Finite Group Databasebeta

← #14458958

Subgroups — #14458958

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5550C211yesmaximal, characteristic, complemented
2C3×#65899C211yesmaximal, characteristic, complemented
3D4×C3⋊#168C211yesmaximal, characteristic, complemented
4#11748545C211yesmaximal, characteristic, complemented
5#11748522C211yesmaximal, characteristic, complemented
6#11748517C211yesmaximal, characteristic, complemented
7#11748516C211yesmaximal, characteristic, complemented
8#11748471C211yesmaximal, characteristic, complemented
9#11748383C211yesmaximal, characteristic, complemented
10#11748382C211yesmaximal, characteristic, complemented
11C2×#90966C211yesmaximal, characteristic, complemented
12#11747027C211yesmaximal, characteristic, complemented
13C4×#6652C211yesmaximal, characteristic, complemented
14#11746903C211yesmaximal, characteristic, complemented
15#11746902C211yesmaximal, characteristic, complemented
16#10615226—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic, complemented
22C5×#937—21no—
23C5×#930C2211yescharacteristic
24C5×#924C2211yescharacteristic
25C5×#894—21no—
26C5×#884—21no—
27C5×D3×C22⋊C4—21no—
28C5×#875C2211yescharacteristic
29C4×C5×D12C2211yescharacteristic
30C3×#4085—21no—
31C3×#4076C2211yescharacteristic
32C3×#4076C2211yescharacteristic, complemented
33C3×#4072C2211yescharacteristic, complemented
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C3×#4044—21no—
36C3×#4029—21no—
37C3×#4027—21no—
38C3×C4×D20C2211yescharacteristic, complemented
39C3×#4016C2211yescharacteristic, complemented
40C2×#6655C2211yescharacteristic, complemented
41C2×#6652C2211yescharacteristic
42C2×#6652C2211yescharacteristic
43#91114C2211yescharacteristic
44#91114C2211yescharacteristic, complemented
45C4⋊(C3⋊#168)C2211yescharacteristic, complemented
46C4×C3⋊#168C2211yescharacteristic, complemented
47#90989C2211yescharacteristic, complemented
48#90989C2211yescharacteristic, complemented
49#90986C2211yescharacteristic, complemented
50#90972C2211yescharacteristic, complemented
51#90972C2211yescharacteristic, complemented
52#90972C2211yescharacteristic, complemented
53#90966C2211yescharacteristic
54#90966C2211yescharacteristic
55#90966C2211yescharacteristic
56#90966C2211yescharacteristic
57#90966C2211yescharacteristic
58#90966C2211yescharacteristic
59#90964C2211yescharacteristic, complemented
60#83614—51nomaximal, Hall
61C5×#546—31no—
62#65899D311yescharacteristic, complemented
63#65527—31no—
64#65522—31no—
65#65506—31no—
66C2×#3964—31no—
67#65346—31no—
68#65345—31no—
69#65337—31no—
70#65333—31no—
71#65327—31no—
72#65324—31no—
73C4×#686—31no—
74D4×#168—31no—
75#65298—31no—
76C23×C5×D3—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C5×#67—21no—
81C2×C5×#67—21no—
82C5×#235—22no—
83C5×#235—41no—
84C2×C5×D12—22no—
85C2×C5×D12—21no—
86C2×C5×D12—41no—
87C2×C5×D12C2311yescharacteristic
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C4×C5×D3—21no—
91C2×C5×Dic6C2311yescharacteristic
92C2×C3×C22⋊D5—21no—
93C2×C3×C22⋊D5—21no—
94C22×C3×Dic5—21no—
95C2×C3×D20C2311yescharacteristic
96C2×C3×C4×D5—21no—
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C22⋊C4D411yescharacteristic
99C3×C5×C22⋊C4D411yescharacteristic
100C3×C42×C5C2311yescharacteristic
101C2×C3⋊#168—41no—
102C2×C3⋊#168—41no—
