Finite Group Databasebeta

← #14417060

Subgroups — #14417060

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
1#11756333C211yesmaximal, characteristic, complemented
2C2×#91506C211yesmaximal, characteristic
3#11752729C211yesmaximal, characteristic, complemented
4C5×#5026C211yesmaximal, characteristic, complemented
5C3×C4×#688C211yesmaximal, characteristic, complemented
6#11749241C211yesmaximal, characteristic, complemented
7#11749240C211yesmaximal, characteristic, complemented
8#11749215C211yesmaximal, characteristic, complemented
9#11747478C211yesmaximal, characteristic, complemented
10#11747458C211yesmaximal, characteristic, complemented
11#11747236C211yesmaximal, characteristic, complemented
12#11747226C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14#11747023C211yesmaximal, characteristic, complemented
15#11746981C211yesmaximal, characteristic, complemented
16#10611506—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×#6777C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic, complemented
20Q8×Dic15C2211yescharacteristic, complemented
21#91782—21no—
22#91782C2211yescharacteristic, complemented
23C4⋊C4×D15—21no—
24C4⋊C4×D15C2211yescharacteristic
25C4×D60—21no—
26C4×D60C2211yescharacteristic, complemented
27#91761—21no—
28#91761C2211yescharacteristic
29C2×C5×#215C2211yescharacteristic
30C4×C5×D12C2211yescharacteristic
31C2×C3×#688C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic
33#91506C418yescomplemented
34D3×#685—21no—
35D5×(C2×D3)⋊C4—21no—
36#91441—21no—
37#91440—21no—
38#91435C2211yescharacteristic
39#91434C2211yescharacteristic
40#91347C2211yescharacteristic
41C2×#6654C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6651C2211yescharacteristic
44C2×#6648C2211yescharacteristic
45C5×#835C2211yescharacteristic, complemented
46C5×#809C2211yescharacteristic
47C5×#807C2211yescharacteristic, complemented
48C5×#803C2211yescharacteristic, complemented
49C3×#3967C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic, complemented
52C3×C4×#168C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90987C2211yescharacteristic, complemented
55#90969C2211yescharacteristic, complemented
56#90968C2211yescharacteristic, complemented
57#90967C2211yescharacteristic
58#90965C2211yescharacteristic
59#90954C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#79647—51nomaximal, Hall
62C2×#4060—31no—
63#65908—31no—
64#65879—31no—
65C5×#440—31no—
66SD16×Dic5—31no—
67C4×#688D311yescharacteristic, complemented
68C4×#686—31no—
69#65170—31no—
70#65161—31no—
71#65106—31no—
72#65093—31no—
73#65074—31no—
74D5×#102—31no—
75#65000—31no—
76#64997—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79#6821—22no—
80#6821C2×C414yescomplemented
81C2×D60—21no—
82C2×D60C2311yescharacteristic
83C2×C4×D15—21no—
84C2×C4×D15—21no—
85C2×C4×D15—21no—
86C2×C4×D15—21no—
87C2×C4×D15C2311yescharacteristic
88C2×C5×D12C2311yescharacteristic
89C2×C4×C5×D3—21no—
90C2×C3×D20C2311yescharacteristic
91C2×C3×C4×D5—21no—
92C2×#1201—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95#6777—22no—
96#6777C2×C414yescomplemented
97C3×C5×C4⋊C4—21no—
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C42×C5—21no—
100C3×C42×C5C2311yescharacteristic
101#6714—21no—
102#6714—21no—
103#6714D411yescharacteristic
104#6714D411yescharacteristic
105C4⋊Dic15—21no—
106C4⋊Dic15C2311yescharacteristic
107#6712—21no—
108#6712D411yescharacteristic
