Finite Group Databasebeta

← #14425349

Subgroups — #14425349

Order 1920.

1524 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1009C211yesmaximal, characteristic, complemented
2C3×#66156C211yesmaximal, characteristic, complemented
3#11754604C211yesmaximal, characteristic, complemented
4#11754138C211yesmaximal, characteristic, complemented
5#11751337C211yesmaximal, characteristic, complemented
6#11749419C214yesmaximal, complemented
7#11749416C214yesmaximal, complemented
8#11748424C211yesmaximal, characteristic, complemented
9C2×#90959C211yesmaximal, characteristic, complemented
10#10615835—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C5×#1009—22no—
13C5×#1009—22no—
14C5×#1009—22no—
15C5×#1009C2214yes—
16C2×C5×#239—21no—
17C2×C5×D3×D4—22no—
18C2×C5×D3×D4—21no—
19C2×C5×#235—21no—
20C2×C5×#235C2211yescharacteristic
21C22×C5×D12—21no—
22C22×C5×D12C2211yescharacteristic
23C2×C3×#709C2211yescharacteristic, complemented
24#91815C2211yescharacteristic, complemented
25C2×#6710C2211yescharacteristic, complemented
26C3×#4097C2212yescomplemented
27C3×#4096—22no—
28C3×#4095C2212yescomplemented
29C3×#4088—21no—
30C3×#4078—21no—
31C2×C3×#681C2211yescharacteristic, complemented
32#91568—22no—
33#91463C2212yescomplemented
34#91449—22no—
35#91370C2212yescomplemented
36#91309C2212yescomplemented
37#91307—21no—
38#91299—21no—
39#91298C2212yescomplemented
40#91297—22no—
41#91121C2214yescomplemented
42#90978C2214yescomplemented
43#90959C2214yescomplemented
44#84005—51nomaximal, Hall
45C2×C5×H(5,𝔽2)—31no—
46#66156—31no—
47#66156D311yescharacteristic, complemented
48#66139—31no—
49#65531—34no—
50#65530—34no—
51#65525—31no—
52#65525—31no—
53C2×#3965—31no—
54C23×C5×D3—22no—
55C23×C5×D3D412yes—
56C3×C5×#41—21no—
57C3×C5×#41—21no—
58C3×C5×#41D412yescomplemented
59C3×C5×#41C2312yes—
60C2×C3×C5×Q8D411yescharacteristic, complemented
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4D411yescharacteristic, complemented
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×C5×#67—22no—
66C2×C5×#67—21no—
67C5×#239—24no—
68C5×#239—24no—
69C5×D3×D4—28no—
70C5×D3×D4—24no—
71C5×D3×D4—28no—
72C5×D3×D4—24no—
73C5×#235—24no—
74C5×#235—21no—
75C5×#235—21no—
76C5×#235—24no—
77C5×#235D412yescomplemented
78C5×#235C2312yes—
79C2×C5×D12—22no—
80C2×C5×D12—24no—
81C2×C5×D12—21no—
82C2×C5×D12—21no—
83C2×C5×D12—21no—
84C2×C5×D12—21no—
85C2×C5×D12—24no—
86C2×C5×D12D412yes—
87C2×C5×D12D411yescharacteristic, complemented
88C2×C5×D12C2312yes—
89C2×C4×C5×D3—22no—
90C2×C4×C5×D3—21no—
91C2×C5×Dic6D411yescharacteristic, complemented
92C2×C3×C22⋊D5—21no—
93C3×#709—21no—
94C3×#709—21no—
95C3×#709—21no—
96C3×#709—21no—
97C2×C3×D20C2311yescharacteristic, complemented
98C2×C3×C4×D5—21no—
99C2×C3×Dic10C2311yescharacteristic, complemented
100C2×#1201—24no—
101#6719—21no—
102C4⋊Dic15—21no—
103C4×Dic15C2312yescomplemented
104#6710—21no—
105#6710C2312yescomplemented
106C2×C3⋊#168—21no—
