Finite Group Databasebeta

← #14458283

Subgroups — #14458283

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
1D4×#1220C211yesmaximal, characteristic, complemented
2#11756266C211yesmaximal, characteristic, complemented
3C2×C3×C5×#102C211yesmaximal, characteristic, complemented
4#11751318C211yesmaximal, characteristic, complemented
5#11751216C211yesmaximal, characteristic, complemented
6C8×#1220C211yesmaximal, characteristic, complemented
7#11751068C211yesmaximal, characteristic, complemented
8#11750887C211yesmaximal, characteristic, complemented
9#11750876C211yesmaximal, characteristic, complemented
10#11750875C211yesmaximal, characteristic, complemented
11#11750874C211yesmaximal, characteristic, complemented
12D15×#102C211yesmaximal, characteristic, complemented
13#11750861C211yesmaximal, characteristic, complemented
14#11750860C211yesmaximal, characteristic, complemented
15#11750857C211yesmaximal, characteristic, complemented
16#10610488—31nomaximal, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×#1220—21no—
19C2×D4×D15C2211yescharacteristic
20C2×#6817—21no—
21C22×C3×C5×C8C2211yescharacteristic, complemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23#91842—21no—
24#91829C2211yescharacteristic
25#91828—21no—
26#91827C2211yescharacteristic
27#91826—21no—
28D4×Dic15C2211yescharacteristic
29C2×#6715C2211yescharacteristic
30C2×#6715C2211yescharacteristic, complemented
31#91819C2211yescharacteristic
32#91819C2211yescharacteristic, complemented
33#91818—21no—
34C4×#1220C2211yescharacteristic
35C2×D120C2211yescharacteristic, complemented
36C2×C8×D15C2211yescharacteristic, complemented
37#91785—21no—
38#91784C2211yescharacteristic, complemented
39#91783—21no—
40#91782C2211yescharacteristic, complemented
41C4⋊C4×D15C2211yescharacteristic, complemented
42#91777C2211yescharacteristic, complemented
43C3×C5×#102C2211yescharacteristic
44C3×C5×#102C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46C3×C5×#102C2211yescharacteristic, complemented
47#91116C2211yescharacteristic
48#91116C2211yescharacteristic, complemented
49#91114C2211yescharacteristic, complemented
50#91105C2211yescharacteristic, complemented
51#91105C2211yescharacteristic, complemented
52#91104C2211yescharacteristic, complemented
53#91102C2211yescharacteristic, complemented
54#91098C2211yescharacteristic, complemented
55C8×Dic15C2211yescharacteristic, complemented
56#91093C2211yescharacteristic, complemented
57#91093C2211yescharacteristic, complemented
58#91091C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60#78757—51nomaximal, Hall
61D4×C22⋊D5—31no—
62#65841—31no—
63C2×C5×#102D311yescharacteristic, complemented
64#65506—31no—
65#65404—31no—
66C8×C22⋊D5—31no—
67#65256—31no—
68#65075—31no—
69#65064—31no—
70#65063—31no—
71#65062—31no—
72D5×#102—31no—
73#65049—31no—
74#65048—31no—
75#65045—31no—
76C24×C3×C5—21no—
77C23×D15—21no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4—41no—
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5C2311yescharacteristic
85C2×#1220—21no—
86C2×#1220—21no—
87C2×#1220—21no—
88C2×#1220—21no—
89C2×#1220—21no—
90C2×#1220—21no—
91C2×#1220—44no—
92C2×#1220D411yescharacteristic