109#6712D411yescharacteristic
110C4×Dic15—21no—
111C4×Dic15C2311yescharacteristic
112C5×#215C2×C414yescomplemented
113C5×(C2×D3)⋊C4—21no—
114C5×C4⋊Dic3C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C2×C5×C3⋊C8C2311yescharacteristic
117C3×#688C2×C414yescomplemented
118C3×#685—21no—
119C3×C4⋊Dic5C2311yescharacteristic
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122#6667—21no—
123(C2×D3)⋊Dic5—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126#6654C2×C414yescomplemented
127#6653C2×C414yescomplemented
128#6651C2×C414yescomplemented
129#6648—22no—
130C2×#914—51no—
131#5574—51no—
132#5545—51no—
133C3×C4×SD16—51no—
134#5164—51no—
135#5026D511yescharacteristic, complemented
136#5014—51no—
137#4869—51no—
138#4861—51no—
139#4804—51no—
140#4788—51no—
141D3×#102—51no—
142#4756—51no—
143C4×D24—51no—
144#4689—51no—
145C2×#713—31no—
146C2×D4×D5—31no—
147C2×C5×SD16—31no—
148C4×C5×Q8C2×D311yescharacteristic, complemented
149C4×C5×D4—31no—
150Q8×Dic5—31no—
151C2×#688C2×D311yescharacteristic
152D4×Dic5—31no—
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C2×#685—61no—
156#4060—38no—
157C2×D40—31no—
158C2×#676—31no—
159C2×C8×D5—31no—
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—61no—
170C4×D20C2×D311yescharacteristic
171#4018—31no—
172#4018—61no—
173C5×#107—31no—
174C5×#103—31no—
175C5×#102—31no—
176C5×#97—31no—
177#3967C2×D311yescharacteristic, complemented
178#3964—31no—
179#3953—31no—
180#3953—31no—
181#3949—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3941—31no—
185#3941C2×D311yescharacteristic
186#3940C2×D311yescharacteristic, complemented
187#3939—31no—
188C4×#168C2×D311yescharacteristic, complemented
189#2946—151noSylow
190C22×D15—21no—
191C22×D15C2×D411yescharacteristic
192C22×C5×D3—21no—
193C22×C3×D5—21no—
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C3×C5×Q8—21no—
198C3×C5×Q8C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C2×Dic15—21no—
205C2×Dic15C2×D411yescharacteristic
206C2×Dic15C2×D411yescharacteristic
207C2×Dic15C2×D411yescharacteristic
208D60—24no—
209D60—21no—
210D60C22×C412yes—
211C4×D15—24no—
212C4×D15—81no—
213C4×D15—81no—
214C4×D15—81no—
215C4×D15C22×C412yes—
216C4×D15#4112yes—
217C2×C5×Dic3—21no—
218C5×D12—21no—
219C5×D12C22×C412yes—
220C4×C5×D3—81no—
221C2×C3×Dic5—21no—
222C3×D20—21no—
223C3×D20C22×C412yes—
224C3×C4×D5—81no—
225#1201—24no—
226D3×Dic5—81no—
227D5×Dic3—81no—
228C3×#168—21no—
229C3×#168C22×C412yes—
230C5×C3⋊C8—21no—
231C5×C3⋊C8C22×C412yes—
232C2×#239—51no—
233C2×D3×D4—51no—
234C2×C3×SD16—51no—
235C3×C4×Q8C2×D511yescharacteristic, complemented
236C3×C4×D4—51no—
237Q8×Dic3—51no—
238C2×#215C2×D511yescharacteristic
239D4×Dic3—51no—
240C2×#213—51no—
241C4×#67—101no—
242C2×(C2×D3)⋊C4—101no—
243#914—58no—
244C2×D24—51no—
245C2×ΓL(1,𝔽25)—51no—
246C2×D3×C8—51no—
247#893—51no—
248#893—51no—
249#893—101no—
250#892—51no—
251D3×C4⋊C4—51no—
252D3×C4⋊C4—101no—
253#67⋊C4—101no—
254D3×C22⋊C4—101no—
255C4×D12—51no—
256C4×D12—101no—
257C4×D12C2×D511yescharacteristic
258#872—51no—
259#872—101no—
260C3×#106—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×C4×C8—51no—
264#835C2×D511yescharacteristic, complemented
265#832—51no—
266#821—51no—
267#821—51no—
268#818—51no—
269#815—51no—
270C8×Dic3—51no—
271#809—51no—
272#809C2×D511yescharacteristic
273#808—51no—
274#807C2×D511yescharacteristic, complemented
275#803C2×D511yescharacteristic, complemented
