Finite Group Databasebeta

← #14417058

Subgroups — #14417058

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91249C211yesmaximal, characteristic
2#11752725C211yesmaximal, characteristic, complemented
3#11752521C211yesmaximal, characteristic, complemented
4C4×D120C211yesmaximal, characteristic, complemented
5C4×C5×#204C211yesmaximal, characteristic, complemented
6C3×#64978C211yesmaximal, characteristic, complemented
7D5×#821C211yesmaximal, characteristic, complemented
8#11747833C211yesmaximal, characteristic, complemented
9#11747772C211yesmaximal, characteristic, complemented
10#11747769C211yesmaximal, characteristic, complemented
11#11747745C211yesmaximal, characteristic, complemented
12#11747642C211yesmaximal, characteristic, complemented
13#11747618C211yesmaximal, characteristic, complemented
14#11747058C211yesmaximal, characteristic, complemented
15#11747025C211yesmaximal, characteristic, complemented
16#10611378—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18C2×#6773C2211yescharacteristic
19C2×D120C2211yescharacteristic
20C4×D60C2211yescharacteristic
21C4×D60C2211yescharacteristic, complemented
22C2×C5×#204C2211yescharacteristic
23C4×C5×D12C2211yescharacteristic
24C4×C5×Dic6C2211yescharacteristic, complemented
25C2×C3×#676C2211yescharacteristic
26C2×C3×C8×D5C2211yescharacteristic
27C3×#4018C2211yescharacteristic
28#91473—21no—
29D3×#685—21no—
30#91446—21no—
31#91418C2211yescharacteristic
32#91418C2211yescharacteristic, complemented
33Dic5×D12C2211yescharacteristic
34D5×C4⋊Dic3C2211yescharacteristic
35#91406—21no—
36#91404—21no—
37#91403—21no—
38#91396—21no—
39#91395—21no—
40#91358C2211yescharacteristic
41Dic5×Dic6C2211yescharacteristic, complemented
42C2×#6660C2211yescharacteristic
43C2×#6654C2211yescharacteristic
44#91249C418yescomplemented
45C3×C4×C5×C8C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91105C2211yescharacteristic, complemented
48#91102C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×#817C2211yescharacteristic, complemented
51C5×#816C2211yescharacteristic, complemented
52C3×#3947C2211yescharacteristic, complemented
53C3×C8×Dic5C2211yescharacteristic, complemented
54C3×#3935C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90985C2211yescharacteristic, complemented
57#90973C2211yescharacteristic, complemented
58#90969C2211yescharacteristic
59#90969C2211yescharacteristic, complemented
60#90967C2211yescharacteristic
61#78560—51nomaximal, Hall
62C2×#4060—31no—
63#65908—31no—
64#65879—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67#65315—31no—
68#65303—31no—
69#65158—31no—
70#65150—31no—
71#65093—31no—
72#65077—31no—
73D5×#102—31no—
74#65045—31no—
75C4×D40—31no—
76#64978D311yescharacteristic, complemented
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C4×D15—21no—
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C5×Dic6C2311yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×#1203—21no—
87C2×#1202—21no—
88C2×#1200—21no—
89C2×#1200—21no—
90C2×#1200—21no—
91C2×D3×Dic5—21no—
92C2×D5×Dic3—21no—
93D5×D12—22no—
94D5×D12C2×C414yescomplemented
95#6773—22no—
96#6773C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C2×C3×C5×C8C2311yescharacteristic
99C3×C42×C5C2311yescharacteristic
100#6714—21no—
101#6714—21no—
102C4⋊Dic15C2311yescharacteristic
103C4⋊Dic15C2311yescharacteristic
104D120C2×C414yescomplemented
105C5×(C2×D3)⋊C4—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C5×C4⋊Dic3C2311yescharacteristic
