Finite Group Databasebeta

← #14417137

Subgroups — #14417137

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#11754923C211yesmaximal, characteristic, complemented
2C2×#91478C211yesmaximal, characteristic
3#11753837C211yesmaximal, characteristic, complemented
4#11750886C211yesmaximal, characteristic, complemented
5C5×#4785C211yesmaximal, characteristic, complemented
6C3×#65061C211yesmaximal, characteristic, complemented
7#11748994C211yesmaximal, characteristic, complemented
8#11748986C211yesmaximal, characteristic, complemented
9D5×#821C211yesmaximal, characteristic, complemented
10#11747743C211yesmaximal, characteristic, complemented
11#11747738C211yesmaximal, characteristic, complemented
12#11747646C211yesmaximal, characteristic, complemented
13#11747272C211yesmaximal, characteristic, complemented
14#11747264C211yesmaximal, characteristic, complemented
15#11747189C211yesmaximal, characteristic, complemented
16#10611597—31nomaximal, Hall
17C2×C3×#711C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19D4×Dic15C2211yescharacteristic, complemented
20C2×#6715C2211yescharacteristic
21#91782C2211yescharacteristic
22C5×D4×Dic3C2211yescharacteristic, complemented
23C2×C5×#213C2211yescharacteristic
24C5×#893C2211yescharacteristic
25C2×C3×C8×D5C2211yescharacteristic
26C3×#4038C2211yescharacteristic
27#91559—21no—
28Dic3×C22⋊D5—21no—
29C2×#6668—21no—
30#91528—21no—
31#91478C418yescomplemented
32#91473—21no—
33D3×#685—21no—
34C4×#1203—21no—
35#91435C2211yescharacteristic
36#91428C2211yescharacteristic
37D5×C4⋊Dic3C2211yescharacteristic
38#91405—21no—
39#91357C2211yescharacteristic
40#91331C2211yescharacteristic, complemented
41Dic3×Dic10C2211yescharacteristic, complemented
42C2×#6658C2211yescharacteristic
43C2×#6656C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91099C2211yescharacteristic, complemented
48#91092C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×#815C2211yescharacteristic, complemented
51C5×#808C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54C3×#3942C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90989C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90967C2211yescharacteristic
59#90951C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#78820—51nomaximal, Hall
62C2×#4057—31no—
63#65880—31no—
64#65879—31no—
65C5×#442—31no—
66D8×Dic5—31no—
67C4×#687—31no—
68C4×#686—31no—
69#65150—31no—
70#65141—31no—
71#65074—31no—
72#65061D311yescharacteristic, complemented
73D5×#102—31no—
74#65046—31no—
75#64999—31no—
76#64997—31no—
77C22×D3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×Dic15—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C22×C5×Dic3—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C3×C22⋊D5—21no—
86C22×C3×Dic5—21no—
87C3×#711—22no—
88C3×#711C2×C414yescomplemented
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×Dic10C2311yescharacteristic
91C2×#1203—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95D5×D12—22no—
96D5×D12C2×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×#217—21no—
106C5×#213C2×C414yescomplemented
107C5×(C2×D3)⋊C4—21no—
108C5×C4⋊Dic3C2311yescharacteristic
109C4×C5×Dic3C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×#685—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4×Dic5—21no—
