Finite Group Databasebeta

← #14417139

Subgroups — #14417139

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#11754920C211yesmaximal, characteristic, complemented
2C2×#91480C211yesmaximal, characteristic
3#11753839C211yesmaximal, characteristic, complemented
4#11750886C211yesmaximal, characteristic, complemented
5C5×#4772C211yesmaximal, characteristic, complemented
6C3×#65074C211yesmaximal, characteristic, complemented
7#11748993C211yesmaximal, characteristic, complemented
8#11748975C211yesmaximal, characteristic, complemented
9D3×#3953C211yesmaximal, characteristic, complemented
10#11747748C211yesmaximal, characteristic, complemented
11#11747736C211yesmaximal, characteristic, complemented
12#11747665C211yesmaximal, characteristic, complemented
13#11747279C211yesmaximal, characteristic, complemented
14#11747261C211yesmaximal, characteristic, complemented
15#11747191C211yesmaximal, characteristic, complemented
16#10610551—31nomaximal, Hall
17C2×C5×#237C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19D4×Dic15C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic
21#91782C2211yescharacteristic
22C2×C5×D3×C8C2211yescharacteristic
23C5×#892C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic, complemented
25C2×C3×#686C2211yescharacteristic
26C3×#4039C2211yescharacteristic
27#67⋊Dic5—21no—
28Dic5×#67—21no—
29C2×Dic3⋊Dic5—21no—
30#91529—21no—
31#91480C418yescomplemented
32#91473—21no—
33D5×(C2×D3)⋊C4—21no—
34C4×#1202—21no—
35#91434C2211yescharacteristic
36D3×C4⋊Dic5C2211yescharacteristic
37#91418C2211yescharacteristic
38#91395—21no—
39#91371C2211yescharacteristic
40#91344C2211yescharacteristic, complemented
41Dic5×Dic6C2211yescharacteristic, complemented
42C2×#6660C2211yescharacteristic
43C2×#6655C2211yescharacteristic
44C2×#6650C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91099C2211yescharacteristic, complemented
48#91092C2211yescharacteristic, complemented
49C5×#832C2211yescharacteristic, complemented
50C5×#816C2211yescharacteristic, complemented
51C5×#810C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×#3947C2211yescharacteristic, complemented
54C3×#3940C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90988C2211yescharacteristic, complemented
57#90968C2211yescharacteristic
58#90965C2211yescharacteristic
59#90951C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61#79866—51nomaximal, Hall
62#66161—31no—
63C2×#4095—31no—
64#65855—31no—
65C5×#416—31no—
66C2×#3953—31no—
67#65390—31no—
68#65284—31no—
69#65106—31no—
70#65106—31no—
71#65077—31no—
72#65077—31no—
73#65074—31no—
74#65074D311yescharacteristic, complemented
75#65045—31no—
76#65045—31no—
77C22×D3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×Dic15—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×C5×#67—21no—
83C22×C5×Dic3—21no—
84C5×#237—22no—
85C5×#237C2×C414yescomplemented
86C2×C4×C5×D3C2311yescharacteristic
87C2×C5×Dic6C2311yescharacteristic
88C22×C3×Dic5—21no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×#1202—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95D3×D20—22no—
96D3×D20C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99#6719—21no—
100#6715C2×C414yescomplemented
101#6714—21no—
102C4⋊Dic15C2311yescharacteristic
103C4×Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×(C2×D3)⋊C4—21no—
106C5×C4⋊Dic3C2311yescharacteristic