108C5×Dic3⋊C4—21no—
109C4×C5×Dic3—21no—
110C5×#204C2×C414yescomplemented
111C3×#685D411yescharacteristic
112C3×#685D411yescharacteristic
113C3×#683D411yescharacteristic
114C3×#683D411yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118C3×#676C2×C414yescomplemented
119C3×C8×D5—22no—
120Dic3⋊Dic5—21no—
121#6668—21no—
122#6667—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125#6665—21no—
126Dic3×Dic5—21no—
127Dic3×Dic5—21no—
128#6660C2×C414yescomplemented
129#6654C2×C414yescomplemented
130C2×#908—51no—
131#5523—51no—
132#5521—51no—
133C3×#405—51no—
134#5121—51no—
135#5113—51no—
136C2×#821—51no—
137#4711—51no—
138#4711—51no—
139#4710—51no—
140#4710—51no—
141C4×D24—51no—
142C4×D24—51no—
143C4×#204—51no—
144C4×#204D511yescharacteristic, complemented
145C2×#713—31no—
146C2×D4×D5—31no—
147C2×C5×SD16—31no—
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150Q8×Dic5—31no—
151C2×#688—31no—
152D4×Dic5—31no—
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C2×#685—61no—
156#4060—38no—
157C2×D40—31no—
158C2×#676C2×D311yescharacteristic
159C2×C8×D5C2×D311yescharacteristic
160#4039—31no—
161#4039—31no—
162#4039—61no—
163#4038—31no—
164D5×C4⋊C4—31no—
165D5×C4⋊C4—61no—
166#4027—61no—
167D5×C22⋊C4—61no—
168C4×D20—31no—
169C4×D20—31no—
170C4×D20—61no—
171#4018—61no—
172#4018C2×D311yescharacteristic
173C5×#106—31no—
174C5×#103—31no—
175C5×#102—31no—
176C4×C5×C8C2×D311yescharacteristic, complemented
177#3967—31no—
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3950—31no—
182#3947C2×D311yescharacteristic, complemented
183C8×Dic5C2×D311yescharacteristic, complemented
184#3941—31no—
185#3941—31no—
186#3940—31no—
187#3939—31no—
188#3935C2×D311yescharacteristic, complemented
189#2946—151noSylow
190C22×D15—21no—
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C3×D5C2×D411yescharacteristic
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2411yescharacteristic
200C2×Dic15—21no—
201C2×Dic15—21no—
202D60—21no—
203D60—21no—
204D60C22×C412yes—
205D60C22×C412yes—
206C4×D15—81no—
207C4×D15—81no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C5×D12—21no—
212C5×D12C22×C412yes—
213C4×C5×D3—81no—
214C5×Dic6—21no—
215C5×Dic6C22×C412yes—
216C2×C3×Dic5C2×D411yescharacteristic
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C3×C4×D5C22×C412yes—
220C3×C4×D5#4112yes—
221#1203—24no—
222#1202—24no—
223#1200—24no—
224#1200—81no—
225#1200—81no—
226D3×Dic5—81no—
227D5×Dic3—81no—
228C3×C5×C8—21no—
229C3×C5×C8C22×C412yes—
230C3×#168—21no—
231C3×#168C22×C412yes—
232C2×#235—51no—
233C22×D12—51no—
234C2×C3×M16—51no—
235C22×C3×C8—51no—
236C3×#117—51no—
237#926—51no—
238C2×C4⋊Dic3—51no—
239#908—58no—
240C2×D24—51no—
241C2×D24—51no—
242C2×#204—51no—
243C2×#204C2×D511yescharacteristic
244#893—101no—
245#893—101no—
246#892—101no—
247D3×C4⋊C4—101no—
248#67⋊C4—101no—
249#67⋊C4—101no—
250D3×C22⋊C4—101no—
251D3×C22⋊C4—101no—
252C4×D12—51no—
253C4×D12—51no—
254C4×D12—51no—
255C4×D12—51no—
256C4×D12—51no—
257C4×D12C2×D511yescharacteristic
258C4×Dic6—51no—
259C4×Dic6C2×D511yescharacteristic, complemented
260C3×#97—51no—
261C3×#97—51no—
262C3×C4×C8—51no—
263C3×C4×C8C2×D511yescharacteristic, complemented
264#821—51no—
265#821—51no—
266#821—51no—
267#821—51no—
268#821—51no—
269#821C2×D511yescharacteristic
270#818—51no—
271#818—51no—
272#817—51no—
273#817C2×D511yescharacteristic, complemented
274#816—51no—
275#816C2×D511yescharacteristic, complemented
276C23×D5—61no—
277C2×C5×Q8—31no—
278C2×C5×D4—31no—