114C2×C3×#168C2311yescharacteristic
115C3×C8×D5—22no—
116#6668—21no—
117#6668—21no—
118#6668—21no—
119#6668D411yescharacteristic
120#6668D411yescharacteristic
121#6667—21no—
122(C2×D3)⋊Dic5—21no—
123#6665D411yescharacteristic
124#6665D411yescharacteristic
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6658C2×C414yescomplemented
128#6656C2×C414yescomplemented
129#6649C2×C414yescomplemented
130#5827—51no—
131C2×#949—51no—
132#5521—51no—
133C3×#416—51no—
134C2×#821—51no—
135#5101—51no—
136#4995—51no—
137#4817—51no—
138#4817—51no—
139#4788—51no—
140#4788—51no—
141#4785—51no—
142#4785D511yescharacteristic, complemented
143#4756—51no—
144#4756—51no—
145C2×#711C2×D311yescharacteristic
146C2×D4×D5—31no—
147C2×C5×D8—31no—
148C4×C5×D4—31no—
149C4×C5×D4—31no—
150D4×Dic5—31no—
151D4×Dic5—31no—
152C2×#687—31no—
153C2×#686—31no—
154C4×C22⋊D5—61no—
155C4×C22⋊D5—61no—
156C2×#685—61no—
157C2×#683—61no—
158#4057—38no—
159C2×#677—31no—
160C2×#676—31no—
161C2×C8×D5C2×D311yescharacteristic
162#4039—31no—
163#4038C2×D311yescharacteristic
164D5×C4⋊C4—31no—
165#4033—31no—
166#4027—61no—
167#4027—61no—
168D5×C22⋊C4—61no—
169#4023—61no—
170C4×D20—31no—
171#4018—31no—
172C4×Dic10—31no—
173C5×#106—31no—
174C5×#102—31no—
175C5×#102C2×D311yescharacteristic, complemented
176C5×#97—31no—
177#3964—31no—
178#3964C2×D311yescharacteristic, complemented
179#3953—31no—
180#3950—31no—
181#3948C2×D311yescharacteristic, complemented
182#3947—31no—
183C8×Dic5—31no—
184#3942C2×D311yescharacteristic, complemented
185#3941—31no—
186#3940—31no—
187#3939—31no—
188C4×#168—31no—
189#2946—151noSylow
190C23×C3×C5—21no—
191C22×D15—21no—
192C22×C5×D3—21no—
193C22×C3×D5C2×D411yescharacteristic
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—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—81no—
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C5×D12—21no—
213C5×D12C22×C412yes—
214C4×C5×D3—81no—
215C3×C22⋊D5—24no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—24no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5C2×D411yescharacteristic
220C3×C4×D5C22×C412yes—
221C3×C4×D5#4112yes—
222C3×Dic10—21no—
223C3×Dic10C22×C412yes—
224#1203—24no—
225#1200—81no—
226D3×Dic5—81no—
227D5×Dic3—81no—
228C3×C5×C8—21no—
229C3⋊#168C22×C412yes—
230C3×#168—21no—
231C5×C3⋊C8C22×C412yes—
232C2×C3×#41—51no—
233C22×D12—51no—
234C22×C3×C8—51no—
235C3×#117—51no—
236#949—58no—
237Q8×Dic3—51no—
238Q8×Dic3—51no—
239C2×#215—51no—
240C2×#215—51no—
241D4×Dic3—51no—
242D4×Dic3—101no—
243D4×Dic3—101no—
244D4×Dic3C2×D511yescharacteristic, complemented
245C2×#213—51no—
246C2×#213C2×D511yescharacteristic
247#926—51no—
248#926—101no—
249C2×C4⋊Dic3—51no—
250C2×C4⋊Dic3—101no—
251C2×#208—51no—
252#893—51no—
253#893—51no—
254#893—51no—
255#893C2×D511yescharacteristic
256D3×C22⋊C4—101no—
257D3×C22⋊C4—101no—
258C4×D12—101no—
259C4×D12—101no—
260C3×#103—51no—
261C3×#103—51no—
262C3×#102—51no—
263C3×#102C2×D511yescharacteristic, complemented
264#821—51no—
265#821—51no—
266#821—51no—
267#821C2×D511yescharacteristic
268#815—51no—
269#815C2×D511yescharacteristic, complemented
270C8×Dic3—51no—
271C8×Dic3—51no—
272#808—51no—
