Finite Group Databasebeta

← C2×#10611204 #12977897

Subgroups — C2×#10611204 #12977897

Order 1280.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65897C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic, complemented
3C2×C5×#435C211yesmaximal, characteristic, complemented
4C2×#65424C211yesmaximal, characteristic, complemented
5C2×#65410C211yesmaximal, characteristic, complemented
6C2×#65404C211yesmaximal, characteristic, complemented
7C2×#65395C211yesmaximal, characteristic, complemented
8#10611204C2116yesmaximal, direct product factor
9C2×#65136C211yesmaximal, characteristic, complemented
10C2×#65135C211yesmaximal, characteristic, complemented
11C2×#65026C211yesmaximal, characteristic, complemented
12C2×#65026C211yesmaximal, characteristic, complemented
13C2×#65026C211yesmaximal, characteristic, complemented
14C2×#65025C211yesmaximal, characteristic, complemented
15C2×#65000C211yesmaximal, characteristic, complemented
16C2×#64991C211yesmaximal, characteristic, complemented
17C22×C5×M16C2211yescharacteristic
18C23×C5×C8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×#4085—21no—
21C2×#4084—21no—
22C2×#4076C2211yescharacteristic
23C2×#4076C2211yescharacteristic
24C2×#4076C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4072C2211yescharacteristic
27C2×#4072C2211yescharacteristic
28C2×#4072C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×D40C2211yescharacteristic
31#65899—24no—
32#65899C2218yescomplemented
33#65897—24no—
34#65897C2218yescomplemented
35C2×#4044—21no—
36C2×#4038—21no—
37C2×#4031—21no—
38C2×#4031—21no—
39C2×#4029—21no—
40C2×#4027—21no—
41C2×C4×D20C2211yescharacteristic
42C2×C4×D20C2211yescharacteristic
43C2×#4016C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C5×#435C2218yescomplemented
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×C22⋊C8C2211yescharacteristic
48C2×C5×C22⋊C8C2211yescharacteristic
49C2×C5×#97C2211yescharacteristic
50#65424C2218yescomplemented
51#65410C2218yescomplemented
52#65404C2218yescomplemented
53C2×#3953C2211yescharacteristic
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59#65395C2218yescomplemented
60C2×#3950C2211yescharacteristic
61C2×#3950C2211yescharacteristic
62C2×#3950C2211yescharacteristic
63C2×#3950C2211yescharacteristic
64C2×#3950C2211yescharacteristic
65C2×#3949C2211yescharacteristic
66C2×#3949C2211yescharacteristic
67C2×#3949C2211yescharacteristic
68C2×#3949C2211yescharacteristic
69#65136C2218yescomplemented
70#65135C2218yescomplemented
71#65026C2218yescomplemented
72#65026C2218yescomplemented
73#65026C2218yescomplemented
74#65025C2218yescomplemented
75#65000C2218yescomplemented
76#64991C2218yescomplemented
77C2×#3347—51nomaximal, Sylow
78C22×C5×D4D411yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C23×Dic5—21no—
86C22×D20C2311yescharacteristic
87C22×D20C2311yescharacteristic
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×Dic10—21no—
91C2×C5×M16—24no—
92C2×C5×M16C2314yes—
93C22×C5×C8—24no—
94C22×C5×C8C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2314yes—
98C22×C5×C8C2311yescharacteristic
