Finite Group Databasebeta

← C2×#10612260 #12980319

Subgroups — C2×#10612260 #12980319

Order 1280.

1938 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
1C2×#66005C211yesmaximal, characteristic, complemented
2C2×#65876C211yesmaximal, characteristic, complemented
3C2×C5×#463C211yesmaximal, characteristic
4C2×#65456C211yesmaximal, characteristic, complemented
5C2×#65455C211yesmaximal, characteristic, complemented
6C2×#65444C211yesmaximal, characteristic
7C2×#65442C211yesmaximal, characteristic
8C2×#65349C211yesmaximal, characteristic, complemented
9C2×#65307C211yesmaximal, characteristic, complemented
10#10612260C2116yesmaximal, direct product factor
11C2×#65138C211yesmaximal, characteristic, complemented
12C2×#65117C211yesmaximal, characteristic, complemented
13C2×#65082C211yesmaximal, characteristic, complemented
14C2×#65079C211yesmaximal, characteristic, complemented
15C2×#65056C211yesmaximal, characteristic, complemented
16C2×#65046C211yesmaximal, characteristic, complemented
17C22×C5×SD16C2211yescharacteristic
18C22×C5×D8C2211yescharacteristic
19C2×C5×#124C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×Q8×Dic5C2211yescharacteristic
22C2×#4090C2211yescharacteristic
23C22×#689C2211yescharacteristic
24C22×#689C2211yescharacteristic
25C2×#4082C2211yescharacteristic
26C2×#4082C2211yescharacteristic
27C2×#4082C2211yescharacteristic
28C2×D4×Dic5C2211yescharacteristic
29C22×#687C2211yescharacteristic
30C22×#687C2211yescharacteristic
31C22×#687C2211yescharacteristic
32C2×#4072—21no—
33C2×#4070—21no—
34C22×Dic20C2211yescharacteristic
35C22×Dic20C2211yescharacteristic
36#66005—24no—
37#66005C2218yescomplemented
38#65876—24no—
39#65876C2218yescomplemented
40C2×#4033C2211yescharacteristic
41C2×#4033C2211yescharacteristic
42C2×#4025—21no—
43C2×#4025—21no—
44C2×#4025—21no—
45C2×#4025—21no—
46C2×#4024—21no—
47C2×#4023—21no—
48C2×#4015C2211yescharacteristic
49C2×C4×Dic10C2211yescharacteristic
50C2×C4×Dic10C2211yescharacteristic
51C5×#463C2218yes—
52C2×C5×C4⋊C8C2211yescharacteristic
53C2×C5×#103C2211yescharacteristic
54C2×C5×#102C2211yescharacteristic
55C2×#3964C2211yescharacteristic
56#65456C2218yescomplemented
57#65455C2218yescomplemented
58#65444C2218yes—
59#65442C2218yes—
60C2×#3948C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3947C2211yescharacteristic
63C2×#3946C2211yescharacteristic
64C2×#3946C2211yescharacteristic
65C2×C8×Dic5C2211yescharacteristic
66#65349C2218yescomplemented
67#65307C2218yescomplemented
68C2×#3942C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3935C2211yescharacteristic
71#65138C2218yescomplemented
72#65117C2218yescomplemented
73#65082C2218yescomplemented
74#65079C2218yescomplemented
75#65056C2218yescomplemented
76#65046C2218yescomplemented
77C2×#3402—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C23×Dic5—21no—
83C22×Dic10D411yescharacteristic
84C22×Dic10C2311yescharacteristic
85C22×Dic10C2311yescharacteristic
86C22×Dic10C2311yescharacteristic
87C2×C5×SD16—42no—
88C2×C5×SD16C2314yes—
89C2×C5×D8—42no—
90C2×C5×D8C2314yes—
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2311yescharacteristic