273#808C2×D511yescharacteristic, complemented
274#807—51no—
275#807—51no—
276C23×D5—61no—
277C2×C5×D4—31no—
278C2×C5×D4C22×D311yescharacteristic
279C22×C4×C5—61no—
280C22×C4×C5—61no—
281C2×C22⋊D5—21no—
282C2×C22⋊D5—61no—
283C22×Dic5—21no—
284C22×Dic5—61no—
285C22×Dic5—61no—
286#711—22no—
287#711C4×D314yescomplemented
288D4×D5—34no—
289D4×D5—62no—
290C2×D20—31no—
291C2×C4×D5—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5C22×D311yescharacteristic
295C2×Dic10C22×D311yescharacteristic
296C5×D8—34no—
297C2×C5×C8—31no—
298C2×C5×C8C22×D311yescharacteristic
299C5×C4⋊C4—31no—
300C5×C4⋊C4C22×D311yescharacteristic
301C5×C22⋊C4—61no—
302C5×C22⋊C4—61no—
303C42×C5—31no—
304C22⋊Dic5—61no—
305C22⋊Dic5—61no—
306#687—34no—
307#686—34no—
308#685—21no—
309#685—31no—
310#685—31no—
311#685—61no—
312#685—61no—
313C4⋊Dic5—31no—
314C4⋊Dic5C22×D311yescharacteristic
315#683—31no—
316#683—31no—
317#683—61no—
318#683—61no—
319#683—61no—
320C4×Dic5—21no—
321C4×Dic5—31no—
322C4×Dic5—61no—
323C4×Dic5—61no—
324C2×#168—31no—
325C2×#168C22×D311yescharacteristic
326#677—34no—
327#676—34no—
328C8×D5—22no—
329C2×AGL(1,ℤ/8)—151no—
330#520—151no—
331#518—151no—
332#442—31no—
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—51no—
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—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—41no—
359C3×C4×C5C23×C411yescharacteristic
360C3×C4×C5C2×#4111yescharacteristic
361Dic15—21no—
362Dic15—21no—
363Dic15—41no—
364C3×Dic5—22no—
365C3×Dic5—41no—
366C3×Dic5C4×D412yes—
367C5×Dic3—21no—
368C5×Dic3—21no—
369C5×Dic3—41no—
370C23×D3—101no—
371C3×#41—54no—
372C3×#41—102no—
373C2×C3×Q8—51no—
374C2×C3×D4—101no—
375C2×C3×D4C22×D511yescharacteristic
376C22×C3×C4—51no—
377C22×C3×C4—101no—
378C22×Dic3—21no—
379C22×Dic3—101no—
380C22×Dic3—101no—
381C2×D12—51no—
382C2×D12—54no—
383C2×D12—102no—
384C2×D12—101no—
385C2×D12C22×D511yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3—101no—
390C2×C3×C8—51no—
391C2×C3×C8—102no—
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—51no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C22⋊C4—101no—
396C3×C42—101no—
397#217—21no—
398#217—51no—
399#217—51no—
400#217—101no—
401#215—54no—
402#215—54no—
403#213—54no—
404#213C4×D514yescomplemented
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⋊Dic3—101no—
414C4⋊Dic3—101no—
415C4⋊Dic3C22×D511yescharacteristic
416C4×Dic3—51no—
417C4×Dic3—101no—
418C4×Dic3—101no—
419C4×Dic3C22×D511yescharacteristic
420#208—54no—
421C2×C3⋊C8—51no—
422C2×C3⋊C8C22×D511yescharacteristic
423C23×C5—21no—
424C23×C5—61no—
425C22×D5—61no—
426C22×D5—64no—
427C22×D5—241no—
428C22×D5—241no—
429C22×D5D3×D411yescharacteristic
430C5×D4—21no—
431C5×D4—32no—
432C5×D4—61no—
433C5×D4C2×C4×D312yes—
434C2×C4×C5—21no—
435C2×C4×C5—31no—
436C2×C4×C5—31no—
437C2×C4×C5—61no—
438C2×C4×C5—241no—
439C2×C4×C5—241no—
440C2×C4×C5C23×D311yescharacteristic
441C22⋊D5—24no—
442C22⋊D5—64no—
443C2×Dic5—21no—
444C2×Dic5—24no—
445C2×Dic5—21no—
446C2×Dic5—31no—
447C2×Dic5—31no—
448C2×Dic5—61no—
449C2×Dic5—241no—
450C2×Dic5—241no—
451C2×Dic5D3×D411yescharacteristic
452D20—32no—
453D20—61no—
454C4×D5—241no—
455C4×D5—241no—
456C4×D5—241no—
457C4×D5C2×C4×D312yes—
458C4×D5#23712yes—
459Dic10—21no—