93C22×Dic15—21no—
94D4×D15—22no—
95D4×D15—41no—
96#6817—44no—
97C2×D60—21no—
98C2×D60C2311yescharacteristic
99C2×D60C2311yescharacteristic
100C2×C4×D15—21no—
101C2×C4×D15—21no—
102C2×C4×D15C2311yescharacteristic
103C2×Dic30—21no—
104C2×C3×C5×C8—41no—
105C2×C3×C5×C8C2311yescharacteristic
106C2×C3×C5×C8C2311yescharacteristic
107C3×C5×C4⋊C4—21no—
108C3×C5×C4⋊C4C2311yescharacteristic
109C3×C5×C4⋊C4C2311yescharacteristic
110#6719—21no—
111#6719—21no—
112#6719D411yescharacteristic
113#6715—22no—
114#6715—41no—
115#6714—21no—
116#6714—21no—
117#6714—21no—
118#6714—21no—
119#6714D411yescharacteristic
120C4⋊Dic15C2311yescharacteristic
121C4⋊Dic15C2311yescharacteristic
122#6712—21no—
123#6712—21no—
124#6712D411yescharacteristic
125C4×Dic15C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128D120—41no—
129C8×D15—41no—
130D4×#67—51no—
131#5507—51no—
132C2×C3×#102D511yescharacteristic, complemented
133#5217—51no—
134#5115—51no—
135C8×#67—51no—
136#4967—51no—
137#4786—51no—
138#4775—51no—
139#4774—51no—
140#4773—51no—
141D3×#102—51no—
142#4760—51no—
143#4759—51no—
144#4756—51no—
145C22×C5×D4C2×D311yescharacteristic
146C22×C22⋊D5—61no—
147C2×D4×D5—31no—
148C2×#709—61no—
149C22×C5×C8C2×D311yescharacteristic, complemented
150C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
151#4099—61no—
152#4086—31no—
153#4085—61no—
154#4084—31no—
155#4083—61no—
156D4×Dic5—31no—
157C2×#686—31no—
158C2×#686—31no—
159#4076—31no—
160#4076—31no—
161#4075—61no—
162C4×C22⋊D5—31no—
163C2×D40—31no—
164C2×C8×D5—31no—
165#4042—61no—
166#4041—31no—
167#4040—61no—
168#4039—31no—
169D5×C4⋊C4—31no—
170#4034—31no—
171C5×#102C2×D311yescharacteristic
172C5×#102C2×D311yescharacteristic
173C5×#102C2×D311yescharacteristic, complemented
174C5×#102C2×D311yescharacteristic, complemented
175#3964—31no—
176#3964—31no—
177C22⋊#168—31no—
178#3953—31no—
179#3953—31no—
180#3952—31no—
181#3950—31no—
182#3946—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941—31no—
186#3939—31no—
187#3939—31no—
188#3294—151noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—42no—
192C23×C3×C5—42no—
193C23×C3×C5—81no—
194C23×C3×C5C2×D411yescharacteristic
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—42no—
198C22×D15—42no—
199C22×D15—81no—
200C22×D15C2×D411yescharacteristic
201C3×C5×D4—21no—
202C3×C5×D4—21no—
203C3×C5×D4—21no—
204C3×C5×D4—42no—
205C3×C5×D4#4112yescomplemented
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—42no—
211C2×C3×C4×C5C2×D411yescharacteristic
212C2×C3×C4×C5C2411yescharacteristic
213#1220—42no—
214#1220—42no—
215#1220—42no—
216#1220—42no—
217#1220—42no—
218#1220—81no—
219#1220D814yescomplemented
220C2×Dic15—21no—
221C2×Dic15—21no—
222C2×Dic15—42no—
223C2×Dic15C2×D411yescharacteristic
224C2×Dic15C2×D411yescharacteristic
225C2×Dic15C2×D411yescharacteristic
226D60—21no—
227D60—21no—
228D60—21no—
229D60—21no—
230D60—42no—
231C4×D15—21no—
232C4×D15—21no—
233C4×D15—42no—
234C4×D15—42no—
235Dic30—42no—
236C3×C5×C8—21no—
237C3×C5×C8—21no—
238C3⋊#168—21no—
239C3⋊#168—21no—
240C22×C3×D4C2×D511yescharacteristic
241C22×#67—101no—
242C2×D3×D4—51no—
243C2×#235—101no—
244C22×C3×C8C2×D511yescharacteristic, complemented