107C3×#689—22no—
108C3×#688—22no—
109C3×#687—22no—
110C3×#686—22no—
111C3×#681—21no—
112C3×#681C2312yescomplemented
113C2×C3×#168—21no—
114(C2×D3)⋊Dic5—24no—
115#6661—22no—
116#6656—22no—
117#6655—22no—
118#6652—22no—
119C2×#1009D511yescharacteristic, complemented
120C3×#575—51no—
121#5830—51no—
122#5822—51no—
123#5236—51no—
124#5202—54no—
125#5198—54no—
126#5139—51no—
127C2×#823—51no—
128C5×H(5,𝔽2)—34no—
129C5×H(5,𝔽2)—62no—
130C5×H(5,𝔽2)—62no—
131C5×H(5,𝔽2)—62no—
132C2×C5×#41—31no—
133C2×C5×#41—61no—
134C2×C5×#41—61no—
135C2×C5×#41C2×D311yescharacteristic
136C22×C5×D4—31no—
137C22×C5×D4—61no—
138C22×C5×D4—62no—
139C22×C5×D4—61no—
140C2×#709C2×D311yescharacteristic, complemented
141#4099—62no—
142#4097—32no—
143#4097C2×D312yescomplemented
144#4096—22no—
145#4096—62no—
146#4095—32no—
147#4095C2×D312yescomplemented
148#4088—21no—
149#4088—61no—
150#4086—32no—
151#4084—62no—
152#4082—32no—
153#4078—21no—
154#4078—61no—
155#4072—31no—
156C2×#681—31no—
157C2×#681C2×D311yescharacteristic, complemented
158#3969—34no—
159#3969—34no—
160#3965—34no—
161#3019—151noSylow
162C23×C3×C5—21no—
163C23×C3×C5C2×D411yescharacteristic
164C22×C5×D3—22no—
165C22×C5×D3—21no—
166C22×C5×D3—28no—
167C22×C5×D3—22no—
168C22×C5×D3—82no—
169C22×C5×D3—84no—
170C22×C5×D3C2×D414yes—
171C22×C3×D5—21no—
172C3×C5×Q8—21no—
173C3×C5×Q8C2×D412yes—
174C3×C5×D4—22no—
175C3×C5×D4—22no—
176C3×C5×D4—21no—
177C3×C5×D4C2×D412yes—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5C2×D411yescharacteristic
182C2×C3×C4×C5C2×D411yescharacteristic
183C2×C3×C4×C5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2411yescharacteristic
187C2×Dic15—22no—
188C5×#67—28no—
189C5×#67—22no—
190C5×#67—22no—
191C2×C5×Dic3—21no—
192C5×D12—28no—
193C5×D12—22no—
194C5×D12—21no—
195C5×D12—22no—
196C5×D12—22no—
197C5×D12—22no—
198C5×D12C2×D412yes—
199C4×C5×D3—28no—
200C4×C5×D3—22no—
201C4×C5×D3—22no—
202C5×Dic6—21no—
203C5×Dic6C2×D412yes—
204C3×C22⋊D5—41no—
205C3×C22⋊D5—41no—
206C2×C3×Dic5—21no—
207C3×D20—21no—
208C3×D20—21no—
209C3×C4×D5—41no—
210C3×C4×D5—41no—
211C3×Dic10—21no—
212C3×Dic10—21no—
213#1201—84no—
214C3⋊#168—22no—
215C3×#168—22no—
216C2×C3×#41—51no—
217C2×C3×#41C2×D511yescharacteristic
218#1009—22no—
219#1009—22no—
220#1009—22no—
221#1009C2×D514yes—
222C2×#239—21no—
223C2×D3×D4—22no—
224C2×D3×D4—21no—
225C2×#235—21no—
226C2×#235C2×D511yescharacteristic
227C22×D12—21no—
228C22×D12C2×D511yescharacteristic
229C3×#137—52no—
230C3×#137—101no—
231C3×AGL(1,ℤ/8)—52no—
232C3×AGL(1,ℤ/8)—101no—
233C3×#135—102no—
234C2×C3×M16—51no—
235#951—101no—
236#950—102no—
237#949—101no—
238#947—52no—
239#942—52no—
240#940—52no—
241#937—102no—
242#932—52no—
243#930—102no—
244#926—51no—
245C2×#208—51no—
246#837—54no—
247#825—54no—
248#823—54no—
249C24×C5—32no—
250C24×C5—62no—
251C5×#41—21no—
252C5×#41—21no—
253C5×#41—32no—
254C5×#41—32no—
255C5×#41—64no—
256C5×#41—64no—
257C5×#41—64no—
258C5×#41—64no—
259C5×#41—61no—