93C5×#124—22no—
94C5×#124C2314yes—
95C4×C5×D4—22no—
96C4×C5×D4C2314yes—
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C42×C5C2311yescharacteristic
102C2×C22⋊Dic5—21no—
103C2×C22⋊Dic5—21no—
104C2×C22⋊Dic5—21no—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5—21no—
109Q8×Dic5—22no—
110Q8×Dic5C2314yes—
111#4090—22no—
112#4090C2314yes—
113C2×#689—24no—
114C2×#689—42no—
115C2×#689C2314yes—
116C2×#689C2314yes—
117#4082—22no—
118#4082—22no—
119#4082—22no—
120#4082C2314yes—
121#4082C2314yes—
122#4082C2314yes—
123D4×Dic5—22no—
124D4×Dic5C2314yes—
125C2×#687—24no—
126C2×#687—24no—
127C2×#687—42no—
128C2×#687C2314yes—
129C2×#687C2314yes—
130C2×#687C2314yes—
131#4072—28no—
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5—21no—
134C2×C4⋊Dic5—21no—
135C2×C4⋊Dic5D411yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137#4070—28no—
138C2×#683—21no—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×#683D411yescharacteristic
144C2×#683D411yescharacteristic
145C2×C4×Dic5—21no—
146C2×C4×Dic5—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—21no—
149C2×C4×Dic5C2311yescharacteristic
150C2×C4×Dic5C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C2×Dic20—42no—
154C2×Dic20—42no—
155C2×Dic20C2314yes—
156C2×Dic20C2314yes—
157#4033—22no—
158#4033—22no—
159#4033C2314yes—
160#4033C2314yes—
161#4025—28no—
162#4025—28no—
163#4025—28no—
164#4025—28no—
165#4024—28no—
166#4023—28no—
167#4015—22no—
168#4015C2314yes—
169C4×Dic10—22no—
170C4×Dic10D414yes—
171C4×Dic10C2314yes—
172C4×Dic10C2314yes—
173C5×C4⋊C8C2314yes—
174C5×#103C2314yes—
175C5×#102C2314yes—
176#3964C2314yes—
177#3948C2314yes—
178#3948C2314yes—
179#3947C2314yes—
180#3946C2314yes—
181#3946C2314yes—
182C8×Dic5C2314yes—
183#3942C2314yes—
184#3939C2314yes—
185#3935C2314yes—
186C2×#556—51no—
187C2×#556—51no—
188#3402—516no—
189C2×#497—51no—
190C2×#497—51no—
191C2×#495—51no—
192C2×#464—51no—
193C2×#464—51no—
194C2×#462—51no—
195C2×#462—51no—
196C2×#463—51no—
197C2×#463D511yescharacteristic
198C2×#446—51no—
199C2×#440—51no—
200C2×#440—51no—
201C2×C4×Q16—51no—
202C24×C5—21no—
203C24×C5—21no—
204C2×C5×Q8—21no—
205C2×C5×Q8—22no—
206C2×C5×Q8—22no—
207C2×C5×Q8C2412yes—
208C2×C5×D4—21no—
209C2×C5×D4—21no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—22no—
214C2×C5×D4C2412yes—
215C2×C5×D4C2412yes—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—24no—
219C22×C4×C5—44no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2411yescharacteristic
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—24no—
228C22×Dic5—44no—
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231C22×Dic5C2×D411yescharacteristic
232C22×Dic5C2×D411yescharacteristic
233C2×Dic10—22no—
234C2×Dic10—22no—
235C2×Dic10—22no—
236C2×Dic10—22no—
237C2×Dic10—22no—
238C2×Dic10—22no—
239C2×Dic10—21no—
240C2×Dic10—21no—
241C2×Dic10—21no—
242C2×Dic10—42no—
243C2×Dic10C2×D414yes—
244C2×Dic10C2412yes—
245C2×Dic10C2412yes—
246C2×Dic10C2412yes—
247C5×SD16—44no—
248C5×D8—44no—
249C2×C5×C8—22no—
250C2×C5×C8—22no—
251C2×C5×C8C2412yes—
252C2×C5×C8C2412yes—
