Finite Group Databasebeta

← #14458959

Subgroups — #14458959

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
1#11756324C211yesmaximal, characteristic, complemented
2C5×#5550C211yesmaximal, characteristic, complemented
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748535C211yesmaximal, characteristic, complemented
5#11748521C211yesmaximal, characteristic, complemented
6#11748520C211yesmaximal, characteristic, complemented
7#11748514C211yesmaximal, characteristic, complemented
8#11748467C211yesmaximal, characteristic, complemented
9#11748388C211yesmaximal, characteristic, complemented
10C2×#90967C211yesmaximal, characteristic, complemented
11#11748378C211yesmaximal, characteristic, complemented
12#11747046C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14#11746907C211yesmaximal, characteristic, complemented
15#11746894C211yesmaximal, characteristic, complemented
16#10615226—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20#91828—21no—
21#91819C2211yescharacteristic
22#91819C2211yescharacteristic, complemented
23#91815C2211yescharacteristic, complemented
24C2×C4⋊Dic15C2211yescharacteristic
25#91787—21no—
26#91772—21no—
27#91770—21no—
28C4×D60C2211yescharacteristic, complemented
29#91759C2211yescharacteristic, complemented
30C5×#937—21no—
31C5×#930C2211yescharacteristic
32C5×#924C2211yescharacteristic
33C5×#894—21no—
34C5×#884—21no—
35C5×D3×C22⋊C4—21no—
36C5×#875C2211yescharacteristic
37C4×C5×D12C2211yescharacteristic
38C22×C3×#168C2211yescharacteristic
39C22×C3×#168C2211yescharacteristic, complemented
40C2×#6660C2211yescharacteristic, complemented
41C2×#6654C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C3×C22⋊#168C2211yescharacteristic
44C3×C22⋊#168C2211yescharacteristic, complemented
45C3×C4⋊#168C2211yescharacteristic, complemented
46C3×C4×#168C2211yescharacteristic, complemented
47#90988C2211yescharacteristic, complemented
48#90988C2211yescharacteristic, complemented
49#90985C2211yescharacteristic, complemented
50#90973C2211yescharacteristic, complemented
51#90973C2211yescharacteristic, complemented
52#90973C2211yescharacteristic, complemented
53#90969C2211yescharacteristic, complemented
54#90967C2211yescharacteristic
55#90967C2211yescharacteristic
56#90967C2211yescharacteristic
57#90967C2211yescharacteristic
58#90967C2211yescharacteristic
59#90967C2211yescharacteristic
60#79441—51nomaximal, Hall
61C5×#546—31no—
62#65899—31no—
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×#168D311yescharacteristic, complemented
75#65298—31no—
76C23×C5×D3—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×#1220—21no—
82C22×Dic15—21no—
83C2×D60C2311yescharacteristic
84C2×C4×D15—21no—
85C2×C5×#67—21no—
86C2×C5×#67—21no—
87C5×#235—22no—
88C5×#235—41no—
89C2×C5×D12—22no—
90C2×C5×D12—21no—
91C2×C5×D12—41no—
92C2×C5×D12C2311yescharacteristic
93C2×C5×D12C2311yescharacteristic
94C2×C4×C5×D3—21no—
95C2×C4×C5×D3—21no—
96C2×C5×Dic6C2311yescharacteristic
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C22⋊C4D411yescharacteristic
99C3×C5×C22⋊C4D411yescharacteristic
100C3×C42×C5C2311yescharacteristic
101#6719—21no—
102#6714—21no—
103#6714—21no—
104#6714—21no—
105C4⋊Dic15—21no—
106C4⋊Dic15C2311yescharacteristic
107C4⋊Dic15C2311yescharacteristic
108C4⋊Dic15C2311yescharacteristic
109#6712—21no—
110#6712—21no—
111C4×Dic15—21no—
112C5×#217—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×C4⋊Dic3C2311yescharacteristic
118C5×Dic3⋊C4—21no—
119C2×C3×#168—41no—
120C2×C3×#168—41no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125#6660—41no—
126#6654—22no—
127#6654—41no—
128#5565—51no—
129#5550D511yescharacteristic, complemented
130C3×C8×D4—51no—
131#5115—51no—
132#5114—51no—
133#5113—51no—
134C2×#821—51no—
135#4847—51no—
136#4844—51no—
137#4737—51no—