99C4×C5×D4D414yes—
100C4×C5×D4C2314yes—
101C2×C5×C4⋊C4D411yescharacteristic
102C2×C5×C22⋊C4D411yescharacteristic
103C2×C5×C22⋊C4D411yescharacteristic
104C2×C42×C5C2311yescharacteristic
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108#4085—28no—
109#4084—28no—
110#4076—22no—
111#4076—22no—
112#4076—22no—
113#4076—22no—
114#4076C2314yes—
115#4076C2314yes—
116#4076C2314yes—
117#4076C2314yes—
118C2×#685—21no—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124#4072—22no—
125#4072—22no—
126#4072—22no—
127#4072C2314yes—
128#4072C2314yes—
129#4072C2314yes—
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5—21no—
132C2×C4⋊Dic5—22no—
133C2×C4⋊Dic5C2314yes—
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137C2×C4⋊Dic5C2311yescharacteristic
138C2×C4⋊Dic5C2311yescharacteristic
139C2×C4⋊Dic5C2311yescharacteristic
140C2×#683—21no—
141C2×#683—21no—
142C2×C4×Dic5—21no—
143C2×C4×Dic5—21no—
144C2×C4×Dic5—21no—
145C2×D40—24no—
146C2×D40C2314yes—
147#4044—28no—
148#4038—28no—
149#4031—28no—
150#4031—28no—
151#4029—28no—
152#4027—28no—
153C4×D20—22no—
154C4×D20—22no—
155C4×D20C2314yes—
156C4×D20C2314yes—
157#4016—22no—
158#4016C2314yes—
159#4015—22no—
160#4015C2314yes—
161C5×C4⋊C8C2314yes—
162C5×C22⋊C8C2314yes—
163C5×C22⋊C8C2314yes—
164C5×#97C2314yes—
165#3953C2314yes—
166#3953C2314yes—
167#3953C2314yes—
168#3953C2314yes—
169#3953C2314yes—
170#3953C2314yes—
171#3950C2314yes—
172#3950C2314yes—
173#3950C2314yes—
174#3950C2314yes—
175#3950C2314yes—
176#3949C2314yes—
177#3949C2314yes—
178#3949C2314yes—
179#3949C2314yes—
180C2×#555—51no—
181C2×#553—51no—
182#3347—516no—
183C2×#501—51no—
184C2×#482—51no—
185C2×#482—51no—
186C2×#482—51no—
187C2×#480—51no—
188C2×#478—51no—
189C2×#474—51no—
190C2×#469—51no—
191C2×#466—51no—
192C2×#442—51no—
193C2×#435D511yescharacteristic, complemented
194C2×#428—51no—
195C2×#427—51no—
196C24×C5C2×D411yescharacteristic
197C24×C5C2×D411yescharacteristic
198C23×D5—21no—
199C23×D5—21no—
200C2×C5×D4—42no—
201C2×C5×D4C2×D414yes—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5C2×D411yescharacteristic
207C22×C4×C5C2×D411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D412yes—
211C22×C4×C5C2×D412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2411yescharacteristic
215C2×C22⋊D5—24no—
216C2×C22⋊D5—24no—
217C2×C22⋊D5—24no—
218C2×C22⋊D5—24no—
219C2×C22⋊D5—44no—
220C2×C22⋊D5—82no—
221C2×C22⋊D5—82no—
222C2×C22⋊D5—82no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—24no—
230C22×Dic5—82no—
231C2×D20—22no—
232C2×D20—22no—
233C2×D20—22no—
234C2×D20—22no—
235C2×D20—21no—
236C2×D20—21no—
237C2×D20C2412yes—
238C2×D20C2412yes—
239C2×C4×D5—24no—
240C2×C4×D5—24no—
241C2×C4×D5—44no—
242C2×C4×D5—82no—
243C2×Dic10—24no—
244C2×Dic10—82no—
245C5×M16—28no—
246C2×C5×C8—22no—
247C2×C5×C8—22no—
248C2×C5×C8—22no—
249C2×C5×C8—28no—
250C2×C5×C8#4114yes—
251C2×C5×C8C2412yes—
252C2×C5×C8C2412yes—
253C2×C5×C8C2412yes—
254C2×C5×C8C2412yes—
255C5×C4⋊C4C2×D414yes—
256C5×C22⋊C4C2×D414yes—
257C5×C22⋊C4C2×D414yes—
258C42×C5C2×D412yes—
259C42×C5C2412yes—
260C22⋊Dic5—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263#685—24no—