253C5×C4⋊C4—21no—
254C5×C4⋊C4C2412yes—
255C5×C22⋊C4—24no—
256C5×C22⋊C4—24no—
257C5×C22⋊C4—24no—
258C42×C5C2×D412yes—
259C42×C5C2412yes—
260C22⋊Dic5—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265C22⋊Dic5—24no—
266C22⋊Dic5—24no—
267#689—28no—
268#689—44no—
269#687—28no—
270#687—28no—
271#687—44no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5—24no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2×D414yes—
277C4⋊Dic5C2412yes—
278#683—24no—
279#683—24no—
280#683—24no—
281#683—24no—
282#683—24no—
283#683C2×D414yes—
284#683C2×D414yes—
285C4×Dic5—24no—
286C4×Dic5—24no—
287C4×Dic5—24no—
288C4×Dic5—24no—
289C4×Dic5C2×D412yes—
290C4×Dic5C2×D412yes—
291C4×Dic5C2412yes—
292C4×Dic5C2412yes—
293C2×#168—22no—
294C2×#168#4114yes—
295C2×#168C2412yes—
296C2×#168C2412yes—
297Dic20—44no—
298Dic20—44no—
299C22×Q16—51no—
300C22×Q16—51no—
301C22×Q16—51no—
302C22×Q16—51no—
303C22×SD16—51no—
304C22×SD16—51no—
305C22×SD16—51no—
306C22×SD16C2×D511yescharacteristic
307C22×D8C2×D511yescharacteristic
308#556—58no—
309#556—58no—
310#556—104no—
311#556—104no—
312C2×C4⋊Q8—51no—
313C2×C4⋊Q8—51no—
314C2×#126—101no—
315C2×#126—101no—
316C2×#126—101no—
317C2×#126—101no—
318C2×#124—51no—
319C2×#124—51no—
320C2×#124—51no—
321C2×#124C2×D511yescharacteristic
322C2×C22⋊Q8—101no—
323C2×C22⋊Q8—101no—
324C2×C4×Q8—51no—
325C2×C4×Q8—51no—
326C2×C4×Q8—51no—
327C2×C4×Q8—51no—
328C2×C4×Q8—51no—
329C2×C4×D4—51no—
330C2×C4×D4C2×D511yescharacteristic
331C2×#117—101no—
332C2×#117—101no—
333#497—58no—
334#497—58no—
335#495—58no—
336#464—58no—
337#464—58no—
338#463—58no—
339#463C2×D518yes—
340#462—58no—
341#462—58no—
342#446—58no—
343#440—58no—
344#440—58no—
345C4×Q16—58no—
346C2×#107—51no—
347C2×C4⋊C8—51no—
348C2×C4⋊C8—51no—
349C2×C4⋊C8C2×D511yescharacteristic
350C2×#103—51no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#103C2×D511yescharacteristic
354C2×#102—51no—
355C2×#102C2×D511yescharacteristic
356C2×#97—51no—
357C2×#97—51no—
358C2×C4×C8—51no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—42no—
362C23×C5—42no—
363C23×C5—42no—
364C23×C5—42no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5C22×D411yescharacteristic
368C5×Q8—22no—
369C5×Q8—22no—
370C5×Q8—42no—
371C5×D4—22no—
372C5×D4—22no—
373C5×D4—22no—
374C5×D4—22no—
375C5×D4—42no—
376C5×D4—42no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—48no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D411yescharacteristic
387C2×C4×C5C2×#4112yes—
388C2×C4×C5H(5,𝔽2)12yes—
389C2×C4×C5C2511yescharacteristic
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—48no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407Dic10—22no—
408Dic10—22no—
409Dic10—22no—
410Dic10—22no—
411Dic10—22no—
412Dic10—22no—
413Dic10—44no—
414Dic10—42no—
415Dic10—42no—
416Dic10—42no—
417C5×C8—22no—
418C5×C8—22no—
419#168—22no—
420#168C2×#4114yes—
421C22×Q8—51no—
422C22×Q8—51no—
423C22×Q8—51no—
424C22×Q8—51no—
425C22×Q8C22×D511yescharacteristic
426C22×D4C22×D511yescharacteristic
427C22×D4C22×D511yescharacteristic
428C23×C4—21no—
429C23×C4—101no—
430C2×Q16—54no—
431C2×Q16—54no—
432C2×Q16—54no—