276C23×D5—61no—
277C2×C5×Q8C22×D311yescharacteristic
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—61no—
288C2×D20C22×D311yescharacteristic
289C2×C4×D5—21no—
290C2×C4×D5—31no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C5×SD16—34no—
297C2×C5×C8—31no—
298C2×C5×C8—31no—
299C5×C4⋊C4—21no—
300C5×C4⋊C4—31no—
301C5×C4⋊C4C22×D311yescharacteristic
302C5×C22⋊C4—61no—
303C42×C5—21no—
304C42×C5C22×D311yescharacteristic
305C22⋊Dic5—61no—
306#688C4×D314yescomplemented
307#686—34no—
308#685—21no—
309#685—31no—
310#685—31no—
311#685—61no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317C4⋊Dic5C22×D311yescharacteristic
318#683—31no—
319#683—31no—
320#683—61no—
321C4×Dic5—31no—
322C4×Dic5—61no—
323C4×Dic5—61no—
324C2×#168C22×D311yescharacteristic
325C2×#168C22×D311yescharacteristic
326D40—34no—
327#676—34no—
328C8×D5—62no—
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—151no—
333#442—151no—
334#440—31no—
335#440—151no—
336C4×SD16—51no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—151no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5C22×D411yescharacteristic
345C2×D15—21no—
346C2×D15—21no—
347C2×D15—22no—
348C2×D15—41no—
349C2×D15—41no—
350C2×D15C4×D412yes—
351C2×C5×D3—22no—
352C2×C5×D3—41no—
353C2×C5×D3—41no—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—22no—
359C3×C4×C5—21no—
360C3×C4×C5—21no—
361C3×C4×C5—41no—
362C3×C4×C5C23×C411yescharacteristic
363C3×C4×C5C2×#4111yescharacteristic
364Dic15—21no—
365Dic15—21no—
366Dic15—41no—
367Dic15C4×D412yes—
368C3×Dic5—41no—
369C5×Dic3—41no—
370C23×D3—101no—
371C2×C3×Q8C22×D511yescharacteristic
372C2×C3×D4—51no—
373C22×C3×C4—101no—
374C2×#67—101no—
375C22×Dic3—101no—
376#239—54no—
377#239—102no—
378D3×D4—54no—
379D3×D4—102no—
380C2×D12—51no—
381C2×D12—101no—
382C2×D12C22×D511yescharacteristic
383C2×C4×D3—21no—
384C2×C4×D3—51no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3—101no—
390C3×SD16—54no—
391C2×C3×C8—51no—
392C2×C3×C8—51no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C22⋊C4—101no—
397C3×C42—21no—
398C3×C42C22×D511yescharacteristic
399#217—101no—
400#215C4×D514yescomplemented
401#213—54no—
402(C2×D3)⋊C4—21no—
403(C2×D3)⋊C4—51no—
404(C2×D3)⋊C4—51no—
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—101no—
411C4⋊Dic3C22×D511yescharacteristic
412Dic3⋊C4—51no—
413Dic3⋊C4—51no—
414Dic3⋊C4—101no—
415C4×Dic3—51no—
416C4×Dic3—101no—
417C4×Dic3—101no—
418C2×C3⋊C8C22×D511yescharacteristic
419C2×C3⋊C8C22×D511yescharacteristic
420D24—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—102no—
423C23×C5—61no—
424C22×D5—21no—
425C22×D5—31no—
426C22×D5—64no—
427C22×D5—61no—
428C22×D5—241no—
429C22×D5—241no—
430C5×Q8—21no—
431C5×Q8C2×C4×D312yes—
432C5×D4—32no—
433C5×D4—61no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—61no—
437C2×C4×C5—241no—
438C2×C4×C5D3×D411yescharacteristic
439C2×C4×C5D3×D411yescharacteristic
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—64no—
442C2×Dic5—21no—
443C2×Dic5—31no—
444C2×Dic5—31no—
445C2×Dic5—31no—
446C2×Dic5—61no—
447C2×Dic5—241no—
448D20—21no—
449D20—32no—
450D20—64no—
451D20—61no—
452D20C2×C4×D312yes—
453C4×D5—32no—
454C4×D5—32no—
455C4×D5—64no—
456C4×D5—81no—
457C4×D5—241no—
458C4×D5—241no—
459C4×D5—241no—
460C4×D5—241no—
461C5×C8—32no—
462C5×C8—61no—
463#168—21no—
464#168C2×C4×D312yes—
465C2×#41—151no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—31no—