138#4734—51no—
139#4732—51no—
140#4722—51no—
141#4697—51no—
142C4×D24—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—61no—
156C2×#686—31no—
157C2×#686—31no—
158#4076—31no—
159#4076—31no—
160#4072—31no—
161C2×C4⋊Dic5—31no—
162C22×#168C2×D311yescharacteristic
163C22×#168C2×D311yescharacteristic, complemented
164#4044—61no—
165#4029—61no—
166#4027—61no—
167C4×D20—31no—
168#4016—31no—
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⋊#168C2×D311yescharacteristic
179C22⋊#168C2×D311yescharacteristic, complemented
180#3941—31no—
181#3940—31no—
182#3939—31no—
183#3939—31no—
184C4⋊#168C2×D311yescharacteristic, complemented
185C4×#168C2×D311yescharacteristic, complemented
186#3297—151noSylow
187C23×C3×C5C2×D411yescharacteristic
188C23×C3×C5C2×D411yescharacteristic
189C22×D15—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—42no—
193C22×C5×D3—42no—
194C22×C5×D3—81no—
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
205#1220—42no—
206#1220—81no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209C2×Dic15—21no—
210C2×Dic15—81no—
211D60—21no—
212D60—21no—
213C4×D15—81no—
214C5×#67—42no—
215C5×#67—81no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3—21no—
218C5×D12—21no—
219C5×D12—21no—
220C5×D12—21no—
221C5×D12—42no—
222C5×D12#4112yes—
223C4×C5×D3—42no—
224C4×C5×D3—81no—
225C5×Dic6—21no—
226C5×Dic6—21no—
227C3×#168—21no—
228C3×#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#235C2×D511yescharacteristic
232C22×D12C2×D511yescharacteristic
233C22×C3×C8—51no—
234C22×C3×C8—51no—
235C3×C4×D4C2×D511yescharacteristic
236#939—101no—
237#937—21no—
238#930—51no—
239#930—51no—
240#930C2×D511yescharacteristic
241#926—51no—
242C2×C4⋊Dic3—51no—
243#924C2×D511yescharacteristic
244C2×D24—51no—
245C2×D24—51no—
246C2×#204—51no—
247#898—101no—
248#894—21no—
249#884—21no—
250#883—101no—
251#67⋊C4—101no—
252D3×C22⋊C4—21no—
253#875C2×D511yescharacteristic
254C4×D12—51no—
255C4×D12C2×D511yescharacteristic
256#870—51no—
257C3×C4⋊C8—51no—
258C3×C22⋊C8—51no—
259C3×C22⋊C8—51no—
260C3×C4×C8—51no—
261#821—51no—
262#821—51no—
263#821—51no—
264#821—51no—
265#821—51no—
266#821—51no—
267#821—51no—
268#818—51no—
269#818—51no—
270#817—51no—
271#816—51no—
272#816—51no—
273#816—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×D4D1211yescharacteristic
286C22×C4×C5—61no—
287C22×C4×C5—61no—
288C22×C4×C5C22×D311yescharacteristic
289C22×C4×C5C22×D311yescharacteristic
290C2×C22⋊D5—61no—
291C2×C22⋊D5—61no—
292C22×Dic5—61no—
293C2×D20—31no—
294C2×C4×D5—61no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—61no—
297C5×C4⋊C4D1211yescharacteristic
298C5×C22⋊C4—61no—
299C5×C22⋊C4—61no—
300C5×C22⋊C4—61no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C5×C22⋊C4D1211yescharacteristic
304C5×C22⋊C4D1211yescharacteristic
305C42×C5C22×D311yescharacteristic
306C22⋊Dic5—61no—
307#688—121no—
308#686—62no—
309#686—121no—
310#685—61no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5—31no—
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317#683—61no—
318#683—61no—
319C4×Dic5—61no—
320C2×#168—41no—
321C2×#168—41no—
322C2×#168C22×D311yescharacteristic
323C2×#168C22×D311yescharacteristic
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—151no—
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—51no—
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×D15—41no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—22no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C5×D3—41no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C2×C5×D3—84no—
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
364Dic15—41no—
365Dic15—41no—
366Dic15—41no—
367C5×Dic3—41no—
368C5×Dic3—41no—
369C23×D3—21no—
370C2×C3×D4C22⋊D511yescharacteristic
371C22×C3×C4C22×D511yescharacteristic