433C2×Q16—54no—
434C2×Q16—104no—
435C2×Q16—202no—
436C2×Q16—202no—
437C2×Q16—202no—
438C2×SD16—42no—
439C2×SD16—54no—
440C2×SD16—54no—
441C2×SD16—54no—
442C2×SD16—104no—
443C2×SD16—104no—
444C2×SD16—202no—
445C2×SD16C22×D514yes—
446C2×D8—42no—
447C2×D8C22×D514yes—
448C22×C8—51no—
449C22×C8—51no—
450C22×C8C22×D511yescharacteristic
451C22×C8C22×D511yescharacteristic
452C4⋊Q8—54no—
453C4⋊Q8—54no—
454C4⋊Q8—102no—
455C4⋊Q8—102no—
456#126—108no—
457#126—108no—
458#126—108no—
459#126—108no—
460#124—22no—
461#124—54no—
462#124—54no—
463#124—54no—
464#124—102no—
465#124—102no—
466#124—102no—
467#124C22×D514yes—
468C22⋊Q8—108no—
469C22⋊Q8—108no—
470C4×Q8—54no—
471C4×Q8—54no—
472C4×Q8—54no—
473C4×Q8—54no—
474C4×Q8—54no—
475C4×Q8—54no—
476C4×Q8—102no—
477C4×Q8—102no—
478C4×Q8—102no—
479C4×Q8—102no—
480C4×D4—22no—
481C4×D4—54no—
482C4×D4—102no—
483C4×D4C22×D514yes—
484#117—108no—
485#117—108no—
486C2×C4⋊C4—51no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—51no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4—101no—
494C2×C4⋊C4—101no—
495C2×C4⋊C4—101no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4C22×D511yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—101no—
503C2×C22⋊C4—101no—
504C2×C22⋊C4—101no—
505C2×C22⋊C4—101no—
506C2×C22⋊C4—101no—
507C2×C22⋊C4—101no—
508C2×C22⋊C4—101no—
509C2×C42—51no—
510C2×C42—51no—
511C2×C42—101no—
512C2×C42—101no—
513C2×C42—101no—
514C2×C42—101no—
515C2×C42C22×D511yescharacteristic
516#107—54no—
517C4⋊C8—54no—
518C4⋊C8—54no—
519C4⋊C8C22×D514yes—
520#103—54no—
521#103—54no—
522#103—54no—
523#103C22×D514yes—
524#102—54no—
525#102C22×D514yes—
526#97—54no—
527#97—54no—
528C4×C8—54no—
529C22×C5—42no—
530C22×C5—42no—
531C22×C5—42no—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—84no—
536C22×C5—84no—
537C22×C5#55012yes—
538C22×C5#57512yes—
539C22×C5#57812yes—
540C22×C5C23×D411yescharacteristic
541C4×C5—22no—
542C4×C5—22no—
543C4×C5—42no—
544C4×C5—42no—
545C4×C5#55012yes—
546C4×C5C22×#4111yescharacteristic
547C4×C5C2×H(5,𝔽2)11yescharacteristic
548Dic5—22no—
549Dic5—22no—
550Dic5—22no—
551Dic5—22no—
552Dic5—42no—
553Dic5—42no—
554Dic5—42no—
555Dic5—42no—
556C24—21no—
557C24—21no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—54no—
562C2×Q8—52no—
563C2×Q8—52no—
564C2×Q8—52no—
565C2×Q8—101no—
566C2×Q8—101no—
567C2×Q8—101no—
568C2×Q8—102no—
569C2×Q8—102no—
570C2×Q8—102no—
571C2×Q8—102no—
572C2×Q8—102no—
573C2×Q8—102no—
574C2×Q8—202no—
575C2×Q8C23×D512yes—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4C23×D512yes—
583C2×D4C23×D512yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—51no—
589C22×C4—51no—
590C22×C4—51no—
591C22×C4—51no—
592C22×C4—104no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—204no—
598C22×C4D4×D511yescharacteristic
599C22×C4D4×D511yescharacteristic
600C22×C4C23×D511yescharacteristic
601Q16—108no—
602Q16—204no—
603Q16—204no—
604Q16—204no—
605SD16—44no—
606SD16—108no—
607SD16—108no—
608SD16—204no—
609D8—44no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—54no—
613C2×C8—52no—
614C2×C8—52no—
615C2×C8—102no—
616C2×C8C23×D512yes—