245C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
246#953—101no—
247#940—51no—
248#939—101no—
249#938—51no—
250#937—101no—
251D4×Dic3—51no—
252C2×#213—51no—
253C2×#213—51no—
254#930—51no—
255#930—51no—
256#929—101no—
257C4×#67—51no—
258C2×D24—51no—
259C2×D3×C8—51no—
260#896—101no—
261#895—51no—
262#894—101no—
263#893—51no—
264D3×C4⋊C4—51no—
265#888—51no—
266C3×#102C2×D511yescharacteristic
267C3×#102C2×D511yescharacteristic
268C3×#102C2×D511yescharacteristic, complemented
269C3×#102C2×D511yescharacteristic, complemented
270#832—51no—
271#832—51no—
272#830—51no—
273#821—51no—
274#821—51no—
275(C2×D3)⋊C8—51no—
276#818—51no—
277Dic3⋊C8—51no—
278C8×Dic3—51no—
279#809—51no—
280#809—51no—
281#807—51no—
282#807—51no—
283C24×C5—21no—
284C23×D5—61no—
285C2×C5×D4—22no—
286C2×C5×D4—21no—
287C2×C5×D4—41no—
288C2×C5×D4C22×D311yescharacteristic
289C2×C5×D4C22×D311yescharacteristic
290C22×C4×C5—21no—
291C22×C4×C5C22×D311yescharacteristic
292C2×C22⋊D5—31no—
293C2×C22⋊D5—61no—
294C2×C22⋊D5—61no—
295C2×C22⋊D5—61no—
296C2×C22⋊D5—61no—
297C2×C22⋊D5—61no—
298C2×C22⋊D5—61no—
299C2×C22⋊D5—124no—
300C22×Dic5—61no—
301D4×D5—62no—
302D4×D5—121no—
303#709—124no—
304C2×D20—31no—
305C2×D20—31no—
306C2×D20—61no—
307C2×C4×D5—31no—
308C2×C4×D5—61no—
309C2×C4×D5—61no—
310C2×Dic10—61no—
311C2×C5×C8—41no—
312C2×C5×C8C22×D311yescharacteristic
313C2×C5×C8C22×D311yescharacteristic
314C5×C4⋊C4—21no—
315C5×C4⋊C4C22×D311yescharacteristic
316C5×C4⋊C4C22×D311yescharacteristic
317C22⋊Dic5—31no—
318C22⋊Dic5—61no—
319C22⋊Dic5—61no—
320#686—62no—
321#686—121no—
322#685—31no—
323#685—61no—
324#685—61no—
325#685—61no—
326#685—61no—
327C4⋊Dic5—31no—
328C4⋊Dic5—31no—
329#683—31no—
330#683—61no—
331#683—61no—
332C4×Dic5—31no—
333C2×#168—31no—
334C2×#168—31no—
335D40—121no—
336C8×D5—121no—
337#547—151no—
338D42—151no—
339#486—151no—
340#480—151no—
341#480—151no—
342#474—151no—
343#466—151no—
344#466—151no—
345#459—151no—
346#447—151no—
347#447—151no—
348C4×D8—151no—
349C8×D4—151no—
350C2×#102—151no—
351C2×#102D1511yescharacteristic, complemented
352C22×C3×C5—21no—
353C22×C3×C5—21no—
354C22×C3×C5—22no—
355C22×C3×C5—41no—
356C22×C3×C5—41no—
357C22×C3×C5—41no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5—84no—
361C22×C3×C5C2×D812yes—
362C22×C3×C5C22×D411yescharacteristic
363C2×D15—21no—
364C2×D15—21no—
365C2×D15—41no—
366C2×D15—41no—
367C2×D15—41no—
368C2×D15—41no—
369C2×D15—41no—
370C2×D15—41no—
371C2×D15—84no—
372C2×D15C2×D812yes—
373C3×C4×C5—21no—
374C3×C4×C5—41no—
375C3×C4×C5—41no—
376C3×C4×C5C2×#4111yescharacteristic
377C3×C4×C5H(5,𝔽2)11yescharacteristic
378Dic15—21no—
379Dic15—21no—
380Dic15—41no—
381Dic15—41no—
382Dic15C2×D812yes—
383C24×C3—21no—
384C23×D3—101no—
385C2×C3×D4—22no—
386C2×C3×D4—21no—
387C2×C3×D4—41no—
388C2×C3×D4C22×D511yescharacteristic
389C2×C3×D4C22×D511yescharacteristic
390C22×C3×C4—21no—
391C22×C3×C4C22×D511yescharacteristic
392C2×#67—51no—
393C2×#67—101no—
394C2×#67—101no—
395C2×#67—101no—
396C2×#67—101no—
397C2×#67—101no—
398C2×#67—101no—
399C2×#67—204no—
400C22×Dic3—101no—
401D3×D4—102no—
402D3×D4—201no—
403#235—204no—
404C2×D12—51no—
405C2×D12—51no—
406C2×D12—101no—