107C4×C5×Dic3—21no—
108C2×C5×C3⋊C8C2311yescharacteristic
109C5×D3×C8—22no—
110C3×C22⋊Dic5—21no—
111C3×#686C2×C414yescomplemented
112C3×#685—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4×Dic5C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116Dic3⋊Dic5—21no—
117Dic3⋊Dic5—21no—
118Dic3⋊Dic5—21no—
119Dic3⋊Dic5D411yescharacteristic
120Dic3⋊Dic5D411yescharacteristic
121#6667—21no—
122(C2×D3)⋊Dic5D411yescharacteristic
123(C2×D3)⋊Dic5D411yescharacteristic
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6660C2×C414yescomplemented
128#6655C2×C414yescomplemented
129#6650C2×C414yescomplemented
130C2×#911—51no—
131#5546—51no—
132#5545—51no—
133C3×#442—51no—
134Dic3×D8—51no—
135C4×#214—51no—
136C4×#213—51no—
137#4861—51no—
138#4852—51no—
139#4785—51no—
140#4772D511yescharacteristic, complemented
141D3×#102—51no—
142#4757—51no—
143#4710—51no—
144#4708—51no—
145C2×C5×#41—31no—
146C22×D20—31no—
147C22×C5×C8—31no—
148C5×#117—31no—
149#4095—38no—
150Q8×Dic5—31no—
151Q8×Dic5—31no—
152C2×#688—31no—
153C2×#688—31no—
154D4×Dic5—31no—
155D4×Dic5—61no—
156D4×Dic5—61no—
157D4×Dic5C2×D311yescharacteristic, complemented
158C2×#686—31no—
159C2×#686C2×D311yescharacteristic
160#4072—31no—
161#4072—61no—
162C2×C4⋊Dic5—31no—
163C2×C4⋊Dic5—61no—
164C2×#681—31no—
165#4039—31no—
166#4039—31no—
167#4039—31no—
168#4039C2×D311yescharacteristic
169D5×C22⋊C4—61no—
170D5×C22⋊C4—61no—
171C4×D20—61no—
172C4×D20—61no—
173C5×#103—31no—
174C5×#103—31no—
175C5×#102—31no—
176C5×#102C2×D311yescharacteristic, complemented
177#3953—31no—
178#3953—31no—
179#3953—31no—
180#3953C2×D311yescharacteristic
181#3947—31no—
182#3947C2×D311yescharacteristic, complemented
183C8×Dic5—31no—
184C8×Dic5—31no—
185#3940—31no—
186#3940C2×D311yescharacteristic, complemented
187#3939—31no—
188#3939—31no—
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C3×D5—21no—
194C2×D3×D5—24no—
195C2×D3×D5—81no—
196C2×D3×D5—81no—
197C3×C5×D4—21no—
198C3×C5×D4C22×C412yes—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2411yescharacteristic
201C2×Dic15—21no—
202C2×Dic15—81no—
203C2×Dic15C2×D411yescharacteristic
204C2×Dic15C2×D411yescharacteristic
205D60—21no—
206D60C22×C412yes—
207C4×D15—81no—
208C5×#67—24no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—24no—
211C2×C5×Dic3—21no—
212C2×C5×Dic3C2×D411yescharacteristic
213C4×C5×D3C22×C412yes—
214C4×C5×D3#4112yes—
215C5×Dic6—21no—
216C5×Dic6C22×C412yes—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—81no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×D20—21no—
222C3×D20C22×C412yes—
223C3×C4×D5—81no—
224#1202—24no—
225#1200—81no—
226D3×Dic5—81no—
227D5×Dic3—81no—
228C3×C5×C8—21no—
229C3⋊#168C22×C412yes—
230C3×#168C22×C412yes—
231C5×C3⋊C8—21no—
232C2×#237C2×D511yescharacteristic
233C2×D3×D4—51no—
234C2×C3×D8—51no—
235C3×C4×D4—51no—
236C3×C4×D4—51no—
237D4×Dic3—51no—
238D4×Dic3—51no—
239C2×#214—51no—
240C2×#213—51no—
241C4×#67—101no—
242C4×#67—101no—
243C2×(C2×D3)⋊C4—101no—
244C2×Dic3⋊C4—101no—
245#911—58no—
246C2×#204—51no—
247C2×ΓL(1,𝔽25)—51no—
248C2×D3×C8C2×D511yescharacteristic
249#893—51no—
250#892C2×D511yescharacteristic
251D3×C4⋊C4—51no—
252#887—51no—
253#67⋊C4—101no—
254#67⋊C4—101no—
255D3×C22⋊C4—101no—
256#877—101no—
257C4×D12—51no—
258#872—51no—
259C4×Dic6—51no—
260C3×#106—51no—
261C3×#102—51no—
262C3×#102C2×D511yescharacteristic, complemented
263C3×#97—51no—