103C2×C3⋊#168C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C2×C3⋊#168C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C5×#217—21no—
108C5×(C2×D3)⋊C4—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4—21no—
111C5×(C2×D3)⋊C4—21no—
112C5×C4⋊Dic3C2311yescharacteristic
113C5×Dic3⋊C4—21no—
114C3×C22⋊Dic5—21no—
115C3×#685—21no—
116C3×#685—21no—
117C3×#685—21no—
118C3×C4⋊Dic5—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C3×C4⋊Dic5C2311yescharacteristic
121C3×C4⋊Dic5C2311yescharacteristic
122C3×#683—21no—
123C3×#683—21no—
124C3×C4×Dic5—21no—
125#6655—41no—
126#6652—22no—
127#6652—41no—
128C3×#553—51no—
129#5550D511yescharacteristic, complemented
130#5068—51no—
131#5066—51no—
132#5041—51no—
133#5038—51no—
134#5037—51no—
135#5036—51no—
136#5016—51no—
137C4×#213—51no—
138D4×C3⋊C8—51no—
139#5003—51no—
140#5002—51no—
141#4970—51no—
142C2×#809—51no—
143C2×C5×#41—31no—
144C22×C5×D4—31no—
145C5×#124—31no—
146C5×#123—61no—
147C5×C22⋊Q8—31no—
148C5×#121—31no—
149C5×#121—61no—
150C5×#120—61no—
151C4×C5×D4—31no—
152C4×C5×D4C2×D311yescharacteristic
153C2×C5×C22⋊C4—61no—
154C2×#688—31no—
155#4085—21no—
156C2×#686—31no—
157C2×#686—31no—
158#4076C2×D311yescharacteristic
159#4076C2×D311yescharacteristic, complemented
160#4072C2×D311yescharacteristic, complemented
161C2×C4⋊Dic5C2×D311yescharacteristic
162C22×#168—31no—
163C22×#168—31no—
164#4044—21no—
165#4029—21no—
166#4027—21no—
167C4×D20C2×D311yescharacteristic, complemented
168#4016C2×D311yescharacteristic, complemented
169#3967—31no—
170#3967—31no—
171#3967—31no—
172#3964—31no—
173#3964—31no—
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964—31no—
178C22⋊#168—31no—
179C22⋊#168—31no—
180#3941—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168—31no—
185C4×#168—31no—
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—42no—
192C22×C5×D3—42no—
193C22×C5×D3—81no—
194C22×C3×D5—21no—
195C3×C5×D4—22no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205C5×#67—42no—
206C5×#67—81no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C5×D12—21no—
210C5×D12—21no—
211C5×D12—21no—
212C5×D12—42no—
213C5×D12#4112yes—
214C4×C5×D3—42no—
215C4×C5×D3—81no—
216C5×Dic6—21no—
217C5×Dic6—21no—
218C3×C22⋊D5—42no—
219C3×C22⋊D5—81no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—81no—
224C3×D20—21no—
225C3×D20—21no—
226C3×C4×D5—81no—
227C3⋊#168—21no—
228C3⋊#168—21no—
229C3⋊#168—21no—
230C3⋊#168—21no—
231C2×#235C2×D511yescharacteristic
232C22×D12C2×D511yescharacteristic
233C3×#126—101no—
234C3×#125—51no—
235C3×#123—101no—
236C3×#121—51no—
237C3×#121—51no—
238C3×#121—101no—
239C3×C4×D4—51no—
240C3×C4×D4—101no—
241C3×C4×D4C2×D511yescharacteristic
242C3×#117—51no—
243C2×C3×C4⋊C4—51no—
244#937—21no—
245C2×#214—51no—
246C2×#213—51no—
247C2×#213—51no—
248#930C2×D511yescharacteristic
249#924C2×D511yescharacteristic
250C22×C3⋊C8—51no—
251C22×C3⋊C8—51no—
252#894—21no—
253#884—21no—
254D3×C22⋊C4—21no—
255#875C2×D511yescharacteristic
256C4×D12C2×D511yescharacteristic
257#832—51no—
258#830—51no—
259#830—51no—
260#810—51no—
261#810—51no—
262#810—51no—
263#809—51no—
264#809—51no—
265#809—51no—
266#809—51no—
267#809—51no—
268#809—51no—
269#808—51no—
270#807—51no—
271#807—51no—
272C4⋊(C3⋊C8)—51no—
273C4×C3⋊C8—51no—
274C24×C5—61no—
275C5×#41—62no—
276C5×#41—121no—
277C2×C5×Q8—31no—
278C2×C5×D4—31no—
279C2×C5×D4—31no—
280C2×C5×D4—62no—
281C2×C5×D4—61no—
282C2×C5×D4—61no—