279C22×C4×C5—61no—
280C2×C22⋊D5—61no—
281C22×Dic5—61no—
282#713—34no—
283#713—62no—
284D4×D5—34no—
285D4×D5—62no—
286C2×D20—31no—
287C2×D20—31no—
288C2×D20—61no—
289C2×C4×D5—61no—
290C2×C4×D5—61no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5C22×D311yescharacteristic
296C5×SD16—34no—
297C2×C5×C8C22×D311yescharacteristic
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4—31no—
301C5×C4⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—61no—
304C42×C5C22×D311yescharacteristic
305C22⋊Dic5—61no—
306#688—34no—
307#686—34no—
308#685—61no—
309#685—61no—
310#685—61no—
311#685—61no—
312#685—61no—
313#685D1211yescharacteristic
314#685D1211yescharacteristic
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—61no—
318#683—61no—
319#683D1211yescharacteristic
320#683D1211yescharacteristic
321C4×Dic5—61no—
322C4×Dic5—61no—
323C4×Dic5C22×D311yescharacteristic
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326D40—34no—
327#676C4×D314yescomplemented
328C8×D5—22no—
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—31no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—51no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—22no—
346C2×D15—22no—
347C2×D15—41no—
348C2×D15—41no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—22no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C3×D5—21no—
355C2×C3×D5—21no—
356C2×C3×D5C4×D412yes—
357D3×D5—84no—
358C3×C4×C5—21no—
359C3×C4×C5—21no—
360C3×C4×C5C23×C411yescharacteristic
361C3×C4×C5C2×#4111yescharacteristic
362Dic15—41no—
363Dic15—41no—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5C4×D412yes—
367C5×Dic3—22no—
368C5×Dic3—41no—
369C5×Dic3—41no—
370C23×D3—101no—
371C22×C3×C4—51no—
372C2×#67—101no—
373C22×Dic3—101no—
374#235—54no—
375#235—102no—
376C2×D12—51no—
377C2×D12—51no—
378C2×D12—54no—
379C2×D12—102no—
380C2×D12—101no—
381C2×D12C22×D511yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—101no—
384C2×C4×D3—101no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×Dic6C22×D511yescharacteristic
390C3×M16—54no—
391C2×C3×C8—51no—
392C2×C3×C8—51no—
393C2×C3×C8—102no—
394C2×C3×C8C22×D511yescharacteristic
395C2×C3×C8C22×D511yescharacteristic
396C3×C4⋊C4—51no—
397C3×C4⋊C4—51no—
398C3×C22⋊C4—51no—
399C3×C22⋊C4—51no—
400C3×C42—51no—
401C3×C42C22×D511yescharacteristic
402#217—101no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—101no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407(C2×D3)⋊C4—101no—
408(C2×D3)⋊C4—101no—
409C4⋊Dic3—51no—
410C4⋊Dic3—51no—
411C4⋊Dic3—101no—
412C4⋊Dic3C22×D511yescharacteristic
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—101no—
416C4×Dic3—21no—
417C4×Dic3—101no—
418C4×Dic3—101no—
419D24—54no—
420D24—54no—
421#204—54no—
422#204C4×D514yescomplemented
423C23×C5—61no—
424C22×D5—61no—
425C22×D5—61no—
426C22×D5—64no—
427C22×D5—241no—
428C22×D5—241no—
429C22×D5C2×D1211yescharacteristic
430C5×Q8—32no—
431C5×Q8—61no—
432C5×D4—32no—
433C5×D4—61no—
434C2×C4×C5—61no—
435C2×C4×C5—61no—
436C2×C4×C5—61no—
437C2×C4×C5—241no—
438C2×C4×C5C2×D1211yescharacteristic
439C2×C4×C5C2×D1211yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—64no—
442C2×Dic5—61no—
443C2×Dic5—61no—
444C2×Dic5—241no—
445C2×Dic5C2×D1211yescharacteristic
446C2×Dic5C2×D1211yescharacteristic
447C2×Dic5C2×D1211yescharacteristic
448D20—32no—
449D20—32no—
450D20—64no—
451D20—61no—
452D20—61no—
453C4×D5—64no—
454C4×D5—241no—
455C4×D5—241no—
456C4×D5—241no—
457C4×D5—241no—
458C4×D5—241no—
459C4×D5C2×C4×D312yes—