264#832—51no—
265#832C2×D511yescharacteristic, complemented
266#821—51no—
267#818—51no—
268#816C2×D511yescharacteristic, complemented
269#815—51no—
270C8×Dic3—51no—
271#810C2×D511yescharacteristic, complemented
272#809—51no—
273#808—51no—
274#807—51no—
275C4×C3⋊C8—51no—
276C23×D5—61no—
277C5×#41—34no—
278C5×#41—62no—
279C2×C5×Q8—31no—
280C2×C5×D4—61no—
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—31no—
283C22×C4×C5—61no—
284C22×Dic5—21no—
285C22×Dic5—61no—
286C22×Dic5—61no—
287C2×D20—31no—
288C2×D20—34no—
289C2×D20—62no—
290C2×D20—61no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C2×C5×C8—31no—
297C2×C5×C8—62no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C22⋊C4—61no—
302C42×C5—61no—
303C22⋊Dic5—21no—
304C22⋊Dic5—31no—
305C22⋊Dic5—31no—
306C22⋊Dic5—61no—
307#688—34no—
308#688—34no—
309#686—34no—
310#686C4×D314yescomplemented
311#685—21no—
312#685—61no—
313#685—61no—
314#685—61no—
315C4⋊Dic5—31no—
316C4⋊Dic5—31no—
317C4⋊Dic5—31no—
318C4⋊Dic5—61no—
319C4⋊Dic5—61no—
320C4⋊Dic5—61no—
321C4⋊Dic5C22×D311yescharacteristic
322C4×Dic5—31no—
323C4×Dic5—61no—
324C4×Dic5—61no—
325C4×Dic5C22×D311yescharacteristic
326#681—34no—
327C2×#168—31no—
328C2×#168C22×D311yescharacteristic
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—51no—
333#442—151no—
334#440—151no—
335#440—151no—
336C4×SD16—151no—
337C4×SD16—151no—
338C4×D8—151no—
339C4×D8—151no—
340#428—151no—
341#416—31no—
342C2×#102—151no—
343#405—151no—
344C22×C3×C5—22no—
345C22×C3×C5—41no—
346C22×C3×C5—41no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3—21no—
352C2×C5×D3—21no—
353C2×C5×D3C4×D412yes—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—84no—
358C3×C4×C5—41no—
359C3×C4×C5C23×C411yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—21no—
362Dic15—21no—
363Dic15—41no—
364C3×Dic5—21no—
365C3×Dic5—21no—
366C3×Dic5—41no—
367C5×Dic3—22no—
368C5×Dic3—41no—
369C5×Dic3C4×D412yes—
370C23×D3—101no—
371C2×C3×D4—51no—
372C2×C3×D4C22×D511yescharacteristic
373C22×C3×C4—101no—
374C22×C3×C4—101no—
375C2×#67—21no—
376C2×#67—101no—
377C22×Dic3—21no—
378C22×Dic3—101no—
379C22×Dic3—101no—
380#237—22no—
381#237C4×D514yescomplemented
382D3×D4—54no—
383D3×D4—102no—
384C2×D12—51no—
385C2×C4×D3—101no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3C22×D511yescharacteristic
389C2×Dic6C22×D511yescharacteristic
390C3×D8—54no—
391C2×C3×C8—51no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C42—51no—
398#217—101no—
399#217—101no—
400#214—54no—
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—
407C4⋊Dic3—51no—
408C4⋊Dic3C22×D511yescharacteristic
409Dic3⋊C4—51no—
410Dic3⋊C4—51no—
411Dic3⋊C4—101no—
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—21no—
415C4×Dic3—51no—
416C4×Dic3—101no—
417C4×Dic3—101no—
418C2×C3⋊C8—51no—
419C2×C3⋊C8C22×D511yescharacteristic
420#204—54no—
421ΓL(1,𝔽25)—54no—
422D3×C8—22no—
423C23×C5—21no—
424C23×C5—31no—
425C22×D5—21no—
426C22×D5—64no—
427C22×D5—61no—
428C22×D5—241no—
429C22×D5—241no—
430C5×Q8—32no—
431C5×Q8—61no—
432C5×D4—21no—
433C5×D4—64no—
434C5×D4C2×C4×D312yes—
435C2×C4×C5—21no—
436C2×C4×C5—31no—
437C2×C4×C5—32no—
438C2×C4×C5—32no—
439C2×C4×C5—64no—
440C2×C4×C5—61no—
441C2×C4×C5—61no—
442C2×C4×C5C23×D311yescharacteristic
443C2×Dic5—21no—
444C2×Dic5—31no—
445C2×Dic5—31no—
446C2×Dic5—61no—
447C2×Dic5—81no—
448C2×Dic5—241no—
449C2×Dic5—241no—