283C2×C5×D4—61no—
284C2×C5×D4—121no—
285C2×C5×D4#6711yescharacteristic
286C22×C4×C5—61no—
287C22×C4×C5—61no—
288C22×C4×C5C22×D311yescharacteristic
289C22×C4×C5C22×D311yescharacteristic
290C2×C22⋊D5—21no—
291C2×C22⋊D5—21no—
292C22×Dic5—21no—
293C2×D20C22×D311yescharacteristic
294C2×C4×D5—21no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4#6711yescharacteristic
298C5×C22⋊C4—61no—
299C5×C22⋊C4—61no—
300C5×C22⋊C4—61no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4#6711yescharacteristic
304C5×C22⋊C4#6711yescharacteristic
305C42×C5C22×D311yescharacteristic
306C22⋊Dic5—21no—
307#688—121no—
308#686—62no—
309#686—121no—
310#685—21no—
311#685—21no—
312#685—21no—
313C4⋊Dic5—21no—
314C4⋊Dic5C22×D311yescharacteristic
315C4⋊Dic5C22×D311yescharacteristic
316C4⋊Dic5C22×D311yescharacteristic
317#683—21no—
318#683—21no—
319C4×Dic5—21no—
320C2×#168—31no—
321C2×#168—31no—
322C2×#168—31no—
323C2×#168—31no—
324C2×#168—121no—
325C2×#168—121no—
326#553—51no—
327#546—31no—
328#488—151no—
329#484—151no—
330#482—151no—
331#478—151no—
332#466—151no—
333#465—151no—
334#463—151no—
335#449—151no—
336#447—151no—
337C4×D8—151no—
338C8×D4—151no—
339#416—151no—
340C2×#102—151no—
341C22×C3×C5—21no—
342C22×C3×C5—21no—
343C22×C3×C5—21no—
344C22×C3×C5—21no—
345C22×C3×C5—21no—
346C22×C3×C5#13512yes—
347C22×C3×C5C22×D411yescharacteristic
348C2×C5×D3—22no—
349C2×C5×D3—41no—
350C2×C5×D3—41no—
351C2×C5×D3—41no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C5×D3—84no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C2×C3×D5—41no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—21no—
362C3×C4×C5C2×#4111yescharacteristic
363C3×C4×C5H(5,𝔽2)11yescharacteristic
364C3×Dic5—41no—
365C3×Dic5—41no—
366C3×Dic5—41no—
367C5×Dic3—41no—
368C5×Dic3—41no—
369C23×D3—21no—
370C2×C3×D4—51no—
371C2×C3×D4—101no—
372C2×C3×D4—101no—
373C2×C3×D4C22⋊D511yescharacteristic
374C22×C3×C4—101no—
375C22×C3×C4—101no—
376C22×C3×C4C22×D511yescharacteristic
377C22×C3×C4C22×D511yescharacteristic
378C2×#67—21no—
379C2×#67—21no—
380#235—22no—
381#235—41no—
382C2×D12—22no—
383C2×D12—21no—
384C2×D12—41no—
385C2×D12C22×D511yescharacteristic
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×Dic6C22×D511yescharacteristic
390C3×C4⋊C4—51no—
391C3×C4⋊C4—51no—
392C3×C4⋊C4—51no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4—101no—
395C3×C4⋊C4—101no—
396C3×C4⋊C4C22⋊D511yescharacteristic
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4C22⋊D511yescharacteristic
402C3×C22⋊C4C22⋊D511yescharacteristic
403C3×C42—101no—
404C3×C42C22×D511yescharacteristic
405#217—21no—
406#214—201no—
407#213—102no—
408#213—201no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—21no—
415C2×C3⋊C8—51no—
416C2×C3⋊C8—51no—
417C2×C3⋊C8—51no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8—201no—
420C2×C3⋊C8—201no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—122no—
424C23×C5—122no—
425C23×C5—241no—
426C23×C5C2×#6711yescharacteristic
427C23×C5C2×#6711yescharacteristic
428C22×D5—21no—
429C5×Q8—61no—
430C5×Q8—61no—
431C5×D4—22no—
432C5×D4—32no—
433C5×D4—61no—
434C5×D4—61no—
435C5×D4—61no—
436C5×D4—122no—
437C5×D4—122no—
438C5×D4—241no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—61no—
444C2×C4×C5—61no—
445C2×C4×C5—122no—
446C2×C4×C5—241no—
447C2×C4×C5C2×#6711yescharacteristic
448C2×C4×C5C2×#6711yescharacteristic