460C4×D5#23512yes—
461C5×C8—21no—
462C5×C8C2×C4×D312yes—
463#168—21no—
464#168C2×C4×D312yes—
465C2×#41—151no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—31no—
469C2×SD16—151no—
470C2×D8—151no—
471C2×D8—151no—
472C2×M16—51no—
473C22×C8—51no—
474C4×Q8—31no—
475C4×Q8—151no—
476C4×D4—31no—
477C4×D4—151no—
478C4×D4—151no—
479C4×D4—151no—
480C4×D4—151no—
481C4×D4—151no—
482C4×D4—301no—
483C4×D4—301no—
484C4×D4—301no—
485C4×D4—301no—
486#117—51no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—151no—
494#107—151no—
495#106—31no—
496#106—151no—
497#103—31no—
498#103—151no—
499#102—31no—
500#102—151no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—51no—
506#97—51no—
507C4×C8—51no—
508C4×C8D3×D511yescharacteristic, complemented
509C2×C3×C5C2×C4×D411yescharacteristic
510C2×C3×C5#57611yescharacteristic
511C2×C3×C5#57711yescharacteristic
512D15—42no—
513D15—42no—
514C3×D5—22no—
515C5×D3—42no—
516C23×C3—51no—
517C22×D3—21no—
518C22×D3—104no—
519C22×D3—101no—
520C22×D3—101no—
521C22×D3—401no—
522C22×D3—401no—
523C2×C3×C4—51no—
524C2×C3×C4—52no—
525C2×C3×C4—52no—
526C2×C3×C4—51no—
527C2×C3×C4—51no—
528C2×C3×C4D4×D511yescharacteristic
529C2×C3×C4D4×D511yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531#67—104no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—101no—
536C2×Dic3—101no—
537C2×Dic3—401no—
538D12—21no—
539D12—52no—
540D12—52no—
541D12—104no—
542D12—101no—
543D12—101no—
544D12C2×C4×D512yes—
545C4×D3—81no—
546C4×D3—104no—
547C4×D3—401no—
548C4×D3—401no—
549C4×D3—401no—
550C4×D3—401no—
551C4×D3—401no—
552Dic6—21no—
553Dic6C2×C4×D512yes—
554C3×C8—21no—
555C3×C8—52no—
556C3×C8—101no—
557C3×C8C2×C4×D512yes—
558C22×C5—62no—
559C22×C5—121no—
560C22×C5—121no—
561C22×C5C22×D1211yescharacteristic
562C2×D5—21no—
563C2×D5—21no—
564C2×D5—62no—
565C2×D5—62no—
566C2×D5—121no—
567C2×D5—121no—
568C2×D5—121no—
569C2×D5—121no—
570C2×D5—244no—
571C2×D5C4×D1212yes—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—62no—
575C4×C5—121no—
576C4×C5—121no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5C2×#23511yescharacteristic
579Dic5—21no—
580Dic5—21no—
581Dic5—121no—
582Dic5—121no—
583Dic5C4×D1212yes—
584C24—301no—
585#41—154no—
586#41—302no—
587C2×Q8—31no—
588C2×D4—31no—
589C2×D4—154no—
590C2×D4—151no—
591C2×D4—151no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4—301no—
595C22×C4—51no—
596C22×C4—61no—
597C22×C4—301no—
598C22×C4—301no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—34no—
605SD16—154no—
606D8—154no—
607D8—154no—
608M16—54no—
609C2×C8—51no—
610C2×C8—51no—
611C2×C8—102no—
612C2×C8C2×D3×D511yescharacteristic
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—51no—
617C4⋊C4—51no—
618C4⋊C4—61no—
619C4⋊C4—151no—
620C4⋊C4—151no—
621C4⋊C4—301no—
622C4⋊C4—301no—
623C22⋊C4—51no—
624C22⋊C4—51no—
625C22⋊C4—61no—
626C22⋊C4—301no—
627C22⋊C4—301no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—51no—
633C42—61no—
634C42—301no—
635C42—301no—
636C42C2×D3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—52no—
639C22×C3—101no—
640C22×C3—101no—
641C22×C3C2×D4×D511yescharacteristic
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—102no—
646C2×D3—102no—
647C2×D3—201no—
648C2×D3—201no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—404no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—52no—
655C3×C4—101no—
656C3×C4—101no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4D5×#4111yescharacteristic
659Dic3—22no—
660Dic3—41no—