372C22×C3×C4C22×D511yescharacteristic
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—101no—
376C2×#67—101no—
377C22×Dic3—101no—
378#235—22no—
379#235—41no—
380C2×D12—22no—
381C2×D12—21no—
382C2×D12—41no—
383C2×D12—51no—
384C2×D12C22×D511yescharacteristic
385C2×D12C22×D511yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—21no—
388C2×C4×D3—101no—
389C2×Dic6C22×D511yescharacteristic
390C2×C3×C8—51no—
391C2×C3×C8—51no—
392C2×C3×C8—51no—
393C2×C3×C8—51no—
394C2×C3×C8—201no—
395C2×C3×C8—201no—
396C3×C4⋊C4C22⋊D511yescharacteristic
397C3×C22⋊C4C22⋊D511yescharacteristic
398C3×C22⋊C4C22⋊D511yescharacteristic
399C3×C42C22×D511yescharacteristic
400#217—21no—
401#217—101no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—51no—
410C4⋊Dic3—51no—
411C4⋊Dic3—51no—
412C4⋊Dic3—101no—
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—101no—
418D24—102no—
419D24—201no—
420#204—201no—
421C23×C5—61no—
422C23×C5—61no—
423C23×C5—122no—
424C23×C5—122no—
425C23×C5—241no—
426C23×C5C2×D1211yescharacteristic
427C23×C5C2×D1211yescharacteristic
428C22×D5—61no—
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×D1211yescharacteristic
448C2×C4×C5C2×D1211yescharacteristic
449C2×C4×C5C2×D1211yescharacteristic
450C2×C4×C5C2×D1211yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—122no—
453C22⋊D5—241no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—241no—
458D20—61no—
459D20—61no—
460C4×D5—241no—
461#168—21no—
462#168—21no—
463#168—21no—
464#168—21no—
465C2×#41—31no—
466C22×D4—31no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—51no—
471C22×C8—51no—
472#126—301no—
473#125—151no—
474#124—31no—
475#123—61no—
476#123—301no—
477C22⋊Q8—31no—
478#121—31no—
479#121—61no—
480#121—151no—
481#121—151no—
482#121—301no—
483#120—61no—
484C4×D4—31no—
485C4×D4—151no—
486C4×D4—301no—
487C4×D4D3×D511yescharacteristic
488#117—151no—
489C2×C4⋊C4—151no—
490C2×C22⋊C4—61no—
491#107—151no—
492#107—151no—
493#106—151no—
494C4⋊C8—51no—
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—51no—
506C22⋊C8—51no—
507C4×C8—51no—
508C2×C3×C5—22no—
509C2×C3×C5—41no—
510C2×C3×C5#54611yescharacteristic
511C2×C3×C5C2×#13511yescharacteristic
512C2×C3×C5#57611yescharacteristic
513D15—81no—
514C5×D3—42no—
515C5×D3—81no—
516C23×C3C2×C22⋊D511yescharacteristic
517C23×C3C2×C22⋊D511yescharacteristic
518C22×D3—21no—
519C22×D3—21no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—81no—
523C22×D3—101no—
524C3×D4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4C2×C22⋊D511yescharacteristic
530C2×C3×C4C2×C22⋊D511yescharacteristic
531C2×C3×C4C2×C22⋊D511yescharacteristic
532C2×C3×C4C2×C22⋊D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—42no—
535#67—81no—
536#67—202no—
537#67—401no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—101no—
541C2×Dic3—101no—
542C2×Dic3—101no—
543C2×Dic3—401no—
544D12—21no—
545D12—21no—
546D12—21no—
547D12—42no—
548D12—101no—
549D12—101no—
550D12#71112yes—
551C4×D3—42no—
552C4×D3—81no—
553C4×D3—401no—
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#90412yes—
573C22×C5C22×D1211yescharacteristic
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—121no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—121no—
582C4×C5—121no—
583C4×C5#100411yescharacteristic
584C4×C5D3×#4111yescharacteristic
585Dic5—121no—
586Dic5—121no—
587Dic5—121no—
588C24—61no—
589#41—62no—
590#41—121no—
591C2×Q8—31no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—62no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4—151no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4#120311yescharacteristic
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—301no—
606C22×C4—301no—
607C22×C4C2×D3×D511yescharacteristic
608C22×C4C2×D3×D511yescharacteristic
609SD16—601no—
610D8—302no—
611D8—601no—
612C2×C8—51no—
