Finite Group Databasebeta

← C2×#10611501 #12969182

Subgroups — C2×#10611501 #12969182

Order 1280.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65916C211yesmaximal, characteristic, complemented
2C2×#65896C211yesmaximal, characteristic, complemented
3C2×C5×#440C211yesmaximal, characteristic, complemented
4C2×#65460C211yesmaximal, characteristic, complemented
5C2×#65465C211yesmaximal, characteristic, complemented
6C2×C4×#688C211yesmaximal, characteristic, complemented
7C2×C4×#686C211yesmaximal, characteristic, complemented
8#10611501C2116yesmaximal, direct product factor
9C2×#65172C211yesmaximal, characteristic, complemented
10C2×#65165C211yesmaximal, characteristic, complemented
11C2×#65101C211yesmaximal, characteristic, complemented
12C2×#65089C211yesmaximal, characteristic, complemented
13C2×#65071C211yesmaximal, characteristic, complemented
14C2×#65049C211yesmaximal, characteristic, complemented
15C2×#65000C211yesmaximal, characteristic, complemented
16C2×#64997C211yesmaximal, characteristic, complemented
17C22×C5×SD16C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×#4093C2211yescharacteristic
21C2×#4092C2211yescharacteristic
22C22×#688C2211yescharacteristic
23C2×#4086C2211yescharacteristic
24C2×#4084C2211yescharacteristic
25C22×#686C2211yescharacteristic
26C2×#4076—21no—
27C2×#4075—21no—
28C22×D40C2211yescharacteristic
29C22×#676C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31#65916—24no—
32#65916C2218yescomplemented
33#65896—24no—
34#65896C2218yescomplemented
35C2×#4042—21no—
36C2×#4041C2211yescharacteristic
37C2×#4041C2211yescharacteristic
38C2×#4040—21no—
39C2×#4036C2211yescharacteristic
40C2×#4034C2211yescharacteristic
41C2×#4030—21no—
42C2×#4029—21no—
43C2×#4022—21no—
44C2×#4021—21no—
45C2×C4×D20C2211yescharacteristic
46C2×C4×D20C2211yescharacteristic
47C2×#4018C2211yescharacteristic
48C5×#440C2218yescomplemented
49C2×C5×#107C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#102C2211yescharacteristic
52C2×C5×#97C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55#65465C2218yescomplemented
56#65460C2218yescomplemented
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3949C2211yescharacteristic
60C2×#3947C2211yescharacteristic
61C2×C8×Dic5C2211yescharacteristic
62C4×#688C2218yescomplemented
63C4×#686C2218yescomplemented
64C2×#3941C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×C4×#168C2211yescharacteristic
69#65172C2218yescomplemented
70#65165C2218yescomplemented
71#65101C2218yescomplemented
72#65089C2218yescomplemented
73#65071C2218yescomplemented
74#65049C2218yescomplemented
75#65000C2218yescomplemented
76#64997C2218yescomplemented
77C2×#3179—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×D20—21no—
85C22×D20—21no—
86C22×D20C2311yescharacteristic
87C22×D20C2311yescharacteristic
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×C4×D5C2311yescharacteristic
91C22×Dic10—21no—
92C2×C5×SD16—24no—
93C2×C5×SD16C2314yes—
94C22×C5×C8C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C4×C5×Q8—22no—
97C4×C5×Q8C2314yes—
98C4×C5×D4—22no—
99C4×C5×D4C2314yes—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C22⋊C4—21no—
104C2×C42×C5—21no—
105C2×C42×C5C2311yescharacteristic
106C2×C22⋊Dic5—21no—
107#4093—22no—
108#4093C2314yes—
109#4092—22no—
110#4092C2314yes—
111C2×#688—24no—
112C2×#688C2314yes—
113#4086—22no—
114#4086C2314yes—
115#4084—22no—
116#4084C2314yes—
117C2×#686—24no—
