—101no—
440#217—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444(C2×D3)⋊C4—101no—
445(C2×D3)⋊C4—101no—
446C4⋊Dic3—51no—
447C4⋊Dic3—51no—
448C4⋊Dic3—101no—
449C4⋊Dic3—101no—
450Dic3⋊C4—101no—
451Dic3⋊C4—101no—
452Dic3⋊C4—101no—
453Dic12—102no—
454Dic12—201no—
455D24—54no—
456D24—102no—
457#204—102no—
458#204—102no—
459#204—102no—
460#204—102no—
461#204—201no—
462C23×C5C2×D1211yescharacteristic
463C23×C5C2×D1211yescharacteristic
464C22×D5—61no—
465C22×D5—61no—
466C22×D5—61no—
467C22×D5—122no—
468C22×D5—122no—
469C22×D5—241no—
470C5×D4—41no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5C2×D1211yescharacteristic
476C2×C4×C5C2×D1211yescharacteristic
477C2×C4×C5C2×D1211yescharacteristic
478C2×C4×C5C2×D1211yescharacteristic
479C2×C4×C5C23×D311yescharacteristic
480C22⋊D5—122no—
481C22⋊D5—122no—
482C22⋊D5—122no—
483C22⋊D5—241no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486C2×Dic5—61no—
487C2×Dic5—61no—
488C2×Dic5—61no—
489D20—32no—
490D20—32no—
491D20—61no—
492D20—61no—
493D20—61no—
494D20—61no—
495D20—122no—
496C4×D5—122no—
497C4×D5—122no—
498C4×D5—122no—
499C4×D5—122no—
500C4×D5—241no—
501Dic10—61no—
502Dic10—61no—
503Dic10—61no—
504Dic10—61no—
505Dic10—61no—
506Dic10—61no—
507C5×C8—21no—
508C5×C8—21no—
509C5×C8—21no—
510C5×C8D3×D412yes—
511C2×#41—151no—
512C2×#41—151no—
513C2×#41—151no—
514C22×D4—151no—
515AGL(1,ℤ/8)—304no—
516#135—304no—
517C2×Q16—151no—
518C2×Q16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—151no—
522C2×SD16—151no—
523C2×SD16—151no—
524C2×D8—151no—
525C2×D8—151no—
526C2×M16C2×D1511yescharacteristic
527C22×C8C2×D1511yescharacteristic, complemented
528C4⋊Q8—151no—
529#124—151no—
530#123—301no—
531#123—301no—
532#123—301no—
533C22⋊Q8—151no—
534C22⋊Q8—151no—
535C22⋊Q8—151no—
536#121—151no—
537#121—301no—
538#121—301no—
539#120—301no—
540C4×D4—151no—
541C4×D4—151no—
542C4×D4C2×D1511yescharacteristic
543C2×C4⋊C4—301no—
544C2×C22⋊C4—301no—
545#106—151no—
546C4⋊C8C2×D1511yescharacteristic, complemented
547#103—151no—
548#103—151no—
549#103—151no—
550#102—151no—
551#102—151no—
552#102—151no—
553C22⋊C8C2×D1511yescharacteristic
554C22⋊C8C2×D1511yescharacteristic, complemented
555#97C2×D1511yescharacteristic, complemented
556C2×C3×C5—41no—
557C2×C3×C5—41no—
558C2×C3×C5D4211yescharacteristic
559C2×C3×C5#57511yescharacteristic
560C2×C3×C5#57711yescharacteristic
561D15—42no—
562D15—42no—
563D15—81no—
564C23×C3C2×D2011yescharacteristic
565C23×C3C2×D2011yescharacteristic
566C22×D3—101no—
567C22×D3—101no—
568C22×D3—101no—
569C22×D3—202no—
570C22×D3—202no—
571C22×D3—401no—
572C3×D4—41no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4C2×D2011yescharacteristic
578C2×C3×C4C2×D2011yescharacteristic
579C2×C3×C4C2×D2011yescharacteristic
580C2×C3×C4C2×D2011yescharacteristic
581C2×C3×C4C23×D511yescharacteristic
582#67—202no—
583#67—202no—
584#67—202no—
585#67—401no—
586C2×Dic3—101no—
587C2×Dic3—101no—
588C2×Dic3—101no—
589C2×Dic3—101no—
590C2×Dic3—101no—
591D12—52no—
592D12—52no—
593D12—101no—
