Finite Group Databasebeta

← C2×#10613723 #12977862

Subgroups — C2×#10613723 #12977862

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66060C211yesmaximal, characteristic, complemented
2C2×#66029C211yesmaximal, characteristic, complemented
3C2×C5×#501C211yesmaximal, characteristic, complemented
4C2×#65373C211yesmaximal, characteristic, complemented
5C2×#65355C211yesmaximal, characteristic, complemented
6#10613723C2116yesmaximal, direct product factor
7C2×#65171C211yesmaximal, characteristic, complemented
8C2×#65172C211yesmaximal, characteristic, complemented
9C2×#65170C211yesmaximal, characteristic, complemented
10C2×#65174C211yesmaximal, characteristic, complemented
11C2×#65152C211yesmaximal, characteristic, complemented
12C2×#65152C211yesmaximal, characteristic, complemented
13C2×#65154C211yesmaximal, characteristic, complemented
14C2×D5×#106C211yesmaximal, characteristic, complemented
15C2×#65000C211yesmaximal, characteristic, complemented
16C2×#64995C211yesmaximal, characteristic, complemented
17C22×#713—21no—
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×C5×#125C2211yescharacteristic
20C2×#4092—21no—
21C22×D40C2211yescharacteristic
22C22×#676C2211yescharacteristic
23C22×C8×D5C2211yescharacteristic
24#66060—24no—
25#66060C2218yescomplemented
26#66029—24no—
27#66029C2218yescomplemented
28C2×#4044—21no—
29C2×#4041—21no—
30C2×#4041C2211yescharacteristic
31C2×#4041C2211yescharacteristic
32C2×#4041C2211yescharacteristic
33C2×#4041C2211yescharacteristic
34C2×#4040—21no—
35C2×#4040—21no—
36C2×#4040—21no—
37C2×#4039—21no—
38C2×#4038C2211yescharacteristic
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×D5×C4⋊C4C2211yescharacteristic
42C2×C4×D20C2211yescharacteristic
43C2×C4×D20C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C5×#501C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#107C2211yescharacteristic
48C2×C5×#106C2211yescharacteristic
49C2×C5×#106C2211yescharacteristic
50C2×C5×#97C2211yescharacteristic
51C2×#3953C2211yescharacteristic
52C2×#3953C2211yescharacteristic
53C2×#3952C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3949C2211yescharacteristic
56#65373C2218yescomplemented
57#65355C2218yescomplemented
58C2×#3941C2211yescharacteristic
59C2×#3941C2211yescharacteristic
60C2×#3941C2211yescharacteristic
61C2×#3941C2211yescharacteristic
62C2×#3940C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3940C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×C4⋊#168C2211yescharacteristic
67#65174C2218yescomplemented
68#65172C2218yescomplemented
69#65171C2218yescomplemented
70#65170C2218yescomplemented
71#65154C2218yescomplemented
72#65152C2218yescomplemented
73#65152C2218yescomplemented
74D5×#106C2218yescomplemented
75#65000C2218yescomplemented
76#64995C2218yescomplemented
77C2×#3345—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C2×#713—28no—
80C2×#713—48no—
81C22×D20—21no—
82C22×D20—21no—
83C22×D20—21no—
84C22×D20—21no—
85C22×D20D411yescharacteristic
86C22×D20C2311yescharacteristic
87C22×D20C2311yescharacteristic
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5C2311yescharacteristic