264#685—24no—
265#685—24no—
266#685—24no—
267#685—24no—
268#685—24no—
269C4⋊Dic5—21no—
270C4⋊Dic5—21no—
271C4⋊Dic5—24no—
272C4⋊Dic5—21no—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5—24no—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280C4⋊Dic5C2412yes—
281C4⋊Dic5C2412yes—
282C4⋊Dic5C2412yes—
283#683—24no—
284#683—24no—
285C4×Dic5—24no—
286C4×Dic5—24no—
287C4×Dic5—24no—
288D40—28no—
289C22×D8—51no—
290C22×M16C2×D511yescharacteristic
291C23×C8C2×D511yescharacteristic
292#555—58no—
293#555—104no—
294#553—58no—
295#553—104no—
296C2×C4⋊Q8—51no—
297C2×#126—101no—
298C2×#125—51no—
299C2×#124—101no—
300C2×#124—101no—
301C2×#123—101no—
302C2×#121—51no—
303C2×#121—51no—
304C2×#121—51no—
305C2×#121—51no—
306C2×#121—101no—
307C2×#121—101no—
308C2×C4×D4—51no—
309C2×C4×D4—51no—
310C2×C4×D4—101no—
311C2×C4×D4C2×D511yescharacteristic
312C2×#117—51no—
313C2×#117—51no—
314C2×#117—51no—
315C2×#117—101no—
316C22×C4⋊C4—51no—
317#501—58no—
318#482—58no—
319#482—58no—
320#482—58no—
321#480—58no—
322#478—58no—
323#474—58no—
324#469—58no—
325#466—58no—
326#442—58no—
327#435C2×D518yescomplemented
328#428—58no—
329#427—58no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#106—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×C4⋊C8C2×D511yescharacteristic
340C2×#102—51no—
341C2×#102—51no—
342C2×#102—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×C22⋊C8C2×D511yescharacteristic
347C2×C22⋊C8C2×D511yescharacteristic
348C2×#97C2×D511yescharacteristic
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5C22×D412yes—
356C23×C5C22×D412yes—
357C23×C5C22×D411yescharacteristic
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—42no—
361C22×D5—42no—
362C22×D5—42no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5—42no—
366C5×D4—44no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—24no—
372C2×C4×C5—24no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5C22×D412yes—
378C2×C4×C5C22×D412yes—
379C2×C4×C5C22×D412yes—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D411yescharacteristic
382C2×C4×C5C2×#4112yes—
383C2×C4×C52−1+412yes—
384C2×C4×C5C2511yescharacteristic
385C22⋊D5—48no—
386C22⋊D5—84no—
387C22⋊D5—84no—
388C22⋊D5—84no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—84no—
402D20—22no—
403D20—22no—
404D20—22no—
405D20—22no—
406D20—42no—
407D20—42no—
408C4×D5—48no—
409C4×D5—84no—
410Dic10—84no—
411C5×C8—22no—
412C5×C8—22no—
413C5×C8—22no—
414C5×C8C2×#4114yes—
415C22×Q8—101no—
416C22×D4—51no—
417C22×D4—51no—
418C22×D4—101no—
419C22×D4—101no—
420C22×D4—101no—
421C22×D4—101no—
422C22×D4D2011yescharacteristic
423C23×C4—101no—
424C23×C4—101no—
425C23×C4—101no—
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C2×D8—54no—
429C2×D8—104no—
430C2×M16—24no—
431C2×M16C22×D514yes—
432C22×C8—24no—
433C22×C8C22×D511yescharacteristic
434C22×C8C22×D514yes—
435C22×C8C22×D511yescharacteristic
436C22×C8C22×D511yescharacteristic
437C22×C8C22×D511yescharacteristic
438C4⋊Q8—54no—
439C4⋊Q8—102no—
440#126—108no—
441#125—54no—
442#125—102no—
443#124—108no—
444#124—108no—
445#123—108no—