613C2×C8—51no—
614C2×C8—51no—
615C2×C8—51no—
616C2×C8—201no—
617C2×C8—201no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—151no—
621C4⋊C4—151no—
622C4⋊C4—151no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4#120311yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4#120311yescharacteristic
637C22⋊C4#120311yescharacteristic
638C42—301no—
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#409612yes—
647C22×C3C22×C22⋊D511yescharacteristic
648C2×D3—22no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—84no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—201no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4C2×#71111yescharacteristic
663C3×C4#414411yescharacteristic
664Dic3—41no—
665Dic3—41no—
666Dic3—201no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5—122no—
672C2×C5—241no—
673C2×C5#555411yescharacteristic
674C2×C5C2×#90411yescharacteristic
675C2×C5#575211yescharacteristic
676D5—241no—
677C23—61no—
678C23—61no—
679C23—122no—
680C23—122no—
681C23—241no—
682C23—301no—
683C23C2×#120311yescharacteristic
684C23C2×#120311yescharacteristic
685Q8—61no—
686Q8—61no—
687D4—22no—
688D4—32no—
689D4—61no—
690D4—61no—
691D4—61no—
692D4—122no—
693D4—122no—
694D4—241no—
695D4—301no—
696D4—301no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—122no—
706C2×C4—241no—
707C2×C4—301no—
708C2×C4—301no—
709C2×C4—301no—
710C2×C4—1201no—
711C2×C4—1201no—
712C2×C4C2×#120311yescharacteristic
713C2×C4C2×#120311yescharacteristic
714C2×C4C2×#120311yescharacteristic
715C2×C4C2×#120311yescharacteristic
716C2×C4C22×D3×D511yescharacteristic
717C8—101no—
718C8—101no—
719C8—101no—
720C8—101no—
721C2×C3—22no—
722C2×C3—41no—
723C2×C3#6614011yescharacteristic
724C2×C3C2×#409611yescharacteristic
725C2×C3#6616911yescharacteristic
726D3—42no—
727D3—81no—
728D3—401no—
729C5#7944111yescharacteristic, 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—244no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22#9130312yes—
746C22C22×#120311yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—121no—
752C4—121no—
753C4—601no—
754C4—601no—
755C4—601no—
756C4D3×#71111yescharacteristic
757C4#9202511yescharacteristic
758C3#1061522611yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—122no—
762C2—241no—
763C2—1201no—
764C2C2×#9130311yescharacteristic
765C2#1175497511yescharacteristic
766C2#1175530511yescharacteristic
subgroupG/H
centerC22C22×#1203
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. #11756324C2semidirect
2. C5×#5550C2semidirect
3. C3×D4×#168C2semidirect
4. #11748535C2semidirect
5. #11748521C2semidirect
6. #11748520C2semidirect
7. #11748514C2semidirect
8. #11748467C2semidirect
9. #11748388C2semidirect
10. C2×#90967C2semidirect
11. #11748378C2semidirect
12. #11747046C2semidirect
13. C4×#6654C2semidirect
14. #11746907C2semidirect
15. #11746894C2semidirect
22. #91819C22semidirect
23. #91815C22semidirect
28. C4×D60C22semidirect
29. #91759C22semidirect
39. C22×C3×#168C22semidirect
40. C2×#6660C22semidirect
44. C3×C22⋊#168C22semidirect
45. C3×C4⋊#168C22semidirect
46. C3×C4×#168C22semidirect
47. #90988C22semidirect
48. #90988C22semidirect
49. #90985C22semidirect
50. #90973C22semidirect
51. #90973C22semidirect
52. #90973C22semidirect
53. #90969C22semidirect
74. D4×#168D3semidirect
129. #5550D5semidirect
163. C22×#168C2×D3semidirect
179. C22⋊#168C2×D3semidirect
184. C4⋊#168C2×D3semidirect
185. C4×#168C2×D3semidirect
640. C3×C5#3297semidirect
729. C5#79441semidirect
758. C3#10615226semidirect

Maximal subgroups

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

subgroupindex
#117563242
C5×#55502
C3×D4×#1682
#117485352
#117485212
#117485202
#117485142
#117484672
#117483882
C2×#909672
#117483782
#117470462
C4×#66542
#117469072
#117468942
#106152263
#794415