118C2×#686C2314yes—
119#4076—28no—
120#4075—28no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685—21no—
127C2×#685—21no—
128C2×#685D411yescharacteristic
129C2×#685D411yescharacteristic
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683D411yescharacteristic
137C2×#683D411yescharacteristic
138C2×C4×Dic5C2311yescharacteristic
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C2×D40—24no—
142C2×D40C2314yes—
143C2×#676—24no—
144C2×#676C2314yes—
145C2×C8×D5—24no—
146C2×C8×D5C2314yes—
147#4042—28no—
148#4041—22no—
149#4041—22no—
150#4041C2314yes—
151#4041C2314yes—
152#4040—28no—
153#4036—22no—
154#4036C2314yes—
155#4034—22no—
156#4034C2314yes—
157#4030—28no—
158#4029—28no—
159#4022—28no—
160#4021—28no—
161C4×D20—22no—
162C4×D20—22no—
163C4×D20C2314yes—
164C4×D20C2314yes—
165#4018D414yes—
166#4018C2314yes—
167C5×#107C2314yes—
168C5×#103C2314yes—
169C5×#102C2314yes—
170C5×#97C2314yes—
171#3967C2314yes—
172#3964C2314yes—
173#3953C2314yes—
174#3953C2314yes—
175#3949C2314yes—
176#3947C2314yes—
177C8×Dic5C2314yes—
178#3941C2314yes—
179#3941C2314yes—
180#3940C2314yes—
181#3939C2314yes—
182C4×#168C2314yes—
183C2×#542—51no—
184C2×#540—51no—
185#3179—516no—
186C2×#501—51no—
187C2×#496—51no—
188C2×#488—51no—
189C2×#486—51no—
190C2×#469—51no—
191C2×#468—51no—
192C2×#466—51no—
193C2×#465—51no—
194C2×#442—51no—
195C2×#440D511yescharacteristic, complemented
196C2×C4×SD16—51no—
197C2×C4×D8—51no—
198C2×#405—51no—
199C24×C5—21no—
200C23×D5—21no—
201C23×D5—21no—
202C23×D5C2×D411yescharacteristic
203C2×C5×Q8—21no—
204C2×C5×Q8—22no—
205C2×C5×Q8—22no—
206C2×C5×Q8C2412yes—
207C2×C5×D4—21no—
208C2×C5×D4—22no—
209C2×C5×D4—22no—
210C2×C5×D4C2412yes—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—24no—
215C22×C4×C5—82no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2411yescharacteristic
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—24no—
222C2×C22⋊D5—82no—
223C2×C22⋊D5—82no—
224C2×C22⋊D5—82no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5C2×D411yescharacteristic
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C2×D20—22no—
231C2×D20—22no—
232C2×D20—22no—
233C2×D20—22no—
234C2×D20—21no—
235C2×D20—21no—
236C2×D20—24no—
237C2×D20—24no—
238C2×D20—82no—
239C2×D20—82no—
240C2×D20C2412yes—
241C2×D20C2412yes—
242C2×C4×D5—22no—
243C2×C4×D5—22no—
244C2×C4×D5—24no—
245C2×C4×D5—24no—
246C2×C4×D5—82no—
247C2×C4×D5—82no—
248C2×C4×D5C2×D412yes—
249C2×C4×D5C2412yes—
250C2×Dic10—24no—
251C2×Dic10—82no—
252C5×SD16—28no—
253C2×C5×C8—22no—
254C2×C5×C8#4114yes—
255C2×C5×C8C2412yes—
256C2×C5×C8C2412yes—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4C2412yes—
261C5×C4⋊C4C2412yes—
262C5×C22⋊C4—24no—
263C42×C5—24no—
264C42×C5C2×D412yes—
265C42×C5C2412yes—
266C22⋊Dic5—24no—
267#688—28no—
268#686—28no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273#685—24no—
274#685—24no—
275#685—24no—
276#685C2×D414yes—
277#685C2×D414yes—
278C4⋊Dic5—21no—
279C4⋊Dic5—21no—
280C4⋊Dic5—24no—
281C4⋊Dic5C2412yes—
282C4⋊Dic5C2412yes—
283#683—24no—
284#683—24no—
285#683—24no—
286#683C2×D414yes—
287#683C2×D414yes—
288C4×Dic5C2×D412yes—
289C4×Dic5C2412yes—
290C2×#168—22no—
291C2×#168#4114yes—
292C2×#168C2412yes—
293C2×#168C2412yes—
294D40—28no—
295#676—28no—
296C8×D5—28no—
297C22×SD16—51no—
298C22×SD16C2×D511yescharacteristic
299C22×D8—51no—
300C22×D8—51no—
301C22×M16—51no—
302C23×C8—51no—
303#542—58no—
304#542—104no—
305#540—58no—
306#540—104no—