260C5×#41—61no—
261C5×#41#6712yescomplemented
262C5×#41C22×D312yes—
263C2×C5×Q8—31no—
264C2×C5×Q8#6711yescharacteristic, complemented
265C2×C5×D4—21no—
266C2×C5×D4—31no—
267C2×C5×D4—32no—
268C2×C5×D4—32no—
269C2×C5×D4—64no—
270C2×C5×D4—62no—
271C2×C5×D4—64no—
272C2×C5×D4—68no—
273C2×C5×D4—68no—
274C2×C5×D4—64no—
275C2×C5×D4—62no—
276C2×C5×D4—61no—
277C2×C5×D4—64no—
278C2×C5×D4—61no—
279C2×C5×D4—61no—
280C2×C5×D4—61no—
281C2×C5×D4—61no—
282C2×C5×D4#6711yescharacteristic, complemented
283C22×C4×C5—21no—
284C22×C4×C5—62no—
285C22×C4×C5—61no—
286C22×C4×C5C22×D311yescharacteristic
287C2×C22⋊D5—21no—
288C2×C22⋊D5—64no—
289#709—21no—
290#709—21no—
291#709—21no—
292#709—21no—
293C2×D20C22×D311yescharacteristic, complemented
294C2×C4×D5—21no—
295C2×Dic10C22×D311yescharacteristic, complemented
296C22⋊Dic5—64no—
297C22⋊Dic5—61no—
298#689—22no—
299#689—62no—
300#688—22no—
301#688—62no—
302#687—22no—
303#687—62no—
304#686—22no—
305#686—62no—
306C4⋊Dic5—61no—
307C4×Dic5—32no—
308#681—21no—
309#681—32no—
310#681—61no—
311#681C22×D312yescomplemented
312C2×#168—21no—
313C2×#168—61no—
314C2×H(5,𝔽2)—31no—
315#575—51no—
316#575—151no—
317#535—151no—
318#455—154no—
319#453—154no—
320#421—151no—
321#421—151no—
322C2×#100—151no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—42no—
326C22×C3×C5#12011yescharacteristic
327C22×C3×C5#12011yescharacteristic
328C22×C3×C5C22×D411yescharacteristic
329C2×C5×D3—24no—
330C2×C5×D3—22no—
331C2×C5×D3—44no—
332C2×C5×D3—42no—
333C2×C5×D3—44no—
334C2×C5×D3—82no—
335C2×C5×D3—88no—
336C2×C3×D5—42no—
337C2×C3×D5—41no—
338C3×C4×C5—22no—
339C3×C4×C5#12011yescharacteristic
340C3×C4×C5#12011yescharacteristic
341C3×C4×C5C22×D411yescharacteristic
342C3×C4×C5C22×D411yescharacteristic
343Dic15—42no—
344C3×Dic5—41no—
345C5×Dic3—22no—
346C23×D3—22no—
347C23×D3C22⋊D512yes—
348C3×#41—21no—
349C3×#41—21no—
350C3×#41—101no—
351C3×#41—101no—
352C3×#41—101no—
353C3×#41—101no—
354C3×#41C22⋊D512yescomplemented
355C3×#41C22×D512yes—
356C2×C3×Q8—51no—
357C2×C3×Q8C22⋊D511yescharacteristic, complemented
358C2×C3×D4—21no—
359C2×C3×D4—51no—
360C2×C3×D4—101no—
361C2×C3×D4C22⋊D511yescharacteristic, complemented
362C22×C3×C4—21no—
363C22×C3×C4—101no—
364C22×C3×C4C22×D511yescharacteristic
365C2×#67—22no—
366C2×#67—21no—
367C2×#67—104no—
368#239—24no—
369#239—24no—
370D3×D4—28no—
371D3×D4—24no—
372D3×D4—28no—
373D3×D4—24no—
374#235—24no—
375#235—21no—
376#235—21no—
377#235—24no—
378#235C22⋊D512yescomplemented
379#235C22×D512yes—
380C2×D12—22no—
381C2×D12—24no—
382C2×D12—21no—
383C2×D12—21no—
384C2×D12—21no—
385C2×D12—21no—
386C2×D12—24no—
387C2×D12C22⋊D512yes—
388C2×D12C22⋊D511yescharacteristic, complemented
389C2×D12C22×D512yes—
390C2×C4×D3—22no—
391C2×C4×D3—21no—
392C2×Dic6C22⋊D511yescharacteristic, complemented
393C3×Q16—102no—
394C3×SD16—102no—
395C3×SD16—102no—
396C3×D8—102no—
397C3×M16—52no—
398C3×M16—101no—
399C2×C3×C8—101no—
400#217—101no—