449C2×C4×C5C2×#6711yescharacteristic
450C2×C4×C5C2×#6711yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—42no—
453C22⋊D5—81no—
454C2×Dic5—21no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—81no—
458D20—21no—
459D20—21no—
460C4×D5—81no—
461#168—61no—
462#168—61no—
463#168—61no—
464#168—61no—
465C2×#41—31no—
466C22×D4—31no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—151no—
471C22×C8—151no—
472#126—101no—
473#125—51no—
474#124—31no—
475#123—61no—
476#123—101no—
477C22⋊Q8—31no—
478#121—31no—
479#121—51no—
480#121—51no—
481#121—61no—
482#121—101no—
483#120—61no—
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—101no—
487C4×D4D3×D511yescharacteristic
488#117—51no—
489C2×C4⋊C4—51no—
490C2×C22⋊C4—61no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—151no—
495#103—151no—
496#103—151no—
497#103—151no—
498#102—151no—
499#102—151no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505C22⋊C8—151no—
506C22⋊C8—151no—
507C4×C8—151no—
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513C3×D5—81no—
514C5×D3—42no—
515C5×D3—81no—
516C23×C3—101no—
517C23×C3C2×C22⋊D511yescharacteristic
518C23×C3C2×C22⋊D511yescharacteristic
519C22×D3—21no—
520C22×D3—21no—
521C22×D3—42no—
522C22×D3—42no—
523C22×D3—81no—
524C3×D4—22no—
525C3×D4—101no—
526C3×D4—101no—
527C3×D4—202no—
528C3×D4—401no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—401no—
537C2×C3×C4—401no—
538C2×C3×C4C2×C22⋊D511yescharacteristic
539C2×C3×C4C2×C22⋊D511yescharacteristic
540C2×C3×C4C2×C22⋊D511yescharacteristic
541C2×C3×C4C2×C22⋊D511yescharacteristic
542C2×C3×C4C23×D511yescharacteristic
543#67—42no—
544#67—81no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547D12—21no—
548D12—21no—
549D12—21no—
550D12—42no—
551D12#71112yes—
552C4×D3—42no—
553C4×D3—81no—
554Dic6—21no—
555Dic6—21no—
556C3⋊C8—101no—
557C3⋊C8—101no—
558C3⋊C8—101no—
559C3⋊C8—101no—
560C22×C5—21no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5—62no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5—121no—
571C22×C5—244no—
572C22×C5#95012yes—
573C22×C5C22×#6711yescharacteristic
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—41no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—121no—
582C4×C5—121no—
583C4×C5D3×#4111yescharacteristic
584C4×C5#100911yescharacteristic
585Dic5—41no—
586Dic5—41no—
587Dic5—41no—
588C24—61no—
589#41—62no—
590#41—121no—
591C2×Q8—31no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—51no—
595C2×D4—62no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—101no—
600C2×D4—101no—
601C2×D4—121no—
602C2×D4#120111yescharacteristic
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4C2×D3×D511yescharacteristic
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—151no—
613C2×C8—151no—
614C2×C8—151no—
615C2×C8—151no—
616C2×C8—601no—
617C2×C8—601no—
618C4⋊C4—31no—
619C4⋊C4—51no—
620C4⋊C4—51no—
621C4⋊C4—51no—
622C4⋊C4—61no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4—101no—
626C4⋊C4#120111yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—101no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4#120111yescharacteristic
637C22⋊C4#120111yescharacteristic
638C42—101no—
639C42C2×D3×D511yescharacteristic
640C3×C5#329711yescharacteristic, complemented, Hall
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—201no—
647C22×C3—201no—
648C22×C3—201no—
649C22×C3#409612yes—
