Finite Group Databasebeta

← #14458957

Subgroups — #14458957

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#11756309C211yesmaximal, characteristic, complemented
2C5×#5565C211yesmaximal, characteristic, complemented
3C3×D4×#168C211yesmaximal, characteristic, complemented
4#11748533C211yesmaximal, characteristic, complemented
5#11748526C211yesmaximal, characteristic, complemented
6#11748525C211yesmaximal, characteristic, complemented
7#11748514C211yesmaximal, characteristic, complemented
8#11748464C211yesmaximal, characteristic, complemented
9C2×#90969C211yesmaximal, characteristic, complemented
10#11748393C211yesmaximal, characteristic, complemented
11#11748373C211yesmaximal, characteristic, complemented
12#11747038C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14#11746913C211yesmaximal, characteristic, complemented
15#11746899C211yesmaximal, characteristic, complemented
16#10615345—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C22×D60C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20#91826—21no—
21#91819C2211yescharacteristic
22#91813C2211yescharacteristic
23#91783—21no—
24#91773—21no—
25C22⋊C4×D15—21no—
26#91764C2211yescharacteristic
27C4×D60C2211yescharacteristic
28C5×#939—21no—
29C5×#930C2211yescharacteristic
30C5×#930C2211yescharacteristic, complemented
31C5×#926C2211yescharacteristic, complemented
32C2×C5×C4⋊Dic3C2211yescharacteristic
33C5×#898—21no—
34C5×#883—21no—
35C5×#67⋊C4—21no—
36C4×C5×D12C2211yescharacteristic, complemented
37C5×#870C2211yescharacteristic, complemented
38C22×C3×#168C2211yescharacteristic
39C22×C3×#168C2211yescharacteristic, complemented
40C2×#6659C2211yescharacteristic, 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#90975C2211yescharacteristic, complemented
51#90975C2211yescharacteristic, complemented
52#90975C2211yescharacteristic, complemented
53#90969C2211yescharacteristic
54#90969C2211yescharacteristic
55#90969C2211yescharacteristic
56#90969C2211yescharacteristic
57#90969C2211yescharacteristic
58#90969C2211yescharacteristic
59#90967C2211yescharacteristic, complemented
60#79441—51nomaximal, Hall
61C5×#553—31no—
62#65884—31no—
63#65357—31no—
64#65355—31no—
65#65330—31no—
66#65327—31no—
67#65326—31no—
68#65325—31no—
69#65305—31no—
70C4×#686—31no—
71D4×#168D311yescharacteristic, complemented
72#65292—31no—
73#65291—31no—
74#65259—31no—
75C2×#3941—31no—
76C23×D15—21no—
77C2×C3×C5×D4D411yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×#1220—21no—
81C2×#1220—21no—
82#6817—22no—
83#6817—41no—
84C2×D60—22no—
85C2×D60—21no—
86C2×D60—41no—
87C2×D60C2311yescharacteristic
88C2×D60C2311yescharacteristic
89C2×C4×D15—21no—
90C2×C4×D15—21no—
91C2×Dic30C2311yescharacteristic
92C2×C5×#67—21no—
93C2×C5×#67—21no—
94C22×C5×Dic3—21no—
95C2×C5×D12C2311yescharacteristic
96C2×C4×C5×D3—21no—
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—
105#6714—21no—
106C4⋊Dic15C2311yescharacteristic
107#6712—21no—
108C5×#217—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4—21no—
111C5×(C2×D3)⋊C4—21no—
112C5×C4⋊Dic3—21no—
113C5×C4⋊Dic3C2311yescharacteristic
114C5×C4⋊Dic3C2311yescharacteristic
115C5×C4⋊Dic3C2311yescharacteristic
116C5×Dic3⋊C4—21no—
117C5×Dic3⋊C4—21no—
118C4×C5×Dic3—21no—
119C2×C3×#168—41no—
120C2×C3×#168—41no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125#6659—41no—
126#6654—22no—
127#6654—41no—
128#5565D511yescharacteristic, complemented