94C22×C4×D5C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C5×C4⋊Q8—22no—
98C5×C4⋊Q8C2314yes—
99C5×#125—22no—
100C5×#125C2314yes—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C42×C5C2311yescharacteristic
109#4092—28no—
110C2×#685—21no—
111C2×#685—21no—
112C2×#685—21no—
113C2×#685—21no—
114C2×#685—21no—
115C2×#685—21no—
116C2×#685—21no—
117C2×#685D411yescharacteristic
118C2×#685D411yescharacteristic
119C2×C4⋊Dic5D411yescharacteristic
120C2×C4⋊Dic5C2311yescharacteristic
121C2×C4⋊Dic5C2311yescharacteristic
122C2×#683—21no—
123C2×#683—21no—
124C2×#683—21no—
125C2×C4×Dic5—21no—
126C22×#168C2311yescharacteristic
127C22×#168C2311yescharacteristic
128C2×D40—24no—
129C2×D40C2314yes—
130C2×#676—24no—
131C2×#676C2314yes—
132C2×C8×D5—24no—
133C2×C8×D5C2314yes—
134#4044—28no—
135#4041—28no—
136#4041—22no—
137#4041—22no—
138#4041—22no—
139#4041—22no—
140#4041C2314yes—
141#4041C2314yes—
142#4041C2314yes—
143#4041C2314yes—
144#4040—28no—
145#4040—28no—
146#4040—28no—
147#4039—28no—
148#4038—22no—
149#4038C2314yes—
150D5×C4⋊C4—22no—
151D5×C4⋊C4—22no—
152D5×C4⋊C4—22no—
153D5×C4⋊C4C2314yes—
154D5×C4⋊C4C2314yes—
155D5×C4⋊C4C2314yes—
156C4×D20—22no—
157C4×D20—22no—
158C4×D20D414yes—
159C4×D20C2314yes—
160C4×D20C2314yes—
161C4×D20C2314yes—
162C5×#107C2314yes—
163C5×#107C2314yes—
164C5×#106C2314yes—
165C5×#106C2314yes—
166C5×#97C2314yes—
167#3953C2314yes—
168#3953C2314yes—
169#3952C2314yes—
170#3952C2314yes—
171#3949C2314yes—
172#3941C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3941C2314yes—
176#3940C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3939C2314yes—
180C4⋊#168C2314yes—
181C2×#553—51no—
182C2×#547—51no—
183#3345—516no—
184C2×#501D511yescharacteristic, complemented
185C2×#481—51no—
186C2×#481—51no—
187C2×#482—51no—
188C2×#480—51no—
189C2×#478—51no—
190C2×#476—51no—
191C2×#469—51no—
192C2×#466—51no—
193C2×#442—51no—
194C2×#435—51no—
195C2×#428—51no—
196C22×#106—51no—
197C23×D5—21no—
198C23×D5—21no—
199C23×D5C2×D411yescharacteristic
200C23×D5C2×D411yescharacteristic
201C2×C5×Q8—24no—
202C2×C5×Q8—44no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5C2×D411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2411yescharacteristic
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5C2×D411yescharacteristic
213C22×Dic5C2×D411yescharacteristic
214#713—432no—
215C2×D20—24no—
216C2×D20—22no—
217C2×D20—22no—
218C2×D20—22no—
219C2×D20—22no—
220C2×D20—24no—
221C2×D20—24no—
222C2×D20—24no—
223C2×D20—21no—
224C2×D20—21no—
225C2×D20—24no—
226C2×D20—44no—
227C2×D20—44no—
228C2×D20—44no—
229C2×D20—82no—
230C2×D20C2×D414yes—
231C2×D20C2412yes—
232C2×D20C2412yes—
233C2×C4×D5—22no—
234C2×C4×D5—22no—
235C2×C4×D5—22no—
236C2×C4×D5—22no—
237C2×C4×D5—24no—
238C2×C4×D5—24no—
239C2×C4×D5—24no—
240C2×C4×D5—24no—
241C2×C4×D5—24no—
242C2×C4×D5—44no—
243C2×C4×D5—44no—
244C2×C4×D5—44no—
245C2×C4×D5—82no—
246C2×C4×D5—82no—
247C2×C4×D5C2×D412yes—
248C2×C4×D5C2×D412yes—
249C2×C4×D5C2412yes—
250C2×C4×D5C2412yes—
251C2×C5×C8—22no—
252C2×C5×C8#4114yescomplemented
253C2×C5×C8C2412yes—
254C2×C5×C8C2412yes—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—24no—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4C2412yes—