594D12—101no—
595D12—101no—
596D12—101no—
597D12—202no—
598C4×D3—202no—
599C4×D3—202no—
600C4×D3—202no—
601C4×D3—202no—
602C4×D3—401no—
603Dic6—101no—
604Dic6—101no—
605Dic6—101no—
606Dic6—101no—
607Dic6—101no—
608Dic6—101no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8D4×D512yes—
613C22×C5—21no—
614C22×C5—21no—
615C22×C5—21no—
616C22×C5—21no—
617C22×C5—21no—
618C22×C5—21no—
619C22×C5C22×D1211yescharacteristic
620C2×D5—62no—
621C2×D5—62no—
622C2×D5—121no—
623C2×D5—121no—
624C2×D5—121no—
625C2×D5—121no—
626C2×D5—121no—
627C2×D5—121no—
628C2×D5—121no—
629C2×D5—244no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—21no—
633C4×C5—21no—
634C4×C5C2×D3×D411yescharacteristic
635C4×C5#100911yescharacteristic
636Dic5—121no—
637Dic5—121no—
638Dic5—121no—
639Dic5—121no—
640Dic5—121no—
641C24—301no—
642#41—302no—
643#41—302no—
644#41—302no—
645#41—601no—
646#41—601no—
647#41—601no—
648C2×Q8—151no—
649C2×Q8—151no—
650C2×Q8—151no—
651C2×D4—151no—
652C2×D4—151no—
653C2×D4—151no—
654C2×D4—302no—
655C2×D4—301no—
656C2×D4—301no—
657C2×D4—301no—
658C2×D4—301no—
659C2×D4—301no—
660C2×D4—601no—
661C2×D4D6011yescharacteristic
662C22×C4—301no—
663C22×C4—301no—
664C22×C4—301no—
665C22×C4—301no—
666C22×C4—301no—
667C22×C4C22×D1511yescharacteristic
668C22×C4C22×D1511yescharacteristic
669Q16—302no—
670Q16—601no—
671SD16—302no—
672SD16—302no—
673SD16—302no—
674SD16—302no—
675SD16—601no—
676D8—154no—
677D8—302no—
678M16—22no—
679C2×C8—22no—
680C2×C8C22×D1511yescharacteristic
681C2×C8C22×D1511yescharacteristic
682C2×C8C22×D1511yescharacteristic
683C2×C8C22×D1511yescharacteristic
684C4⋊C4—151no—
685C4⋊C4—151no—
686C4⋊C4—301no—
687C4⋊C4—301no—
688C4⋊C4—301no—
689C4⋊C4—301no—
690C4⋊C4—301no—
691C4⋊C4D6011yescharacteristic
692C22⋊C4—301no—
693C22⋊C4—301no—
694C22⋊C4—301no—
695C22⋊C4—301no—
696C22⋊C4—301no—
697C22⋊C4—301no—
698C22⋊C4—301no—
699C22⋊C4—301no—
700C22⋊C4D6011yescharacteristic
701C22⋊C4D6011yescharacteristic
702C42C22×D1511yescharacteristic
703C3×C5#326711yescharacteristic, complemented, Hall
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3C22×D2011yescharacteristic
711C2×D3—102no—
712C2×D3—102no—
713C2×D3—201no—
714C2×D3—201no—
715C2×D3—201no—
716C2×D3—201no—
717C2×D3—201no—
718C2×D3—201no—
719C2×D3—201no—
720C2×D3—404no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4C2×D4×D511yescharacteristic
726C3×C4#414911yescharacteristic
727Dic3—201no—
728Dic3—201no—
729Dic3—201no—
730Dic3—201no—
731Dic3—201no—
732C2×C5—41no—
733C2×C5—41no—
734C2×C5D4×D1211yescharacteristic
735C2×C5#574811yescharacteristic
736C2×C5#575111yescharacteristic
737D5—122no—
738D5—122no—
739D5—241no—
740C23—301no—
741C23—301no—
742C23—301no—
743C23—602no—
744C23—602no—
745C23—1201no—
746C23C2×D6011yescharacteristic
747C23C2×D6011yescharacteristic
748Q8—301no—
749Q8—301no—
750Q8—301no—
751Q8—301no—
752Q8—301no—
753Q8—301no—
754D4—41no—
755D4—152no—
756D4—152no—
757D4—301no—
758D4—301no—
759D4—301no—
760D4—301no—
761D4—602no—
762D4—602no—
763D4—602no—
764D4—602no—