407C2×C4×D3—51no—
408C2×C4×D3—101no—
409C2×C4×D3—101no—
410C2×Dic6—101no—
411C2×C3×C8—41no—
412C2×C3×C8C22×D511yescharacteristic
413C2×C3×C8C22×D511yescharacteristic
414C3×C4⋊C4—21no—
415C3×C4⋊C4C22×D511yescharacteristic
416C3×C4⋊C4C22×D511yescharacteristic
417#217—51no—
418#217—101no—
419#217—101no—
420#213—102no—
421#213—201no—
422(C2×D3)⋊C4—51no—
423(C2×D3)⋊C4—101no—
424(C2×D3)⋊C4—101no—
425(C2×D3)⋊C4—101no—
426(C2×D3)⋊C4—101no—
427C4⋊Dic3—51no—
428C4⋊Dic3—51no—
429Dic3⋊C4—51no—
430Dic3⋊C4—101no—
431Dic3⋊C4—101no—
432C4×Dic3—51no—
433C2×C3⋊C8—51no—
434C2×C3⋊C8—51no—
435D24—201no—
436D3×C8—201no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—42no—
440C23×C5—42no—
441C23×C5—81no—
442C23×C5D3×D411yescharacteristic
443C22×D5—31no—
444C22×D5—61no—
445C22×D5—61no—
446C22×D5—122no—
447C22×D5—122no—
448C22×D5—241no—
449C5×D4—21no—
450C5×D4—21no—
451C5×D4—21no—
452C5×D4—42no—
453C5×D4#23512yescomplemented
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—42no—
459C2×C4×C5D3×D411yescharacteristic
460C2×C4×C5C23×D311yescharacteristic
461C22⋊D5—34no—
462C22⋊D5—122no—
463C22⋊D5—122no—
464C22⋊D5—122no—
465C22⋊D5—122no—
466C22⋊D5—122no—
467C22⋊D5—241no—
468C2×Dic5—31no—
469C2×Dic5—31no—
470C2×Dic5—31no—
471C2×Dic5—61no—
472C2×Dic5—61no—
473C2×Dic5—122no—
474D20—61no—
475D20—61no—
476D20—61no—
477D20—61no—
478D20—122no—
479C4×D5—61no—
480C4×D5—61no—
481C4×D5—122no—
482C4×D5—122no—
483Dic10—122no—
484C5×C8—21no—
485C5×C8—21no—
486#168—61no—
487#168—61no—
488C2×#41—301no—
489C22×D4—151no—
490C22×D4—301no—
491C22×D4C2×D1511yescharacteristic
492C2×D8—151no—
493C2×D8—151no—
494C2×D8—151no—
495C22×C8—151no—
496C22×C8C2×D1511yescharacteristic, complemented
497C4⋊Q8—151no—
498#127—151no—
499#123—301no—
500#123—301no—
501C22⋊Q8—301no—
502#121—151no—
503#121—151no—
504#121—151no—
505#121—151no—
506#121—301no—
507#120—301no—
508#120—301no—
509C4×D4—151no—
510C4×D4—151no—
511C4×D4—151no—
512C2×C4⋊C4—151no—
513C2×C4⋊C4C2×D1511yescharacteristic, complemented
514#107—151no—
515#107—151no—
516#107—151no—
517C4⋊C8—151no—
518#102—151no—
519#102—151no—
520#102—151no—
521#102—151no—
522#102—151no—
523#102—151no—
524#102C2×D1511yescharacteristic
525#102C2×D1511yescharacteristic
526#102C2×D1511yescharacteristic, complemented
527#102C2×D1511yescharacteristic, complemented
528C22⋊C8—151no—
529C22⋊C8—151no—
530C4×C8—151no—
531C2×C3×C5—22no—
532C2×C3×C5—42no—
533C2×C3×C5—81no—
534C2×C3×C5#54611yescharacteristic
535C2×C3×C5C22×D811yescharacteristic
536C2×C3×C5#57711yescharacteristic
537D15—22no—
538D15—81no—
539D15—81no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—42no—
543C23×C3—42no—
544C23×C3—81no—
545C23×C3D4×D511yescharacteristic
546C22×D3—51no—
547C22×D3—101no—
548C22×D3—101no—
549C22×D3—202no—
550C22×D3—202no—
551C22×D3—401no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—42no—
556C3×D4#70912yescomplemented
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—42no—
562C2×C3×C4D4×D511yescharacteristic
563C2×C3×C4C23×D511yescharacteristic
564#67—54no—
565#67—202no—
566#67—202no—
567#67—202no—
568#67—202no—
569#67—202no—
570#67—401no—
571C2×Dic3—51no—
572C2×Dic3—51no—
573C2×Dic3—51no—
574C2×Dic3—101no—