469C2×SD16—51no—
470C2×D8—151no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—151no—
474C4×Q8—151no—
475C4×Q8D3×D511yescharacteristic, complemented
476C4×D4—31no—
477C4×D4—51no—
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—151no—
487#117—151no—
488#117—301no—
489C2×C4⋊C4—151no—
490C2×C4⋊C4—301no—
491C2×C22⋊C4—301no—
492C2×C22⋊C4—301no—
493#107—31no—
494#107—151no—
495#106—51no—
496#106—151no—
497#103—31no—
498#103—51no—
499#102—31no—
500#102—51no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102—151no—
505#97—31no—
506#97—151no—
507C4×C8—51no—
508C4×C8—151no—
509C2×C3×C5C2×C4×D411yescharacteristic
510C2×C3×C5#57611yescharacteristic
511C2×C3×C5#57711yescharacteristic
512D15—22no—
513D15—42no—
514C3×D5—42no—
515C5×D3—42no—
516C23×C3—101no—
517C22×D3—21no—
518C22×D3—51no—
519C22×D3—104no—
520C22×D3—101no—
521C22×D3—401no—
522C22×D3—401no—
523C3×Q8—21no—
524C3×Q8C2×C4×D512yes—
525C3×D4—52no—
526C3×D4—101no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—101no—
530C2×C3×C4—401no—
531C2×C3×C4D4×D511yescharacteristic
532C2×C3×C4D4×D511yescharacteristic
533C2×C3×C4C23×D511yescharacteristic
534#67—104no—
535C2×Dic3—21no—
536C2×Dic3—51no—
537C2×Dic3—51no—
538C2×Dic3—51no—
539C2×Dic3—101no—
540C2×Dic3—401no—
541D12—21no—
542D12—52no—
543D12—104no—
544D12—101no—
545D12C2×C4×D512yes—
546C4×D3—52no—
547C4×D3—52no—
548C4×D3—81no—
549C4×D3—104no—
550C4×D3—401no—
551C4×D3—401no—
552C4×D3—401no—
553C4×D3—401no—
554C3×C8—52no—
555C3×C8—101no—
556C3⋊C8—21no—
557C3⋊C8C2×C4×D512yes—
558C22×C5—62no—
559C22×C5—121no—
560C22×C5—121no—
561C22×C5C2×D3×D411yescharacteristic
562C2×D5—22no—
563C2×D5—32no—
564C2×D5—41no—
565C2×D5—41no—
566C2×D5—61no—
567C2×D5—61no—
568C2×D5—62no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—244no—
572C4×C5—21no—
573C4×C5—21no—
574C4×C5—22no—
575C4×C5—41no—
576C4×C5—121no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5D3×#4111yescharacteristic
579Dic5—32no—
580Dic5—41no—
581Dic5—61no—
582Dic5—61no—
583Dic5—121no—
584C24—301no—
585#41—154no—
586#41—302no—
587C2×Q8C2×D3×D511yescharacteristic
588C2×D4—31no—
589C2×D4—51no—
590C2×D4—154no—
591C2×D4—151no—
592C2×D4—301no—
593C2×D4—302no—
594C2×D4—301no—
595C22×C4—61no—
596C22×C4—101no—
597C22×C4—151no—
598C22×C4—301no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—34no—
605SD16—54no—
606D8—154no—
607D8—154no—
608M16—154no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—51no—
612C2×C8—51no—
613C2×C8—302no—
614C4⋊C4—21no—
615C4⋊C4—31no—
616C4⋊C4—51no—
617C4⋊C4—151no—
618C4⋊C4—151no—
619C4⋊C4—151no—
620C4⋊C4—301no—
621C4⋊C4—301no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—101no—
625C22⋊C4—151no—
626C22⋊C4—151no—
627C22⋊C4—301no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—21no—
633C42—151no—
634C42—301no—
635C42—301no—
636C42C2×D3×D511yescharacteristic
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—102no—
639C22×C3—201no—
640C22×C3—201no—
641C22×C3C2×D4×D511yescharacteristic
642C2×D3—22no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—52no—
646C2×D3—101no—
647C2×D3—101no—
648C2×D3—102no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—404no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—22no—
655C3×C4—41no—
656C3×C4—201no—
657C3×C4C22×C4×D511yescharacteristic
658C3×C4D5×#4111yescharacteristic
659Dic3—41no—
660Dic3—52no—
661Dic3—101no—
662Dic3—101no—
663Dic3—201no—
664C2×C5—122no—