263C5×C4⋊C4C2412yes—
264C5×C4⋊C4C2412yes—
265C5×C4⋊C4C2412yes—
266C42×C5C2×D412yes—
267C42×C5C2412yes—
268#685—24no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273#685—24no—
274#685—24no—
275#685C2×D414yes—
276#685C2×D414yes—
277C4⋊Dic5—21no—
278C4⋊Dic5—21no—
279C4⋊Dic5C2×D414yes—
280C4⋊Dic5C2412yes—
281C4⋊Dic5C2412yes—
282#683—24no—
283#683—24no—
284#683—24no—
285C4×Dic5—24no—
286C2×#168—22no—
287C2×#168—22no—
288C2×#168C2412yes—
289C2×#168C2412yes—
290D40—28no—
291#676—28no—
292C8×D5—28no—
293C22×#41—101no—
294C22×D8—51no—
295C22×M16—51no—
296C23×C8—51no—
297#553—58no—
298#553—104no—
299#547—58no—
300#547—104no—
301C2×C4⋊Q8C2×D511yescharacteristic
302C2×#126—101no—
303C2×#125C2×D511yescharacteristic
304C2×#123—101no—
305C2×#123—101no—
306C2×#123—101no—
307C2×C22⋊Q8—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×#121—51no—
311C2×#121—51no—
312C2×#121—101no—
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—51no—
316C2×C4×D4—101no—
317C2×#117—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321#501C2×D518yescomplemented
322#482—58no—
323#481—58no—
324#481—58no—
325#480—58no—
326#478—58no—
327#476—58no—
328#469—58no—
329#466—58no—
330#442—58no—
331#435—58no—
332#428—58no—
333C2×#107—51no—
334C2×#107C2×D511yescharacteristic
335C2×#107C2×D511yescharacteristic
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×#106—58no—
341C2×#106C2×D511yescharacteristic
342C2×#106C2×D511yescharacteristic
343C2×C4⋊C8—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×C22⋊C8—51no—
351C2×C22⋊C8—51no—
352C2×#97C2×D511yescharacteristic
353C23×C5C22×D411yescharacteristic
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—42no—
362C22×D5—42no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5—42no—
366C22×D5—42no—
367C22×D5AGL(1,ℤ/8)14yes—
368C22×D5C22×D412yes—
369C22×D5C22×D412yes—
370C5×Q8—48no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5C22×D412yes—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D411yescharacteristic
384C2×C4×C5C2×#4112yes—
385C2×C4×C52−1+412yes—
386C2×C4×C5C2511yescharacteristic
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5C22×D412yes—
394C2×Dic5C22×D412yes—
395D20—28no—
396D20—22no—
397D20—22no—
398D20—22no—
399D20—22no—
400D20—48no—
401D20—48no—
402D20—48no—
403D20—42no—
404D20—42no—
405D20—84no—
406C4×D5—24no—
407C4×D5—24no—
408C4×D5—22no—
409C4×D5—22no—
410C4×D5—22no—
411C4×D5—22no—
412C4×D5—48no—
413C4×D5—48no—
414C4×D5—48no—
415C4×D5—84no—
416C4×D5—84no—
417C5×C8—22no—
418C5×C8C2×#4114yescomplemented
419#168—22no—
420#168—22no—
421C2×#41—108no—
422C2×#41—208no—
423C22×Q8—21no—
424C22×D4—51no—
425C22×D4—51no—
426C22×D4—51no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4—101no—
430C22×D4—101no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—101no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4—101no—
438C2×D8—54no—
439C2×D8—104no—
440C2×M16—54no—
441C2×M16—104no—
442C22×C8—51no—
443C22×C8—51no—
444C22×C8—54no—
445C22×C8—104no—
446C22×C8C22×D511yescharacteristic
447C22×C8C22×D511yescharacteristic
448C4⋊Q8—22no—
449C4⋊Q8C22×D514yes—