575C2×Dic3—101no—
576C2×Dic3—202no—
577D12—101no—
578D12—101no—
579D12—101no—
580D12—101no—
581D12—202no—
582C4×D3—101no—
583C4×D3—101no—
584C4×D3—202no—
585C4×D3—202no—
586Dic6—202no—
587C3×C8—21no—
588C3×C8—21no—
589C3⋊C8—101no—
590C3⋊C8—101no—
591C22×C5—21no—
592C22×C5—21no—
593C22×C5—22no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5—41no—
597C22×C5—41no—
598C22×C5—41no—
599C22×C5—84no—
600C22×C5D3×D812yes—
601C22×C5C2×D3×D411yescharacteristic
602C2×D5—32no—
603C2×D5—61no—
604C2×D5—61no—
605C2×D5—121no—
606C2×D5—121no—
607C2×D5—121no—
608C2×D5—121no—
609C2×D5—121no—
610C2×D5—121no—
611C2×D5—244no—
612C4×C5—21no—
613C4×C5—41no—
614C4×C5—41no—
615C4×C5C2×#23511yescharacteristic
616C4×C5#100411yescharacteristic
617Dic5—32no—
618Dic5—61no—
619Dic5—61no—
620Dic5—121no—
621Dic5—121no—
622C24—21no—
623C24—301no—
624#41—604no—
625C2×Q8—301no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—151no—
630C2×D4—151no—
631C2×D4—151no—
632C2×D4—301no—
633C2×D4—301no—
634C2×D4—301no—
635C2×D4—301no—
636C2×D4—302no—
637C2×D4—301no—
638C2×D4—301no—
639C2×D4—301no—
640C2×D4—601no—
641C2×D4—604no—
642C2×D4C22×D1511yescharacteristic
643C2×D4C22×D1511yescharacteristic
644C22×C4—21no—
645C22×C4—151no—
646C22×C4—301no—
647C22×C4—301no—
648C22×C4—301no—
649C22×C4C22×D1511yescharacteristic
650D8—302no—
651D8—601no—
652D8—601no—
653C2×C8—41no—
654C2×C8—151no—
655C2×C8—151no—
656C2×C8—601no—
657C2×C8C22×D1511yescharacteristic
658C2×C8C22×D1511yescharacteristic
659C4⋊C4—21no—
660C4⋊C4—151no—
661C4⋊C4—151no—
662C4⋊C4—151no—
663C4⋊C4—301no—
664C4⋊C4—301no—
665C4⋊C4C22×D1511yescharacteristic
666C4⋊C4C22×D1511yescharacteristic
667C22⋊C4—151no—
668C22⋊C4—151no—
669C22⋊C4—301no—
670C22⋊C4—301no—
671C22⋊C4—301no—
672C22⋊C4—301no—
673C22⋊C4—301no—
674C22⋊C4—301no—
675C42—151no—
676C3×C5#329411yescharacteristic, complemented, Hall
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—22no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—84no—
686C22×C3D5×D812yes—
687C22×C3C2×D4×D511yescharacteristic
688C2×D3—52no—
689C2×D3—101no—
690C2×D3—101no—
691C2×D3—201no—
692C2×D3—201no—
693C2×D3—201no—
694C2×D3—201no—
695C2×D3—201no—
696C2×D3—201no—
697C2×D3—404no—
698C3×C4—21no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4C2×#70911yescharacteristic
702C3×C4#414411yescharacteristic
703Dic3—52no—
704Dic3—101no—
705Dic3—101no—
706Dic3—201no—
707Dic3—201no—
708C2×C5—22no—
709C2×C5—42no—
710C2×C5—81no—
711C2×C5#549011yescharacteristic
712C2×C5C2×D3×D811yescharacteristic
713C2×C5#576211yescharacteristic
714D5—62no—
715D5—241no—
716D5—241no—
717C23—21no—
718C23—21no—
719C23—42no—
720C23—42no—
721C23—81no—
722C23—151no—
723C23—301no—
724C23—301no—
725C23—602no—
726C23—602no—
727C23—1201no—
728C23D4×D1511yescharacteristic
729Q8—602no—
730D4—21no—
731D4—21no—
732D4—21no—
733D4—42no—
734D4—154no—
735D4—301no—
736D4—301no—
737D4—301no—
738D4—301no—
739D4—602no—
740D4—602no—
741D4—602no—
742D4—602no—
743D4—602no—
744D4—602no—
745D4—1201no—
746D4#681712yescomplemented
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—42no—
752C2×C4—151no—
753C2×C4—151no—
754C2×C4—151no—
755C2×C4—301no—
756C2×C4—301no—