661Dic3—41no—
662Dic3—201no—
663Dic3—201no—
664C2×C5—122no—
665C2×C5C2×C4×D1211yescharacteristic
666C2×C5#575111yescharacteristic
667C2×C5#575211yescharacteristic
668D5—22no—
669D5—122no—
670D5—122no—
671C23—51no—
672C23—61no—
673C23—304no—
674C23—301no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—32no—
679Q8—61no—
680D4—32no—
681D4—61no—
682D4—152no—
683D4—152no—
684D4—304no—
685D4—304no—
686D4—301no—
687D4—301no—
688C2×C4—51no—
689C2×C4—52no—
690C2×C4—52no—
691C2×C4—51no—
692C2×C4—51no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—241no—
697C2×C4—304no—
698C2×C4—301no—
699C2×C4—301no—
700C2×C4—1201no—
701C2×C4—1201no—
702C2×C4—1201no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4D5×D1211yescharacteristic
707C2×C4D5×D1211yescharacteristic
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—52no—
711C8—101no—
712C8C4×D3×D512yes—
713C2×C3—102no—
714C2×C3C4×D4×D511yescharacteristic
715C2×C3#6609611yescharacteristic
716C2×C3#6610311yescharacteristic
717D3—42no—
718D3—202no—
719D3—202no—
720C5#7856011yescharacteristic, complemented, Sylow
721C22—52no—
722C22—62no—
723C22—101no—
724C22—101no—
725C22—121no—
726C22—121no—
727C22—302no—
728C22—302no—
729C22—601no—
730C22—601no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22C2×D5×D1211yescharacteristic
735C4—21no—
736C4—21no—
737C4—52no—
738C4—62no—
739C4—101no—
740C4—101no—
741C4—121no—
742C4—121no—
743C4—601no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D5×#23511yescharacteristic
747C3#1061137811yescharacteristic, complemented, Sylow
748C2—102no—
749C2—122no—
750C2—602no—
751C2—602no—
752C2C4×D5×D1211yescharacteristic
753C2#1175396011yescharacteristic
754C2#1175396311yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91249C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11752725C2semidirect
3. #11752521C2semidirect
4. C4×D120C2semidirect
5. C4×C5×#204C2semidirect
6. C3×#64978C2semidirect
7. D5×#821C2semidirect
8. #11747833C2semidirect
9. #11747772C2semidirect
10. #11747769C2semidirect
11. #11747745C2semidirect
12. #11747642C2semidirect
13. #11747618C2semidirect
14. #11747058C2semidirect
15. #11747025C2semidirect
21. C4×D60C22semidirect
24. C4×C5×Dic6C22semidirect
32. #91418C22semidirect
41. Dic5×Dic6C22semidirect
44. #91249C4semidirect
45. C3×C4×C5×C8C22semidirect
47. #91105C22semidirect
48. #91102C22semidirect
50. C5×#817C22semidirect
51. C5×#816C22semidirect
52. C3×#3947C22semidirect
53. C3×C8×Dic5C22semidirect
54. C3×#3935C22semidirect
55. #90988C22semidirect
56. #90985C22semidirect
57. #90973C22semidirect
59. #90969C22semidirect
76. #64978D3semidirect
94. D5×D12C2×C4semidirect
96. #6773C2×C4semidirect
104. D120C2×C4semidirect
110. C5×#204C2×C4semidirect
118. C3×#676C2×C4semidirect
128. #6660C2×C4semidirect
129. #6654C2×C4semidirect
144. C4×#204D5semidirect
176. C4×C5×C8C2×D3semidirect
182. #3947C2×D3semidirect
183. C8×Dic5C2×D3semidirect
188. #3935C2×D3semidirect
259. C4×Dic6C2×D5semidirect
263. C3×C4×C8C2×D5semidirect
273. #817C2×D5semidirect
275. #816C2×D5semidirect
327. #676C4×D3semidirect
422. #204C4×D5semidirect
508. C4×C8D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#78560semidirect
747. C3#10611378semidirect

Maximal subgroups

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

subgroupindex
C2×#912492
#117527252
#117525212
C4×D1202
C4×C5×#2042
C3×#649782
D5×#8212
#117478332
#117477722
#117477692
#117477452
#117476422
#117476182
#117470582
#117470252
#106113783
#785605