450#126—108no—
451#125—22no—
452#125C22×D514yes—
453#123—108no—
454#123—108no—
455#123—108no—
456C22⋊Q8—108no—
457#121—54no—
458#121—54no—
459#121—54no—
460#121—54no—
461#121—102no—
462#121—102no—
463#121—102no—
464#121—102no—
465#121—108no—
466C4×D4—54no—
467C4×D4—54no—
468C4×D4—54no—
469C4×D4—54no—
470C4×D4—108no—
471C4×D4—102no—
472C4×D4—102no—
473#117—54no—
474#117—102no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—102no—
485C2×C4⋊C4—102no—
486C2×C4⋊C4—102no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C4⋊C4C22×D511yescharacteristic
492C2×C4⋊C4C22×D511yescharacteristic
493C2×C4⋊C4C22×D511yescharacteristic
494C2×C22⋊C4—51no—
495C2×C22⋊C4—51no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C42—101no—
504C2×C42C22×D511yescharacteristic
505#107—54no—
506#107C22×D514yes—
507#107C22×D514yes—
508#106—54no—
509#106—54no—
510#106—54no—
511#106—54no—
512#106C22×D514yes—
513#106C22×D514yes—
514C4⋊C8—54no—
515#102—54no—
516#102—54no—
517#102—54no—
518#102—54no—
519#102—54no—
520#102—54no—
521C22⋊C8—54no—
522C22⋊C8—54no—
523#97C22×D514yes—
524C22×C5#54712yes—
525C22×C5C2×AGL(1,ℤ/8)12yes—
526C22×C5#57712yes—
527C22×C5C23×D411yescharacteristic
528C2×D5—28no—
529C2×D5—22no—
530C2×D5—22no—
531C2×D5—22no—
532C2×D5—22no—
533C2×D5—22no—
534C2×D5—44no—
535C2×D5—42no—
536C2×D5—42no—
537C2×D5—42no—
538C2×D5—42no—
539C2×D5—42no—
540C2×D5—42no—
541C2×D5—84no—
542C2×D5—84no—
543C2×D5C2×AGL(1,ℤ/8)14yes—
544C4×C5—22no—
545C4×C5—22no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5#54712yes—
551C4×C5C22×#4111yescharacteristic
552C4×C5C2×2−1+411yescharacteristic
553Dic5—22no—
554Dic5—22no—
555Dic5—42no—
556Dic5—42no—
557C24—51no—
558C24—51no—
559C24—101no—
560C24—101no—
561#41—2032no—
562C2×Q8—24no—
563C2×Q8—44no—
564C2×D4—54no—
565C2×D4—52no—
566C2×D4—52no—
567C2×D4—104no—
568C2×D4—104no—
569C2×D4—104no—
570C2×D4—104no—
571C2×D4—104no—
572C2×D4—101no—
573C2×D4—101no—
574C2×D4—102no—
575C2×D4—102no—
576C2×D4—102no—
577C2×D4—102no—
578C2×D4—204no—
579C2×D4—204no—
580C2×D4—204no—
581C2×D4—402no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—51no—
587C22×C4—51no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—104no—
593C22×C4—104no—
594C22×C4—104no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—104no—
602C22×C4—104no—
603C22×C4—204no—
604C22×C4—204no—
605C22×C4—204no—
606C22×C4—402no—
607C22×C4—402no—
608C22×C4D4×D511yescharacteristic
609C22×C4D4×D511yescharacteristic
610C22×C4C23×D511yescharacteristic
611D8—108no—
612M16—108no—
613C2×C8—22no—
614C2×C8—52no—
615C2×C8—52no—
616C2×C8—102no—
617C2×C8—102no—
618C2×C8—108no—
619C2×C8#71314yescomplemented
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—54no—
630C4⋊C4—52no—
631C4⋊C4—52no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—101no—
636C4⋊C4—101no—
637C4⋊C4C23×D512yes—
638C4⋊C4C23×D512yes—
639C4⋊C4C23×D512yes—
640C4⋊C4C23×D512yes—
641C22⋊C4—54no—
642C22⋊C4—54no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C22⋊C4—104no—
650C42—104no—
651C42D4×D512yes—
652C42C23×D512yes—
653C2×C5#334514yescomplemented
654C2×C5C2×#54711yescharacteristic