757C2×C4—301no—
758C2×C4—301no—
759C2×C4—602no—
760C2×C4—602no—
761C2×C4—602no—
762C2×C4D4×D1511yescharacteristic
763C2×C4C23×D1511yescharacteristic
764C8—21no—
765C8—21no—
766C8—301no—
767C8—301no—
768C2×C3—22no—
769C2×C3—42no—
770C2×C3—81no—
771C2×C3#6582411yescharacteristic
772C2×C3C2×D5×D811yescharacteristic
773C2×C3#6609611yescharacteristic
774D3—102no—
775D3—401no—
776D3—401no—
777C5#7875711yescharacteristic, complemented, Sylow
778C22—21no—
779C22—21no—
780C22—22no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—84no—
787C22—152no—
788C22—301no—
789C22—301no—
790C22—601no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22D8×D1512yes—
798C22C2×D4×D1511yescharacteristic
799C4—21no—
800C4—41no—
801C4—41no—
802C4—152no—
803C4—301no—
804C4—301no—
805C4—601no—
806C4—601no—
807C4C2×#681711yescharacteristic
808C4#9209511yescharacteristic
809C3#1061048811yescharacteristic, complemented, Sylow
810C2—22no—
811C2—42no—
812C2—81no—
813C2—302no—
814C2—1201no—
815C2—1201no—
816C2#1175624911yescharacteristic
817C2C2×D8×D1511yescharacteristic
818C2#1175652111yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#102C2
socleC22×C3×C5C22×D4
hypercenterC2×#102D15
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. D4×#1220C2semidirect
2. #11756266C2semidirect
3. C2×C3×C5×#102C2semidirect
4. #11751318C2semidirect
5. #11751216C2semidirect
6. C8×#1220C2semidirect
7. #11751068C2semidirect
8. #11750887C2semidirect
9. #11750876C2semidirect
10. #11750875C2semidirect
11. #11750874C2semidirect
12. D15×#102C2semidirect
13. #11750861C2semidirect
14. #11750860C2semidirect
15. #11750857C2semidirect
21. C22×C3×C5×C8C22semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
30. C2×#6715C22semidirect
32. #91819C22semidirect
35. C2×D120C22semidirect
36. C2×C8×D15C22semidirect
38. #91784C22semidirect
40. #91782C22semidirect
41. C4⋊C4×D15C22semidirect
42. #91777C22semidirect
45. C3×C5×#102C22semidirect
46. C3×C5×#102C22semidirect
48. #91116C22semidirect
49. #91114C22semidirect
50. #91105C22semidirect
51. #91105C22semidirect
52. #91104C22semidirect
53. #91102C22semidirect
54. #91098C22semidirect
55. C8×Dic15C22semidirect
56. #91093C22semidirect
57. #91093C22semidirect
58. #91091C22semidirect
59. #91091C22semidirect
63. C2×C5×#102D3semidirect
132. C2×C3×#102D5semidirect
149. C22×C5×C8C2×D3semidirect
150. C2×C5×C4⋊C4C2×D3semidirect
173. C5×#102C2×D3semidirect
174. C5×#102C2×D3semidirect
205. C3×C5×D4#41semidirect
219. #1220D8semidirect
244. C22×C3×C8C2×D5semidirect
245. C2×C3×C4⋊C4C2×D5semidirect
268. C3×#102C2×D5semidirect
269. C3×#102C2×D5semidirect
351. C2×#102D15semidirect
453. C5×D4#235semidirect
496. C22×C8C2×D15semidirect
513. C2×C4⋊C4C2×D15semidirect
526. #102C2×D15semidirect
527. #102C2×D15semidirect
556. C3×D4#709semidirect
676. C3×C5#3294semidirect
746. D4#6817semidirect
777. C5#78757semidirect
809. C3#10610488semidirect

Maximal subgroups

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

subgroupindex
D4×#12202
#117562662
C2×C3×C5×#1022
#117513182
#117512162
C8×#12202
#117510682
#117508872
#117508762
#117508752
#117508742
D15×#1022
#117508612
#117508602
#117508572
#106104883
#787575