129#5550—51no—
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×#709—31no—
144C22×D20—31no—
145C5×#126—61no—
146C5×#125—31no—
147C5×#123—61no—
148C5×#121—31no—
149C5×#121—31no—
150C5×#121—61no—
151C4×C5×D4—31no—
152C4×C5×D4—61no—
153C4×C5×D4C2×D311yescharacteristic
154C5×#117—31no—
155C2×C5×C4⋊C4—31no—
156#4083—61no—
157C2×#687—31no—
158C2×#686—31no—
159C2×#686—31no—
160#4076—31no—
161#4070—31no—
162C22×#168C2×D311yescharacteristic
163C22×#168C2×D311yescharacteristic, complemented
164#4040—61no—
165#4030—61no—
166D5×C22⋊C4—61no—
167#4021—31no—
168C4×D20—31no—
169#3964—31no—
170C22⋊#168C2×D311yescharacteristic
171C22⋊#168C2×D311yescharacteristic, complemented
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3941—31no—
176#3941—31no—
177#3941—31no—
178#3941—31no—
179#3941—31no—
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×D15—21no—
191C22×D15—42no—
192C22×D15—42no—
193C22×D15—81no—
194C22×C5×D3—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
205#1220—42no—
206#1220—81no—
207C2×Dic15—21no—
208C2×Dic15—21no—
209D60—21no—
210D60—21no—
211D60—21no—
212D60—42no—
213D60#4112yes—
214C4×D15—42no—
215C4×D15—81no—
216Dic30—21no—
217Dic30—21no—
218C5×#67—42no—
219C5×#67—81no—
220C2×C5×Dic3—21no—
221C2×C5×Dic3—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—81no—
224C5×D12—21no—
225C5×D12—21no—
226C4×C5×D3—81no—
227C3×#168—21no—
228C3×#168—21no—
229C3×#168—21no—
230C3×#168—21no—
231C2×#235—51no—
232C22×D12—51no—
233C22×C3×C8—51no—
234C22×C3×C8—51no—
235C3×C4×D4C2×D511yescharacteristic
236#939—21no—
237#937—101no—
238#930—51no—
239#930C2×D511yescharacteristic
240#930C2×D511yescharacteristic, complemented
241#926C2×D511yescharacteristic, complemented
242C2×C4⋊Dic3C2×D511yescharacteristic
243#924—51no—
244C2×D24—51no—
245C2×D24—51no—
246C2×#204—51no—
247#898—21no—
248#894—101no—
249#884—101no—
250#883—21no—
251#67⋊C4—21no—
252D3×C22⋊C4—101no—
253#875—51no—
254C4×D12—51no—
255C4×D12C2×D511yescharacteristic, complemented
256#870C2×D511yescharacteristic, complemented
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—
274C23×D5—61no—
275C2×C5×D4—31no—
276C2×C5×D4—61no—
277C2×C5×D4—61no—
278C2×C5×D4D1211yescharacteristic
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C22×C4×C5C22×D311yescharacteristic
282C22×C4×C5C22×D311yescharacteristic
283C2×C22⋊D5—61no—
284C2×C22⋊D5—61no—
285#709—62no—
286#709—121no—
287C2×D20—31no—
288C2×D20—31no—
289C2×D20—62no—
290C2×D20—61no—
291C2×D20—121no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×Dic10—31no—
295C5×C4⋊C4—31no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—31no—
298C5×C4⋊C4—61no—
299C5×C4⋊C4—61no—
300C5×C4⋊C4—61no—
301C5×C4⋊C4D1211yescharacteristic
302C5×C22⋊C4—61no—
303C5×C22⋊C4—61no—
304C5×C22⋊C4—61no—
305C5×C22⋊C4—61no—
306C5×C22⋊C4D1211yescharacteristic
307C5×C22⋊C4D1211yescharacteristic
308C42×C5—61no—
309C42×C5C22×D311yescharacteristic
310C22⋊Dic5—61no—
311#687—121no—
312#686—62no—
313#686—121no—
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318C4⋊Dic5—31no—
319#683—61no—
320C2×#168—41no—
321C2×#168—41no—
322C2×#168C22×D311yescharacteristic
323C2×#168C22×D311yescharacteristic
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326#553—31no—
327#546—151no—
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—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—84no—
355C2×C5×D3—41no—
356C2×C5×D3—41no—