617C2×C8C23×D512yes—
618C4⋊C4—21no—
619C4⋊C4—54no—
620C4⋊C4—54no—
621C4⋊C4—54no—
622C4⋊C4—52no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—104no—
628C4⋊C4—101no—
629C4⋊C4—104no—
630C4⋊C4—104no—
631C4⋊C4—104no—
632C4⋊C4C23×D512yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—104no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C22⋊C4—104no—
643C42—52no—
644C42—52no—
645C42—52no—
646C42—52no—
647C42—104no—
648C42—104no—
649C42—104no—
650C42—104no—
651C42D4×D512yes—
652C42C23×D512yes—
653C2×C5—82no—
654C2×C5—82no—
655C2×C5#340214yescomplemented
656C2×C5C2×#55011yescharacteristic
657C2×C5C2×#57511yescharacteristic
658C2×C5C2×#57811yescharacteristic
659C23—22no—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23C2×D4×D511yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—102no—
672Q8—102no—
673Q8—102no—
674Q8—102no—
675Q8—102no—
676Q8—102no—
677Q8—204no—
678Q8—202no—
679Q8—202no—
680Q8—202no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—42no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—52no—
695C2×C4—52no—
696C2×C4—52no—
697C2×C4—52no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—208no—
707C2×C4—202no—
708C2×C4—202no—
709C2×C4—202no—
710C2×C4—202no—
711C2×C4C2×D4×D512yes—
712C2×C4C2×D4×D512yes—
713C2×C4C2×D4×D511yescharacteristic
714C2×C4#414412yes—
715C2×C4D5×#4112yes—
716C2×C4C24×D511yescharacteristic
717C8—22no—
718C8—22no—
719C8—54no—
720C8—102no—
721C5C2×#340211yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22#6593312yes—
731C22#6610512yes—
732C22#6610712yes—
733C22C22×D4×D511yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—102no—
739C4—102no—
740C4—102no—
741C4—102no—
742C4—202no—
743C4—202no—
744C4—202no—
745C4—202no—
746C4#6593312yes—
747C4C2×#414411yescharacteristic
748C4C2×D5×#4111yescharacteristic
749C2—82no—
750C2—82no—
751C2#1061226014yesdirect product factor
752C2C2×#6593311yescharacteristic
753C2C2×#6610511yescharacteristic
754C2C2×#6610711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#463C2
socleC23×C5C22×D4
prime radicalC22×C5×D8C22
hypercenterC2×#463D5
hypocenterC5C2×#3402
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#66005C2semidirect
2. C2×#65876C2semidirect
4. C2×#65456C2semidirect
5. C2×#65455C2semidirect
8. C2×#65349C2semidirect
9. C2×#65307C2semidirect
10. #10612260C2direct (N × H)
11. C2×#65138C2semidirect
12. C2×#65117C2semidirect
13. C2×#65082C2semidirect
14. C2×#65079C2semidirect
15. C2×#65056C2semidirect
16. C2×#65046C2semidirect
37. #66005C22semidirect
39. #65876C22semidirect
56. #65456C22semidirect
57. #65455C22semidirect
66. #65349C22semidirect
67. #65307C22semidirect
71. #65138C22semidirect
72. #65117C22semidirect
73. #65082C22semidirect
74. #65079C22semidirect
75. #65056C22semidirect
76. #65046C22semidirect
655. C2×C5#3402semidirect
721. C5C2×#3402semidirect
751. C2#10612260direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660052
C2×#658762
C2×C5×#4632
C2×#654562
C2×#654552
C2×#654442
C2×#654422
C2×#653492
C2×#653072
#106122602
C2×#651382
C2×#651172
C2×#650822
C2×#650792
C2×#650562
C2×#650462
C2×#34025