460Dic10C2×C4×D312yes—
461C5×C8—21no—
462C5×C8—32no—
463#168—21no—
464#168—32no—
465C2×#41—51no—
466C22×D4—151no—
467AGL(1,ℤ/8)—158no—
468C2×SD16—151no—
469C2×SD16—151no—
470C2×D8—31no—
471C2×D8—151no—
472C2×M16—151no—
473C22×C8—51no—
474C4×Q8—151no—
475C4×Q8—151no—
476C4×D4—31no—
477C4×D4—31no—
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—51no—
498#103—51no—
499#102—31no—
500#102—51no—
501#102—151no—
502#102—151no—
503#102—151no—
504#102D3×D511yescharacteristic, complemented
505#97—31no—
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—22no—
515C5×D3—42no—
516C23×C3—21no—
517C23×C3—51no—
518C22×D3—21no—
519C22×D3—104no—
520C22×D3—101no—
521C22×D3—401no—
522C22×D3—401no—
523C3×Q8—52no—
524C3×Q8—101no—
525C3×D4—21no—
526C3×D4—104no—
527C3×D4C2×C4×D512yes—
528C2×C3×C4—21no—
529C2×C3×C4—51no—
530C2×C3×C4—52no—
531C2×C3×C4—52no—
532C2×C3×C4—104no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4C23×D511yescharacteristic
536C2×Dic3—21no—
537C2×Dic3—51no—
538C2×Dic3—51no—
539C2×Dic3—81no—
540C2×Dic3—101no—
541C2×Dic3—401no—
542C2×Dic3—401no—
543C2×Dic3D4×D511yescharacteristic
544C2×Dic3D4×D511yescharacteristic
545D12—21no—
546D12—52no—
547D12—104no—
548D12—101no—
549D12C2×C4×D512yes—
550C4×D3—81no—
551C4×D3—401no—
552C4×D3—401no—
553C4×D3—401no—
554C3×C8—21no—
555C3×C8—101no—
556C3⋊C8—52no—
557C3⋊C8C2×C4×D512yes—
558C22×C5—22no—
559C22×C5—41no—
560C22×C5—41no—
561C22×C5—62no—
562C22×C5—121no—
563C22×C5—121no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—21no—
566C2×D5—21no—
567C2×D5—62no—
568C2×D5—121no—
569C2×D5—121no—
570C2×D5—244no—
571C2×D5#67⋊C412yes—
572C4×C5—41no—
573C4×C5—61no—
574C4×C5—61no—
575C4×C5—121no—
576C4×C5C22×C4×D311yescharacteristic
577C4×C5C2×#23711yescharacteristic
578Dic5—22no—
579Dic5—41no—
580Dic5—61no—
581Dic5—61no—
582Dic5—121no—
583Dic5#67⋊C412yes—
584C24—301no—
585#41—54no—
586#41—102no—
587C2×Q8—51no—
588C2×D4—31no—
589C2×D4—101no—
590C2×D4—154no—
591C2×D4—151no—
592C2×D4—302no—
593C2×D4—301no—
594C2×D4C2×D3×D511yescharacteristic
595C22×C4—51no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—101no—
599C22×C4—301no—
600C22×C4—301no—
601C22×C4—301no—
602C22×C4—301no—
603C22×C4—301no—
604SD16—154no—
605SD16—154no—
606D8—34no—
607D8—154no—
608M16—154no—
609C2×C8—31no—
610C2×C8—51no—
611C2×C8—102no—
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—61no—
625C22⋊C4—101no—
626C22⋊C4—151no—
627C22⋊C4—151no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C22⋊C4—301no—
632C42—31no—
633C42—101no—
634C42—151no—
635C42—301no—
636C42—301no—
637C3×C5#294611yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—52no—
642C22×C3—101no—
643C22×C3—101no—
644C22×C3C2×D4×D511yescharacteristic
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—102no—
649C2×D3—201no—
650C2×D3—201no—
651C2×D3—404no—
652C3×C4—41no—
653C3×C4—52no—
654C3×C4—102no—
655C3×C4—201no—
656C3×C4C22×C4×D511yescharacteristic
657C3×C4D5×#4111yescharacteristic
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—101no—
662Dic3—101no—
663Dic3—201no—
664C2×C5—42no—
665C2×C5—122no—
666C2×C5C2×#67⋊C411yescharacteristic
667C2×C5#576911yescharacteristic
668C2×C5#577011yescharacteristic
669D5—22no—
670D5—122no—
671C23—21no—