357C2×C5×D3—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
364Dic15—41no—
365Dic15—41no—
366C5×Dic3—41no—
367C5×Dic3—41no—
368C5×Dic3—41no—
369C23×D3—101no—
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—21no—
378#235—102no—
379#235—201no—
380C2×D12—51no—
381C2×D12—51no—
382C2×D12—102no—
383C2×D12—101no—
384C2×D12—201no—
385C2×D12C22×D511yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6—51no—
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—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—21no—
410C4⋊Dic3—51no—
411C4⋊Dic3C22×D511yescharacteristic
412C4⋊Dic3C22×D511yescharacteristic
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—101no—
417C4×Dic3—21no—
418D24—102no—
419D24—201no—
420#204—201no—
421C23×C5—61no—
422C23×C5C2×D1211yescharacteristic
423C23×C5C2×D1211yescharacteristic
424C22×D5—61no—
425C22×D5—61no—
426C22×D5—122no—
427C22×D5—122no—
428C22×D5—241no—
429C5×D4—22no—
430C5×D4—61no—
431C5×D4—61no—
432C5×D4—122no—
433C5×D4—241no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—241no—
442C2×C4×C5—241no—
443C2×C4×C5C2×D1211yescharacteristic
444C2×C4×C5C2×D1211yescharacteristic
445C2×C4×C5C2×D1211yescharacteristic
446C2×C4×C5C2×D1211yescharacteristic
447C2×C4×C5C23×D311yescharacteristic
448C22⋊D5—122no—
449C22⋊D5—241no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452D20—32no—
453D20—61no—
454D20—61no—
455D20—61no—
456D20—122no—
457C4×D5—122no—
458C4×D5—241no—
459Dic10—61no—
460Dic10—61no—
461#168—21no—
462#168—21no—
463#168—21no—
464#168—21no—
465C2×#41—151no—
466C22×D4—151no—
467C2×SD16—151no—
468C2×D8—151no—
469C2×D8—151no—
470C22×C8—51no—
471C22×C8—51no—
472#126—61no—
473#125—31no—
474#124—151no—
475#123—61no—
476#123—301no—
477C22⋊Q8—151no—
478#121—31no—
479#121—31no—
480#121—61no—
481#121—151no—
482#121—301no—
483#120—301no—
484C4×D4—31no—
485C4×D4—61no—
486C4×D4—151no—
487C4×D4D3×D511yescharacteristic
488#117—31no—
489C2×C4⋊C4—31no—
490C2×C22⋊C4—301no—
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—42no—
514D15—81no—
515C5×D3—81no—
516C23×C3C2×C22⋊D511yescharacteristic
517C23×C3C2×C22⋊D511yescharacteristic
518C22×D3—21no—
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3—401no—
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—21no—
541C2×Dic3—81no—
542C2×Dic3—101no—
543C2×Dic3—101no—
544D12—21no—
545D12—21no—
546D12—52no—
547D12—101no—
548D12—101no—
549D12—101no—
550D12—202no—
551C4×D3—81no—
552C4×D3—202no—
553C4×D3—401no—
554Dic6—101no—
555Dic6—101no—
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—121no—
566C22×C5—121no—
567C22×C5—121no—
568C22×C5#90412yes—
569C22×C5C22×D1211yescharacteristic
570C2×D5—62no—
571C2×D5—121no—
572C2×D5—121no—
573C2×D5—121no—
574C2×D5—121no—
575C2×D5—121no—
576C2×D5—244no—
577C4×C5—21no—
578C4×C5—21no—
579C4×C5—21no—
580C4×C5—21no—
581C4×C5—121no—
582C4×C5—121no—
583C4×C5—121no—
584C4×C5#100411yescharacteristic
585C4×C5D3×#4111yescharacteristic
586Dic5—121no—
587Dic5—121no—
588C24—301no—
589#41—302no—
590#41—601no—
591C2×Q8—151no—
592C2×D4—31no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—151no—
596C2×D4—151no—
597C2×D4—302no—
598C2×D4—301no—
599C2×D4—301no—
600C2×D4—301no—
601C2×D4—601no—
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—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—151no—
625C4⋊C4—301no—
626C4⋊C4#120311yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—301no—
632C22⋊C4—301no—