446#121—54no—
447#121—54no—
448#121—54no—
449#121—54no—
450#121—108no—
451#121—108no—
452#121—102no—
453#121—102no—
454#121—102no—
455#121—102no—
456C4×D4—54no—
457C4×D4—54no—
458C4×D4—108no—
459C4×D4—102no—
460C4×D4—102no—
461C4×D4D2014yes—
462C4×D4C22×D514yes—
463#117—54no—
464#117—54no—
465#117—54no—
466#117—102no—
467#117—102no—
468#117—102no—
469#117—108no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—51no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4—101no—
482C2×C4⋊C4D2011yescharacteristic
483C2×C22⋊C4—101no—
484C2×C22⋊C4—101no—
485C2×C22⋊C4—101no—
486C2×C22⋊C4—101no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4D2011yescharacteristic
493C2×C22⋊C4D2011yescharacteristic
494C2×C42—101no—
495C2×C42—101no—
496C2×C42—101no—
497C2×C42C22×D511yescharacteristic
498#107—54no—
499#107—54no—
500#107—54no—
501#107—54no—
502#107—54no—
503#106—54no—
504#106—54no—
505#106—54no—
506#106—54no—
507C4⋊C8C22×D514yes—
508#102—54no—
509#102—54no—
510#102—54no—
511#102—54no—
512#102—54no—
513#102—54no—
514C22⋊C8C22×D514yes—
515C22⋊C8C22×D514yes—
516#97C22×D514yes—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—22no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—44no—
524C22×C5—44no—
525C22×C5#54712yes—
526C22×C5#57512yes—
527C22×C5#57612yes—
528C22×C5C23×D411yescharacteristic
529C2×D5—42no—
530C2×D5—42no—
531C2×D5—42no—
532C2×D5—42no—
533C2×D5—42no—
534C2×D5—42no—
535C2×D5—84no—
536C2×D5—84no—
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—22no—
540C4×C5—22no—
541C4×C5#54712yes—
542C4×C5C22×#4111yescharacteristic
543C4×C5C2×2−1+411yescharacteristic
544Dic5—42no—
545Dic5—42no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5—42no—
550C24—101no—
551C24—101no—
552C24C2×D2011yescharacteristic
553C24C2×D2011yescharacteristic
554C2×Q8—104no—
555C2×Q8—402no—
556C2×D4—42no—
557C2×D4—52no—
558C2×D4—52no—
559C2×D4—104no—
560C2×D4—104no—
561C2×D4—104no—
562C2×D4—104no—
563C2×D4—101no—
564C2×D4—101no—
565C2×D4—102no—
566C2×D4—102no—
567C2×D4—102no—
568C2×D4—102no—
569C2×D4—204no—
570C2×D4—402no—
571C2×D4—402no—
572C2×D4—402no—
573C2×D4C2×D2014yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—104no—
585C22×C4—104no—
586C22×C4—104no—
587C22×C4—204no—
588C22×C4—402no—
589C22×C4—402no—
590C22×C4C2×D2012yes—
591C22×C4C2×D2012yes—
592C22×C4C2×D2011yescharacteristic
593C22×C4C2×D2011yescharacteristic
594C22×C4C2×D2011yescharacteristic
595C22×C4C2×D2011yescharacteristic
596C22×C4C23×D512yes—
597C22×C4C23×D512yes—
598C22×C4C23×D511yescharacteristic
599D8—108no—
600M16—28no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8#71114yes—
606C2×C8C23×D512yes—
607C2×C8C23×D512yes—
608C2×C8C23×D512yes—
609C2×C8C23×D512yes—
610C4⋊C4—52no—
611C4⋊C4—52no—
612C4⋊C4—52no—
613C4⋊C4—52no—
614C4⋊C4—52no—
615C4⋊C4—52no—
616C4⋊C4—101no—
617C4⋊C4—101no—
618C4⋊C4—104no—
619C4⋊C4—101no—
620C4⋊C4—101no—
621C4⋊C4—101no—
622C4⋊C4—101no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4C2×D2014yes—
627C22⋊C4—104no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4—104no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4C2×D2014yes—