401#216—102no—
402#215—102no—
403#214—102no—
404#213—102no—
405(C2×D3)⋊C4—104no—
406C4⋊Dic3—101no—
407C4×Dic3—52no—
408#208—52no—
409#208—101no—
410C2×C3⋊C8—101no—
411C23×C5—21no—
412C23×C5—34no—
413C23×C5—68no—
414C23×C5—61no—
415C23×C5—62no—
416C23×C5—62no—
417C23×C5—242no—
418C23×C5—244no—
419C23×C5D3×D411yescharacteristic
420C22×D5—21no—
421C5×Q8—21no—
422C5×Q8—32no—
423C5×Q8—61no—
424C5×Q8C2×#6712yes—
425C5×D4—22no—
426C5×D4—22no—
427C5×D4—21no—
428C5×D4—32no—
429C5×D4—68no—
430C5×D4—68no—
431C5×D4—62no—
432C5×D4—62no—
433C5×D4—61no—
434C5×D4—62no—
435C5×D4—62no—
436C5×D4—62no—
437C5×D4—62no—
438C5×D4C2×#6712yes—
439C2×C4×C5—21no—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—68no—
443C2×C4×C5—61no—
444C2×C4×C5—62no—
445C2×C4×C5—62no—
446C2×C4×C5D3×D411yescharacteristic
447C2×C4×C5D3×D411yescharacteristic
448C2×C4×C5D3×D411yescharacteristic
449C2×C4×C5C2×#6711yescharacteristic
450C2×C4×C5C2×#6711yescharacteristic
451C2×C4×C5C23×D311yescharacteristic
452C22⋊D5—41no—
453C22⋊D5—41no—
454C22⋊D5—244no—
455C2×Dic5—21no—
456C2×Dic5—62no—
457D20—21no—
458D20—21no—
459C4×D5—41no—
460C4×D5—41no—
461Dic10—21no—
462Dic10—21no—
463#168—22no—
464#168—62no—
465H(5,𝔽2)—34no—
466H(5,𝔽2)—62no—
467H(5,𝔽2)—62no—
468H(5,𝔽2)—62no—
469C2×#41—31no—
470C2×#41—51no—
471C2×#41—61no—
472C2×#41—61no—
473C2×#41D3×D511yescharacteristic
474C22×D4—31no—
475C22×D4—61no—
476C22×D4—62no—
477C22×D4—61no—
478#137—52no—
479#137—101no—
480#137—152no—
481#137—301no—
482AGL(1,ℤ/8)—52no—
483AGL(1,ℤ/8)—101no—
484AGL(1,ℤ/8)—152no—
485AGL(1,ℤ/8)—301no—
486#135—102no—
487#135—302no—
488C2×M16—51no—
489C2×M16—151no—
490#127—152no—
491#124—152no—
492#121—302no—
493#120—302no—
494#117—151no—
495#104—154no—
496#104—154no—
497#100—154no—
498C2×C3×C5—21no—
499C2×C3×C5—21no—
500C2×C3×C5—21no—
501C2×C3×C5—42no—
502C2×C3×C5C2×#12011yescharacteristic
503C3×D5—81no—
504C5×D3—44no—
505C5×D3—42no—
506C23×C3—21no—
507C23×C3—101no—
508C23×C3C2×C22⋊D511yescharacteristic
509C22×D3—22no—
510C22×D3—21no—
511C22×D3—28no—
512C22×D3—22no—
513C22×D3—82no—
514C22×D3—84no—
515C22×D3C2×C22⋊D514yes—
516C3×Q8—21no—
517C3×Q8—101no—
518C3×Q8—101no—
519C3×Q8C2×C22⋊D512yes—
520C3×D4—22no—
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—101no—
524C3×D4—101no—
525C3×D4—201no—
526C3×D4—201no—
527C3×D4C2×C22⋊D512yes—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—101no—
532C2×C3×C4—201no—
533C2×C3×C4—201no—
534C2×C3×C4C2×C22⋊D511yescharacteristic
535C2×C3×C4C2×C22⋊D511yescharacteristic
536C2×C3×C4C2×C22⋊D511yescharacteristic
537C2×C3×C4C2×C22⋊D511yescharacteristic
538C2×C3×C4C2×C22⋊D511yescharacteristic
539C2×C3×C4C23×D511yescharacteristic
540#67—28no—
541#67—22no—
542#67—22no—
543#67—404no—
544C2×Dic3—21no—
545C2×Dic3—102no—
546D12—28no—
547D12—22no—
548D12—21no—
549D12—22no—
550D12—22no—
551D12—22no—
552D12C2×C22⋊D512yes—
553C4×D3—28no—
554C4×D3—22no—
555C4×D3—22no—
556Dic6—21no—
557Dic6C2×C22⋊D512yes—