765D4—1201no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—301no—
771C2×C4—301no—
772C2×C4—301no—
773C2×C4—301no—
774C2×C4—301no—
775C2×C4—602no—
776C2×C4—602no—
777C2×C4—602no—
778C2×C4—602no—
779C2×C4—1201no—
780C2×C4C2×D6011yescharacteristic
781C2×C4C2×D6011yescharacteristic
782C2×C4C2×D6011yescharacteristic
783C2×C4C2×D6011yescharacteristic
784C2×C4C23×D1511yescharacteristic
785C8—21no—
786C8—21no—
787C8—21no—
788C8D4×D1512yes—
789C2×C3—41no—
790C2×C3—41no—
791C2×C3D4×D2011yescharacteristic
792C2×C3#6608211yescharacteristic
793C2×C3#6608511yescharacteristic
794D3—202no—
795D3—202no—
796D3—401no—
797C5#7949611yescharacteristic, complemented, Sylow
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—302no—
805C22—302no—
806C22—601no—
807C22—601no—
808C22—601no—
809C22—601no—
810C22—601no—
811C22—601no—
812C22—601no—
813C22—1204no—
814C22C22×D6011yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—601no—
820C4—601no—
821C4—601no—
822C4—601no—
823C4—601no—
824C4C2×D4×D1511yescharacteristic
825C4#9210011yescharacteristic
826C3#1061122711yescharacteristic, complemented, Sylow
827C2—41no—
828C2—41no—
829C2—602no—
830C2—602no—
831C2—1201no—
832C2D4×D6011yescharacteristic
833C2#1175650711yescharacteristic
834C2#1175651011yescharacteristic
subgroupG/H
centerC22C22×D60
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#435C2
socleC22×C3×C5C22×D4
hypercenter#435D15
hypocenterC3×C5#3267
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×#91797C2semidirect
2. C2×#91793C2semidirect
3. #11756310C2semidirect
4. #11756309C2semidirect
5. C3×C5×#435C2semidirect
6. #11751238C2semidirect
7. #11751215C2semidirect
8. #11750945C2semidirect
9. #11750942C2semidirect
10. #11750835C2semidirect
11. #11750834C2semidirect
12. #11750834C2semidirect
13. #11750832C2semidirect
14. #11750816C2semidirect
15. #11750812C2semidirect
19. C2×#6817C22semidirect
22. C22×C3×C5×C8C22semidirect
29. #91813C22semidirect
31. C2×Dic60C22semidirect
32. C2×Dic60C22semidirect
40. C2×#6706C22semidirect
49. C4×D60C22semidirect
50. #91758C22semidirect
51. C3×C5×C4⋊C8C22semidirect
53. C3×C5×C22⋊C8C22semidirect
54. C3×C5×#97C22semidirect
57. #91105C22semidirect
58. #91101C22semidirect
59. #91100C22semidirect
60. #91100C22semidirect
61. #91100C22semidirect
67. C5×#435D3semidirect
134. D120D4semidirect
144. C3×#435D5semidirect
160. C22×C5×C8C2×D3semidirect
189. C5×C4⋊C8C2×D3semidirect
191. C5×C22⋊C8C2×D3semidirect
192. C5×#97C2×D3semidirect
255. C22×C3×C8C2×D5semidirect
284. C3×C4⋊C8C2×D5semidirect
286. C3×C22⋊C8C2×D5semidirect
287. C3×#97C2×D5semidirect
371. #435D15semidirect
527. C22×C8C2×D15semidirect
546. C4⋊C8C2×D15semidirect
554. C22⋊C8C2×D15semidirect
555. #97C2×D15semidirect
703. C3×C5#3267semidirect
797. C5#79496semidirect
826. C3#10611227semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
C2×#917932
#117563102
#117563092
C3×C5×#4352
#117512382
#117512152
#117509452
#117509422
#117508352
#117508342
#117508322
#117508162
#117508122
#106112273
#794965