650C22×C3C22×C22⋊D511yescharacteristic
651C2×D3—22no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—201no—
663C3×C4—201no—
664C3×C4—201no—
665C3×C4C2×#71111yescharacteristic
666C3×C4#414411yescharacteristic
667Dic3—41no—
668Dic3—41no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5—122no—
672C2×C5—241no—
673C2×C5C2×#95011yescharacteristic
674C2×C5#582911yescharacteristic
675C2×C5#583511yescharacteristic
676D5—81no—
677C23—61no—
678C23—61no—
679C23—101no—
680C23—122no—
681C23—122no—
682C23—241no—
683C23C2×#120111yescharacteristic
684C23C2×#120111yescharacteristic
685Q8—61no—
686Q8—61no—
687D4—22no—
688D4—32no—
689D4—61no—
690D4—61no—
691D4—61no—
692D4—101no—
693D4—101no—
694D4—122no—
695D4—122no—
696D4—202no—
697D4—241no—
698D4—401no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—101no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—122no—
709C2×C4—241no—
710C2×C4—401no—
711C2×C4—401no—
712C2×C4C2×#120111yescharacteristic
713C2×C4C2×#120111yescharacteristic
714C2×C4C2×#120111yescharacteristic
715C2×C4C2×#120111yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—301no—
718C8—301no—
719C8—301no—
720C8—301no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3—401no—
724C2×C3#6614011yescharacteristic
725C2×C3C2×#409611yescharacteristic
726C2×C3#6616911yescharacteristic
727D3—42no—
728D3—81no—
729C5#8361411yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—62no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—201no—
742C22—201no—
743C22—201no—
744C22—244no—
745C22#9129712yes—
746C22C22×#120111yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—121no—
752C4—121no—
753C4—201no—
754C4—201no—
755C4—201no—
756C4D3×#71111yescharacteristic
757C4#9202711yescharacteristic
758C3#1061522611yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—122no—
762C2—241no—
763C2—401no—
764C2C2×#9129711yescharacteristic
765C2#1175496811yescharacteristic
766C2#1175530111yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#3297
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5550C2semidirect
2. C3×#65899C2semidirect
3. D4×C3⋊#168C2semidirect
4. #11748545C2semidirect
5. #11748522C2semidirect
6. #11748517C2semidirect
7. #11748516C2semidirect
8. #11748471C2semidirect
9. #11748383C2semidirect
10. #11748382C2semidirect
11. C2×#90966C2semidirect
12. #11747027C2semidirect
13. C4×#6652C2semidirect
14. #11746903C2semidirect
15. #11746902C2semidirect
21. C22×C3⋊#168C22semidirect
32. C3×#4076C22semidirect
33. C3×#4072C22semidirect
38. C3×C4×D20C22semidirect
39. C3×#4016C22semidirect
40. C2×#6655C22semidirect
44. #91114C22semidirect
45. C4⋊(C3⋊#168)C22semidirect
46. C4×C3⋊#168C22semidirect
47. #90989C22semidirect
48. #90989C22semidirect
49. #90986C22semidirect
50. #90972C22semidirect
51. #90972C22semidirect
52. #90972C22semidirect
59. #90964C22semidirect
62. #65899D3semidirect
129. #5550D5semidirect
159. #4076C2×D3semidirect
160. #4072C2×D3semidirect
167. C4×D20C2×D3semidirect
168. #4016C2×D3semidirect
640. C3×C5#3297semidirect
729. C5#83614semidirect
758. C3#10615226semidirect

Maximal subgroups

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

subgroupindex
C5×#55502
C3×#658992
D4×C3⋊#1682
#117485452
#117485222
#117485172
#117485162
#117484712
#117483832
#117483822
C2×#909662
#117470272
C4×#66522
#117469032
#117469022
#106152263
#836145