450C2×Dic5D3×D411yescharacteristic
451C2×Dic5D3×D411yescharacteristic
452D20—21no—
453D20—32no—
454D20—64no—
455D20—61no—
456D20C2×C4×D312yes—
457C4×D5—81no—
458C4×D5—241no—
459C4×D5—241no—
460C4×D5—241no—
461C5×C8—21no—
462C5×C8—61no—
463#168—32no—
464#168C2×C4×D312yes—
465C2×#41—31no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—151no—
469C2×SD16—151no—
470C2×D8—51no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—31no—
474C4×Q8—151no—
475C4×Q8—151no—
476C4×D4—51no—
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—31no—
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—51no—
496#106—151no—
497#103—31no—
498#103—31no—
499#102—31no—
500#102—51no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102D3×D511yescharacteristic, complemented
505#97—51no—
506#97—151no—
507C4×C8—151no—
508C4×C8—151no—
509C2×C3×C5—42no—
510C2×C3×C5C2×C4×D411yescharacteristic
511C2×C3×C5#57611yescharacteristic
512C2×C3×C5#57711yescharacteristic
513D15—42no—
514C3×D5—42no—
515C5×D3—22no—
516C23×C3—21no—
517C23×C3—101no—
518C22×D3—101no—
519C22×D3—104no—
520C22×D3—401no—
521C22×D3—401no—
522C22×D3D4×D511yescharacteristic
523C3×D4—21no—
524C3×D4—52no—
525C3×D4—101no—
526C3×D4C2×C4×D512yes—
527C2×C3×C4—21no—
528C2×C3×C4—51no—
529C2×C3×C4—51no—
530C2×C3×C4—101no—
531C2×C3×C4—401no—
532C2×C3×C4—401no—
533C2×C3×C4C23×D511yescharacteristic
534#67—24no—
535#67—104no—
536C2×Dic3—21no—
537C2×Dic3—24no—
538C2×Dic3—21no—
539C2×Dic3—51no—
540C2×Dic3—51no—
541C2×Dic3—101no—
542C2×Dic3—401no—
543C2×Dic3—401no—
544C2×Dic3D4×D511yescharacteristic
545D12—52no—
546D12—101no—
547C4×D3—401no—
548C4×D3—401no—
549C4×D3—401no—
550C4×D3C2×C4×D512yes—
551C4×D3#71112yes—
552Dic6—21no—
553Dic6C2×C4×D512yes—
554C3×C8—21no—
555C3×C8—52no—
556C3⋊C8—21no—
557C3⋊C8—52no—
558C22×C5—22no—
559C22×C5—32no—
560C22×C5—41no—
561C22×C5—41no—
562C22×C5—61no—
563C22×C5—61no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—22no—
566C2×D5—41no—
567C2×D5—41no—
568C2×D5—62no—
569C2×D5—121no—
570C2×D5—121no—
571C2×D5—244no—
572C4×C5—32no—
573C4×C5—41no—
574C4×C5—62no—
575C4×C5—121no—
576C4×C5C22×C4×D311yescharacteristic
577C4×C5D3×#4111yescharacteristic
578Dic5—21no—
579Dic5—21no—
580Dic5—41no—
581Dic5—61no—
582Dic5—61no—
583Dic5—121no—
584C24—301no—
585#41—34no—
586#41—62no—
587C2×Q8—31no—
588C2×D4—51no—
589C2×D4—61no—
590C2×D4—154no—
591C2×D4—151no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—154no—
605SD16—154no—
606D8—54no—
607D8—154no—
608M16—154no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—62no—
612C2×C8—151no—
613C2×C8C2×D3×D511yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—51no—
616C4⋊C4—151no—
617C4⋊C4—151no—
618C4⋊C4—151no—
619C4⋊C4—301no—
620C4⋊C4—301no—
621C4⋊C4—301no—
622C4⋊C4C2×D3×D511yescharacteristic
623C22⋊C4—61no—
624C22⋊C4—101no—
625C22⋊C4—101no—
626C22⋊C4—151no—
627C22⋊C4—151no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—51no—
633C42—61no—
634C42—151no—
635C42—301no—
636C42—301no—
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—102no—
642C22×C3—201no—
643C22×C3—201no—
644C22×C3C2×D4×D511yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—102no—
648C2×D3—201no—
649C2×D3—201no—
650C2×D3—404no—
651C2×D3#402712yes—
652C3×C4—41no—
653C3×C4—101no—
654C3×C4—101no—
655C3×C4—201no—
656C3×C4C22×C4×D511yescharacteristic
657C3×C4C2×#71111yescharacteristic
658Dic3—22no—