655C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
656C2×C5C2×#57711yescharacteristic
657D5—24no—
658D5—42no—
659D5—82no—
660D5—82no—
661C23—54no—
662C23—52no—
663C23—52no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—202no—
672C23—202no—
673C23—202no—
674C23—202no—
675C23—202no—
676C23—202no—
677C23C2×D4×D511yescharacteristic
678Q8—48no—
679D4—108no—
680D4—102no—
681D4—102no—
682D4—102no—
683D4—102no—
684D4—208no—
685D4—208no—
686D4—208no—
687D4—202no—
688D4—202no—
689D4—404no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—52no—
701C2×C4—52no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—104no—
705C2×C4—104no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—208no—
713C2×C4—208no—
714C2×C4—208no—
715C2×C4—202no—
716C2×C4—202no—
717C2×C4—404no—
718C2×C4—404no—
719C2×C4C2×D4×D512yes—
720C2×C4C2×D4×D512yes—
721C2×C4C2×D4×D511yescharacteristic
722C2×C4C2×#71312yes—
723C2×C4#414712yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—102no—
727C8—102no—
728C8C2×#71314yescomplemented
729C5C2×#334511yescharacteristic, complemented, Sylow
730C22—54no—
731C22—102no—
732C22—102no—
733C22—108no—
734C22—102no—
735C22—102no—
736C22—102no—
737C22—204no—
738C22—202no—
739C22—202no—
740C22—202no—
741C22—202no—
742C22—202no—
743C22—202no—
744C22—404no—
745C22—404no—
746C22#6606012yes—
747C22D5×AGL(1,ℤ/8)12yes—
748C22#6611212yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—102no—
757C4—102no—
758C4—202no—
759C4—202no—
760C4#6606012yes—
761C4C22×#71311yescharacteristic
762C4C2×#414711yescharacteristic
763C2—104no—
764C2—202no—
765C2—402no—
766C2—402no—
767C2#1061372314yesdirect product factor
768C2C2×#6606011yescharacteristic
769C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
770C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#501C2
socleC23×C5C22×D4
hypercenterC2×#501D5
hypocenterC5C2×#3345
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#66060C2semidirect
2. C2×#66029C2semidirect
3. C2×C5×#501C2semidirect
4. C2×#65373C2semidirect
5. C2×#65355C2semidirect
6. #10613723C2direct (N × H)
7. C2×#65171C2semidirect
8. C2×#65172C2semidirect
9. C2×#65170C2semidirect
10. C2×#65174C2semidirect
11. C2×#65152C2semidirect
12. C2×#65152C2semidirect
13. C2×#65154C2semidirect
14. C2×D5×#106C2semidirect
15. C2×#65000C2semidirect
16. C2×#64995C2semidirect
25. #66060C22semidirect
27. #66029C22semidirect
45. C5×#501C22semidirect
56. #65373C22semidirect
57. #65355C22semidirect
67. #65174C22semidirect
68. #65172C22semidirect
69. #65171C22semidirect
70. #65170C22semidirect
71. #65154C22semidirect
72. #65152C22semidirect
73. #65152C22semidirect
74. D5×#106C22semidirect
75. #65000C22semidirect
76. #64995C22semidirect
184. C2×#501D5semidirect
252. C2×C5×C8#41semidirect
321. #501C2×D5semidirect
418. C5×C8C2×#41semidirect
619. C2×C8#713semidirect
653. C2×C5#3345semidirect
728. C8C2×#713semidirect
729. C5C2×#3345semidirect
767. C2#10613723direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660602
C2×#660292
C2×C5×#5012
C2×#653732
C2×#653552
#106137232
C2×#651712
C2×#651722
C2×#651702
C2×#651742
C2×#651522
C2×#651542
C2×D5×#1062
C2×#650002
C2×#649952
C2×#33455