637C22⋊C4C2×D2014yes—
638C42—104no—
639C42—104no—
640C42—104no—
641C42C2×D2012yes—
642C42C23×D512yes—
643C2×C5—42no—
644C2×C5—42no—
645C2×C5#334714yescomplemented
646C2×C5C2×#54711yescharacteristic
647C2×C5C2×#57511yescharacteristic
648C2×C5C2×#57611yescharacteristic
649D5—82no—
650D5—82no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—102no—
658C23—102no—
659C23—202no—
660C23—202no—
661C23—202no—
662C23—202no—
663C23—202no—
664C23—202no—
665C23C22×D2012yes—
666C23C22×D2012yes—
667C23C22×D2011yescharacteristic
668Q8—404no—
669D4—44no—
670D4—102no—
671D4—102no—
672D4—102no—
673D4—102no—
674D4—208no—
675D4—202no—
676D4—202no—
677D4—404no—
678D4—404no—
679D4—404no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—208no—
697C2×C4—202no—
698C2×C4—202no—
699C2×C4—202no—
700C2×C4—202no—
701C2×C4—202no—
702C2×C4—202no—
703C2×C4—404no—
704C2×C4—404no—
705C2×C4C22×D2012yes—
706C2×C4C22×D2012yes—
707C2×C4C22×D2012yes—
708C2×C4C22×D2012yes—
709C2×C4C22×D2011yescharacteristic
710C2×C4C2×#71112yes—
711C2×C4#415012yes—
712C2×C4C24×D511yescharacteristic
713C8—22no—
714C8—22no—
715C8—22no—
716C8C2×#71114yes—
717C5C2×#334711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—202no—
727C22—202no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—202no—
732C22—404no—
733C22—404no—
734C22#6588912yes—
735C22#6608212yes—
736C22#6608612yes—
737C22C23×D2011yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—202no—
743C4—202no—
744C4—202no—
745C4—202no—
746C4—202no—
747C4—202no—
748C4#6588912yes—
749C4C22×#71111yescharacteristic
750C4C2×#415011yescharacteristic
751C2—42no—
752C2—42no—
753C2—402no—
754C2—402no—
755C2#1061120414yesdirect product factor
756C2C2×#6588911yescharacteristic
757C2C2×#6608211yescharacteristic
758C2C2×#6608611yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#435C2
socleC23×C5C22×D4
hypercenterC2×#435D5
hypocenterC5C2×#3347
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#65897C2semidirect
2. C2×#65899C2semidirect
3. C2×C5×#435C2semidirect
4. C2×#65424C2semidirect
5. C2×#65410C2semidirect
6. C2×#65404C2semidirect
7. C2×#65395C2semidirect
8. #10611204C2direct (N × H)
9. C2×#65136C2semidirect
10. C2×#65135C2semidirect
11. C2×#65026C2semidirect
12. C2×#65026C2semidirect
13. C2×#65026C2semidirect
14. C2×#65025C2semidirect
15. C2×#65000C2semidirect
16. C2×#64991C2semidirect
32. #65899C22semidirect
34. #65897C22semidirect
45. C5×#435C22semidirect
50. #65424C22semidirect
51. #65410C22semidirect
52. #65404C22semidirect
59. #65395C22semidirect
69. #65136C22semidirect
70. #65135C22semidirect
71. #65026C22semidirect
72. #65026C22semidirect
73. #65026C22semidirect
74. #65025C22semidirect
75. #65000C22semidirect
76. #64991C22semidirect
193. C2×#435D5semidirect
327. #435C2×D5semidirect
645. C2×C5#3347semidirect
717. C5C2×#3347semidirect
755. C2#10611204direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658972
C2×#658992
C2×C5×#4352
C2×#654242
C2×#654102
C2×#654042
C2×#653952
#106112042
C2×#651362
C2×#651352
C2×#650262
C2×#650252
C2×#650002
C2×#649912
C2×#33475