672C23—51no—
673C23—61no—
674C23—304no—
675C23—301no—
676C23—1201no—
677C23—1201no—
678Q8—52no—
679Q8—101no—
680D4—21no—
681D4—32no—
682D4—61no—
683D4—104no—
684D4—152no—
685D4—304no—
686D4—301no—
687D4C4×D3×D512yes—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—51no—
692C2×C4—52no—
693C2×C4—52no—
694C2×C4—61no—
695C2×C4—104no—
696C2×C4—101no—
697C2×C4—101no—
698C2×C4—151no—
699C2×C4—151no—
700C2×C4—241no—
701C2×C4—241no—
702C2×C4—301no—
703C2×C4—1201no—
704C2×C4—1201no—
705C2×C4—1201no—
706C2×C4—1201no—
707C2×C4—1201no—
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—32no—
711C8—101no—
712C8—152no—
713C2×C3—42no—
714C2×C3—102no—
715C2×C3C4×D4×D511yescharacteristic
716C2×C3#6610811yescharacteristic
717C2×C3#6610911yescharacteristic
718D3—42no—
719D3—202no—
720C5#7882011yescharacteristic, complemented, Sylow
721C22—22no—
722C22—41no—
723C22—41no—
724C22—52no—
725C22—62no—
726C22—101no—
727C22—101no—
728C22—121no—
729C22—121no—
730C22—302no—
731C22—601no—
732C22—601no—
733C22—1204no—
734C22D3×D4×D511yescharacteristic
735C4—41no—
736C4—52no—
737C4—61no—
738C4—61no—
739C4—102no—
740C4—121no—
741C4—201no—
742C4—301no—
743C4—301no—
744C4—601no—
745C4C2×C4×D3×D511yescharacteristic
746C4D5×#23711yescharacteristic
747C3#1061159711yescharacteristic, complemented, Sylow
748C2—42no—
749C2—102no—
750C2—122no—
751C2—602no—
752C2D5×#67⋊C411yescharacteristic
753C2#1175406211yescharacteristic
754C2#1175409311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#91478C2
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. #11754923C2semidirect
3. #11753837C2semidirect
4. #11750886C2semidirect
5. C5×#4785C2semidirect
6. C3×#65061C2semidirect
7. #11748994C2semidirect
8. #11748986C2semidirect
9. D5×#821C2semidirect
10. #11747743C2semidirect
11. #11747738C2semidirect
12. #11747646C2semidirect
13. #11747272C2semidirect
14. #11747264C2semidirect
15. #11747189C2semidirect
19. D4×Dic15C22semidirect
22. C5×D4×Dic3C22semidirect
31. #91478C4semidirect
40. #91331C22semidirect
41. Dic3×Dic10C22semidirect
45. C3×C5×#102C22semidirect
47. #91099C22semidirect
48. #91092C22semidirect
50. C5×#815C22semidirect
51. C5×#808C22semidirect
52. C3×#3964C22semidirect
53. C3×#3948C22semidirect
54. C3×#3942C22semidirect
55. #90990C22semidirect
56. #90989C22semidirect
59. #90951C22semidirect
60. Dic3×#168C22semidirect
72. #65061D3semidirect
88. C3×#711C2×C4semidirect
96. D5×D12C2×C4semidirect
100. #6715C2×C4semidirect
106. C5×#213C2×C4semidirect
127. #6658C2×C4semidirect
128. #6656C2×C4semidirect
129. #6649C2×C4semidirect
142. #4785D5semidirect
175. C5×#102C2×D3semidirect
178. #3964C2×D3semidirect
181. #3948C2×D3semidirect
184. #3942C2×D3semidirect
244. D4×Dic3C2×D5semidirect
263. C3×#102C2×D5semidirect
269. #815C2×D5semidirect
273. #808C2×D5semidirect
287. #711C4×D3semidirect
404. #213C4×D5semidirect
504. #102D3×D5semidirect
637. C3×C5#2946semidirect
720. C5#78820semidirect
747. C3#10611597semidirect

Maximal subgroups

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

subgroupindex
#117549232
C2×#914782
#117538372
#117508862
C5×#47852
C3×#650612
#117489942
#117489862
D5×#8212
#117477432
#117477382
#117476462
#117472722
#117472642
#117471892
#106115973
#788205