558C3×C8—102no—
559C3⋊C8—102no—
560C22×C5—22no—
561C22×C5—41no—
562C22×C5—42no—
563C22×C5—62no—
564C22×C5—64no—
565C22×C5—124no—
566C22×C5—124no—
567C22×C5—122no—
568C22×C5—242no—
569C22×C5—248no—
570C22×C5#93711yescharacteristic
571C22×C5#93711yescharacteristic
572C22×C5C2×D3×D411yescharacteristic
573C2×D5—42no—
574C2×D5—41no—
575C4×C5—22no—
576C4×C5—62no—
577C4×C5#93711yescharacteristic
578C4×C5#93711yescharacteristic
579C4×C5C2×D3×D411yescharacteristic
580C4×C5C22×#6711yescharacteristic
581Dic5—41no—
582Dic5—122no—
583C24—32no—
584C24—62no—
585#41—21no—
586#41—21no—
587#41—32no—
588#41—32no—
589#41—64no—
590#41—64no—
591#41—64no—
592#41—64no—
593#41—61no—
594#41—61no—
595#41—101no—
596#41—101no—
597#41—101no—
598#41—101no—
599#41#120112yescomplemented
600#41C2×D3×D512yes—
601C2×Q8—31no—
602C2×Q8—51no—
603C2×Q8#120111yescharacteristic, complemented
604C2×D4—21no—
605C2×D4—31no—
606C2×D4—32no—
607C2×D4—32no—
608C2×D4—51no—
609C2×D4—64no—
610C2×D4—62no—
611C2×D4—64no—
612C2×D4—68no—
613C2×D4—68no—
614C2×D4—64no—
615C2×D4—62no—
616C2×D4—61no—
617C2×D4—64no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—101no—
623C2×D4—304no—
624C2×D4#120111yescharacteristic, complemented
625C22×C4—21no—
626C22×C4—62no—
627C22×C4—61no—
628C22×C4—101no—
629C22×C4C2×D3×D511yescharacteristic
630Q16—102no—
631Q16—302no—
632SD16—102no—
633SD16—102no—
634SD16—302no—
635SD16—302no—
636D8—102no—
637D8—302no—
638M16—52no—
639M16—101no—
640M16—152no—
641M16—301no—
642C2×C8—101no—
643C2×C8—301no—
644C4⋊C4—301no—
645C22⋊C4—304no—
646C22⋊C4—301no—
647C42—152no—
648C3×C5#301911yescharacteristic, complemented, Hall
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—42no—
652C22×C3—202no—
653C22×C3—201no—
654C22×C3#409911yescharacteristic
655C22×C3#409911yescharacteristic
656C22×C3C22×C22⋊D511yescharacteristic
657C2×D3—24no—
658C2×D3—22no—
659C2×D3—44no—
660C2×D3—42no—
661C2×D3—44no—
662C2×D3—82no—
663C2×D3—88no—
664C3×C4—22no—
665C3×C4—201no—
666C3×C4#409911yescharacteristic
667C3×C4#409911yescharacteristic
668C3×C4C22×C22⋊D511yescharacteristic
669C3×C4C22×C22⋊D511yescharacteristic
670Dic3—22no—
671Dic3—202no—
672C2×C5—21no—
673C2×C5—21no—
674C2×C5—21no—
675C2×C5—42no—
676C2×C5—124no—
677C2×C5—122no—
678C2×C5C2×#93711yescharacteristic
679D5—81no—
680C23—21no—
681C23—34no—
682C23—68no—
683C23—61no—
684C23—62no—
685C23—62no—
686C23—101no—
687C23—242no—
688C23—244no—
689C23D3×C22⋊D511yescharacteristic
690Q8—21no—
691Q8—32no—
692Q8—61no—
693Q8—101no—
694Q8—101no—
695Q8C2×#120112yes—
696D4—22no—
697D4—22no—
698D4—21no—
699D4—32no—
700D4—68no—
701D4—68no—
702D4—62no—
703D4—62no—
704D4—62no—
705D4—62no—
706D4—61no—
707D4—62no—
708D4—62no—
709D4—101no—
710D4—101no—
711D4—201no—
712D4—201no—
713D4—1204no—
714D4C2×#120112yes—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—68no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—101no—
723C2×C4—201no—