633C22⋊C4—301no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4#120311yescharacteristic
637C22⋊C4#120311yescharacteristic
638C42—61no—
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—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—102no—
652C2×D3—201no—
653C2×D3—201no—
654C2×D3—201no—
655C2×D3—201no—
656C2×D3—201no—
657C2×D3—404no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4D5×#4111yescharacteristic
663C3×C4#414911yescharacteristic
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—201no—
668Dic3—201no—
669C2×C5—22no—
670C2×C5—41no—
671C2×C5—241no—
672C2×C5#555411yescharacteristic
673C2×C5C2×#90411yescharacteristic
674C2×C5#575211yescharacteristic
675D5—122no—
676D5—241no—
677C23—61no—
678C23—301no—
679C23—301no—
680C23—602no—
681C23—602no—
682C23—1201no—
683C23C2×#120311yescharacteristic
684C23C2×#120311yescharacteristic
685Q8—301no—
686Q8—301no—
687D4—22no—
688D4—61no—
689D4—61no—
690D4—122no—
691D4—152no—
692D4—241no—
693D4—301no—
694D4—301no—
695D4—301no—
696D4—602no—
697D4—602no—
698D4—1201no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—241no—
707C2×C4—241no—
708C2×C4—301no—
709C2×C4—301no—
710C2×C4—602no—
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×C3C2×#409611yescharacteristic
724C2×C3#6616311yescharacteristic
725C2×C3#6616911yescharacteristic
726D3—81no—
727D3—202no—
728D3—401no—
729C5#7944111yescharacteristic, complemented, Sylow
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—302no—
739C22—601no—
740C22—601no—
741C22—601no—
742C22—601no—
743C22—601no—
744C22—1204no—
745C22#9130312yes—
746C22C22×#120311yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—601no—
755C4—601no—
756C4#9202411yescharacteristic
757C4#9202611yescharacteristic
758C3#1061534511yescharacteristic, complemented, Sylow
759C2—22no—
760C2—41no—
761C2—241no—
762C2—602no—
763C2—1201no—
764C2C2×#9130311yescharacteristic
765C2#1175498211yescharacteristic
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. #11756309C2semidirect
2. C5×#5565C2semidirect
3. C3×D4×#168C2semidirect
4. #11748533C2semidirect
5. #11748526C2semidirect
6. #11748525C2semidirect
7. #11748514C2semidirect
8. #11748464C2semidirect
9. C2×#90969C2semidirect
10. #11748393C2semidirect
11. #11748373C2semidirect
12. #11747038C2semidirect
13. C4×#6654C2semidirect
14. #11746913C2semidirect
15. #11746899C2semidirect
30. C5×#930C22semidirect
31. C5×#926C22semidirect
36. C4×C5×D12C22semidirect
37. C5×#870C22semidirect
39. C22×C3×#168C22semidirect
40. C2×#6659C22semidirect
44. C3×C22⋊#168C22semidirect
45. C3×C4⋊#168C22semidirect
46. C3×C4×#168C22semidirect
47. #90988C22semidirect
48. #90988C22semidirect
49. #90985C22semidirect
50. #90975C22semidirect
51. #90975C22semidirect
52. #90975C22semidirect
59. #90967C22semidirect
71. D4×#168D3semidirect
128. #5565D5semidirect
163. C22×#168C2×D3semidirect
171. C22⋊#168C2×D3semidirect
184. C4⋊#168C2×D3semidirect
185. C4×#168C2×D3semidirect
240. #930C2×D5semidirect
241. #926C2×D5semidirect
255. C4×D12C2×D5semidirect
256. #870C2×D5semidirect
640. C3×C5#3297semidirect
729. C5#79441semidirect
758. C3#10615345semidirect

Maximal subgroups

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

subgroupindex
#117563092
C5×#55652
C3×D4×#1682
#117485332
#117485262
#117485252
#117485142
#117484642
C2×#909692
#117483932
#117483732
#117470382
C4×#66542
#117469132
#117468992
#106153453
#794415