659Dic3—41no—
660Dic3—101no—
661Dic3—101no—
662Dic3—201no—
663Dic3#402712yes—
664C2×C5—42no—
665C2×C5—62no—
666C2×C5C4×D3×D411yescharacteristic
667C2×C5#577411yescharacteristic
668C2×C5#577511yescharacteristic
669D5—42no—
670D5—122no—
671C23—21no—
672C23—31no—
673C23—101no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—32no—
679Q8—61no—
680D4—21no—
681D4—52no—
682D4—64no—
683D4—101no—
684D4—152no—
685D4—304no—
686D4—301no—
687D4C4×D3×D512yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—51no—
693C2×C4—51no—
694C2×C4—64no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—101no—
698C2×C4—151no—
699C2×C4—151no—
700C2×C4—301no—
701C2×C4—401no—
702C2×C4—401no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—52no—
711C8—61no—
712C8—152no—
713C2×C3—42no—
714C2×C3—202no—
715C2×C3C2×#402711yescharacteristic
716C2×C3#6610311yescharacteristic
717C2×C3#6610411yescharacteristic
718D3—22no—
719D3—202no—
720C5#7986611yescharacteristic, complemented, Sylow
721C22—22no—
722C22—32no—
723C22—41no—
724C22—41no—
725C22—61no—
726C22—61no—
727C22—102no—
728C22—201no—
729C22—201no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22D3×D4×D511yescharacteristic
735C4—32no—
736C4—41no—
737C4—62no—
738C4—101no—
739C4—101no—
740C4—121no—
741C4—201no—
742C4—301no—
743C4—301no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D3×#71111yescharacteristic
747C3#1061055111yescharacteristic, complemented, Sylow
748C2—42no—
749C2—62no—
750C2—202no—
751C2—602no—
752C2D3×#402711yescharacteristic
753C2#1175406011yescharacteristic
754C2#1175408911yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#91480C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #11754920C2semidirect
3. #11753839C2semidirect
4. #11750886C2semidirect
5. C5×#4772C2semidirect
6. C3×#65074C2semidirect
7. #11748993C2semidirect
8. #11748975C2semidirect
9. D3×#3953C2semidirect
10. #11747748C2semidirect
11. #11747736C2semidirect
12. #11747665C2semidirect
13. #11747279C2semidirect
14. #11747261C2semidirect
15. #11747191C2semidirect
19. D4×Dic15C22semidirect
24. C3×D4×Dic5C22semidirect
31. #91480C4semidirect
40. #91344C22semidirect
41. Dic5×Dic6C22semidirect
45. C3×C5×#102C22semidirect
47. #91099C22semidirect
48. #91092C22semidirect
49. C5×#832C22semidirect
50. C5×#816C22semidirect
51. C5×#810C22semidirect
53. C3×#3947C22semidirect
54. C3×#3940C22semidirect
55. #90989C22semidirect
56. #90988C22semidirect
59. #90951C22semidirect
60. Dic5×C3⋊C8C22semidirect
74. #65074D3semidirect
85. C5×#237C2×C4semidirect
96. D3×D20C2×C4semidirect
100. #6715C2×C4semidirect
111. C3×#686C2×C4semidirect
127. #6660C2×C4semidirect
128. #6655C2×C4semidirect
129. #6650C2×C4semidirect
140. #4772D5semidirect
157. D4×Dic5C2×D3semidirect
176. C5×#102C2×D3semidirect
182. #3947C2×D3semidirect
186. #3940C2×D3semidirect
262. C3×#102C2×D5semidirect
265. #832C2×D5semidirect
268. #816C2×D5semidirect
271. #810C2×D5semidirect
310. #686C4×D3semidirect
381. #237C4×D5semidirect
504. #102D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#79866semidirect
747. C3#10610551semidirect

Maximal subgroups

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

subgroupindex
#117549202
C2×#914802
#117538392
#117508862
C5×#47722
C3×#650742
#117489932
#117489752
D3×#39532
#117477482
#117477362
#117476652
#117472792
#117472612
#117471912
#106105513
#798665