665C2×C5C4×D3×D411yescharacteristic
666C2×C5#576211yescharacteristic
667C2×C5#576911yescharacteristic
668D5—42no—
669D5—62no—
670D5—122no—
671C23—61no—
672C23—101no—
673C23—151no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—21no—
679Q8C4×D3×D512yes—
680D4—32no—
681D4—52no—
682D4—61no—
683D4—101no—
684D4—152no—
685D4—304no—
686D4—304no—
687D4—301no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—61no—
691C2×C4—101no—
692C2×C4—151no—
693C2×C4—152no—
694C2×C4—152no—
695C2×C4—151no—
696C2×C4—151no—
697C2×C4—241no—
698C2×C4—304no—
699C2×C4—301no—
700C2×C4—401no—
701C2×C4—1201no—
702C2×C4—1201no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4#679011yescharacteristic
707C2×C4#679011yescharacteristic
708C2×C4C22×D3×D511yescharacteristic
709C8—32no—
710C8—52no—
711C8—61no—
712C8—101no—
713C2×C3—202no—
714C2×C3C4×D4×D511yescharacteristic
715C2×C3#6610811yescharacteristic
716C2×C3#6611211yescharacteristic
717D3—42no—
718D3—102no—
719D3—202no—
720C5#7964711yescharacteristic, complemented, Sylow
721C22—62no—
722C22—102no—
723C22—121no—
724C22—121no—
725C22—152no—
726C22—201no—
727C22—201no—
728C22—301no—
729C22—301no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22C2×#679011yescharacteristic
735C4—21no—
736C4—21no—
737C4—22no—
738C4—41no—
739C4—121no—
740C4—152no—
741C4—201no—
742C4—301no—
743C4—301no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4#9201611yescharacteristic
747C3#1061150611yescharacteristic, complemented, Sylow
748C2—122no—
749C2—202no—
750C2—302no—
751C2—602no—
752C2C4×#679011yescharacteristic
753C2#1175509711yescharacteristic
754C2#1175533211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91506C2
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756333C2semidirect
3. #11752729C2semidirect
4. C5×#5026C2semidirect
5. C3×C4×#688C2semidirect
6. #11749241C2semidirect
7. #11749240C2semidirect
8. #11749215C2semidirect
9. #11747478C2semidirect
10. #11747458C2semidirect
11. #11747236C2semidirect
12. #11747226C2semidirect
13. C4×#6654C2semidirect
14. #11747023C2semidirect
15. #11746981C2semidirect
19. C3×C4×C5×Q8C22semidirect
20. Q8×Dic15C22semidirect
22. #91782C22semidirect
26. C4×D60C22semidirect
33. #91506C4semidirect
45. C5×#835C22semidirect
47. C5×#807C22semidirect
48. C5×#803C22semidirect
49. C3×#3967C22semidirect
51. C3×#3940C22semidirect
52. C3×C4×#168C22semidirect
53. #90988C22semidirect
54. #90987C22semidirect
55. #90969C22semidirect
56. #90968C22semidirect
59. #90954C22semidirect
60. #90951C22semidirect
67. C4×#688D3semidirect
80. #6821C2×C4semidirect
96. #6777C2×C4semidirect
112. C5×#215C2×C4semidirect
117. C3×#688C2×C4semidirect
126. #6654C2×C4semidirect
127. #6653C2×C4semidirect
128. #6651C2×C4semidirect
135. #5026D5semidirect
148. C4×C5×Q8C2×D3semidirect
177. #3967C2×D3semidirect
186. #3940C2×D3semidirect
188. C4×#168C2×D3semidirect
235. C3×C4×Q8C2×D5semidirect
264. #835C2×D5semidirect
274. #807C2×D5semidirect
275. #803C2×D5semidirect
306. #688C4×D3semidirect
400. #215C4×D5semidirect
475. C4×Q8D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#79647semidirect
747. C3#10611506semidirect

Maximal subgroups

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

subgroupindex
#117563332
C2×#915062
#117527292
C5×#50262
C3×C4×#6882
#117492412
#117492402
#117492152
#117474782
#117474582
#117472362
#117472262
C4×#66542
#117470232
#117469812
#106115063
#796475