724C2×C4—201no—
725C2×C4—302no—
726C2×C4C2×#120111yescharacteristic
727C2×C4C2×#120111yescharacteristic
728C2×C4D3×C22⋊D511yescharacteristic
729C2×C4D3×C22⋊D511yescharacteristic
730C2×C4D3×C22⋊D511yescharacteristic
731C2×C4C22×D3×D511yescharacteristic
732C8—102no—
733C8—302no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—401no—
739C2×C3C2×#409911yescharacteristic
740D3—44no—
741D3—42no—
742C5#8400511yescharacteristic, complemented, Sylow
743C22—22no—
744C22—41no—
745C22—42no—
746C22—62no—
747C22—64no—
748C22—124no—
749C22—124no—
750C22—122no—
751C22—202no—
752C22—201no—
753C22—242no—
754C22—248no—
755C22#9156811yescharacteristic
756C22#9156811yescharacteristic
757C22C2×D3×C22⋊D511yescharacteristic
758C4—22no—
759C4—62no—
760C4—201no—
761C4—602no—
762C4#9156811yescharacteristic
763C4#9156811yescharacteristic
764C4C22×#120111yescharacteristic
765C4C2×D3×C22⋊D511yescharacteristic
766C3#1061583511yescharacteristic, complemented, Sylow
767C2—21no—
768C2—21no—
769C2—21no—
770C2—42no—
771C2—124no—
772C2—122no—
773C2—401no—
774C2C2×#9156811yescharacteristic
subgroupG/H
centerC2C2×#91568
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#120
hypercenterC2×#41D3×D5
hypocenterC3×C5#3019
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1009C2semidirect
2. C3×#66156C2semidirect
3. #11754604C2semidirect
4. #11754138C2semidirect
5. #11751337C2semidirect
6. #11749419C2semidirect
7. #11749416C2semidirect
8. #11748424C2semidirect
9. C2×#90959C2semidirect
23. C2×C3×#709C22semidirect
24. #91815C22semidirect
25. C2×#6710C22semidirect
26. C3×#4097C22semidirect
28. C3×#4095C22semidirect
31. C2×C3×#681C22semidirect
33. #91463C22semidirect
35. #91370C22semidirect
36. #91309C22semidirect
39. #91298C22semidirect
41. #91121C22semidirect
42. #90978C22semidirect
43. #90959C22semidirect
47. #66156D3semidirect
58. C3×C5×#41D4semidirect
60. C2×C3×C5×Q8D4semidirect
62. C2×C3×C5×D4D4semidirect
77. C5×#235D4semidirect
87. C2×C5×D12D4semidirect
91. C2×C5×Dic6D4semidirect
97. C2×C3×D20C23semidirect
99. C2×C3×Dic10C23semidirect
103. C4×Dic15C23semidirect
105. #6710C23semidirect
112. C3×#681C23semidirect
119. C2×#1009D5semidirect
140. C2×#709C2×D3semidirect
143. #4097C2×D3semidirect
147. #4095C2×D3semidirect
157. C2×#681C2×D3semidirect
261. C5×#41#67semidirect
264. C2×C5×Q8#67semidirect
282. C2×C5×D4#67semidirect
293. C2×D20C22×D3semidirect
295. C2×Dic10C22×D3semidirect
311. #681C22×D3semidirect
354. C3×#41C22⋊D5semidirect
357. C2×C3×Q8C22⋊D5semidirect
361. C2×C3×D4C22⋊D5semidirect
378. #235C22⋊D5semidirect
388. C2×D12C22⋊D5semidirect
392. C2×Dic6C22⋊D5semidirect
599. #41#1201semidirect
603. C2×Q8#1201semidirect
624. C2×D4#1201semidirect
648. C3×C5#3019semidirect
742. C5#84005semidirect
766. C3#10615835semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10092
C3×#661562
#117546042
#117541382
#117513372
#117494192
#117494162
#117484242
C2×#909592
#106158353
#840055