307C2×C4⋊Q8—51no—
308C2×#127—51no—
309C2×#126—101no—
310C2×#125—51no—
311C2×#124—51no—
312C2×#124—101no—
313C2×#123—101no—
314C2×#123—101no—
315C2×#123—101no—
316C2×C22⋊Q8—51no—
317C2×C22⋊Q8—101no—
318C2×#121—51no—
319C2×#121—51no—
320C2×#121—51no—
321C2×#121—101no—
322C2×#121—101no—
323C2×C4×Q8C2×D511yescharacteristic
324C2×C4×D4—51no—
325C2×C4×D4—51no—
326C2×C4×D4C2×D511yescharacteristic
327C2×#117—51no—
328#501—58no—
329#496—58no—
330#488—58no—
331#486—58no—
332#469—58no—
333#468—58no—
334#466—58no—
335#465—58no—
336#442—58no—
337#440C2×D518yescomplemented
338C4×SD16—58no—
339C4×D8—58no—
340C2×#107—51no—
341C2×#107C2×D511yescharacteristic
342C2×#106—51no—
343C2×#106—51no—
344C2×#103—51no—
345C2×#103C2×D511yescharacteristic
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102C2×D511yescharacteristic
352#405—58no—
353C2×#97—51no—
354C2×#97C2×D511yescharacteristic
355C2×C4×C8—51no—
356C2×C4×C8—51no—
357C23×C5—22no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C22×D5—42no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5C22×D412yes—
374C5×Q8—22no—
375C5×Q8—22no—
376C5×Q8—42no—
377C5×D4—22no—
378C5×D4—22no—
379C5×D4—42no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—84no—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D412yes—
391C2×C4×C5C22×D411yescharacteristic
392C2×C4×C5C2×#4112yes—
393C2×C4×C5C2×#4112yes—
394C2×C4×C5C2511yescharacteristic
395C22⋊D5—84no—
396C22⋊D5—84no—
397C22⋊D5—84no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407C2×Dic5C22×D412yes—
408D20—22no—
409D20—22no—
410D20—22no—
411D20—22no—
412D20—42no—
413D20—42no—
414D20—84no—
415D20—84no—
416C4×D5—24no—
417C4×D5—22no—
418C4×D5—22no—
419C4×D5—84no—
420C4×D5—84no—
421Dic10—84no—
422C5×C8—22no—
423C5×C8C2×#4114yes—
424#168—22no—
425#168C2×#4114yes—
426C22×Q8—101no—
427C22×Q8C22×D511yescharacteristic
428C22×D4—51no—
429C22×D4—51no—
430C22×D4—101no—
431C22×D4—101no—
432C22×D4—101no—
433C22×D4—101no—
434C22×D4—101no—
435C22×D4C22×D511yescharacteristic
436C23×C4—21no—
437C23×C4—51no—
438C23×C4—101no—
439C23×C4—101no—
440C2×SD16—24no—
441C2×SD16—54no—
442C2×SD16—104no—
443C2×SD16C22×D514yes—
444C2×D8—54no—
445C2×D8—54no—
446C2×D8—104no—
447C2×D8—104no—
448C2×M16—54no—
449C2×M16—104no—
450C22×C8—51no—
451C22×C8—51no—
452C22×C8—54no—
453C22×C8—104no—
454C22×C8C22×D511yescharacteristic
455C22×C8C22×D511yescharacteristic
456C4⋊Q8—54no—
457C4⋊Q8—102no—
458#127—54no—
459#127—102no—
460#126—108no—
461#125—54no—
462#125—102no—
463#124—54no—
464#124—108no—
465#124—102no—
466#123—108no—
467#123—108no—
468#123—108no—
469C22⋊Q8—54no—
470C22⋊Q8—108no—
471C22⋊Q8—102no—
472#121—54no—
473#121—54no—
474#121—54no—
475#121—108no—
476#121—108no—
477#121—102no—
478#121—102no—
479#121—102no—
480C4×Q8—22no—
481C4×Q8C22×D514yes—
482C4×D4—22no—
483C4×D4—54no—
484C4×D4—54no—
485C4×D4—102no—
486C4×D4—102no—
487C4×D4C22×D514yes—
488#117—54no—
489#117—54no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—51no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—101no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4—101no—
499C2×C4⋊C4C22×D511yescharacteristic
500C2×C4⋊C4C22×D511yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—51no—
503C2×C22⋊C4—51no—
504C2×C22⋊C4—101no—
505C2×C22⋊C4—101no—
506C2×C22⋊C4—101no—
507C2×C22⋊C4—101no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C22⋊C4—101no—
511C2×C22⋊C4—101no—
512C2×C42—21no—
513C2×C42—51no—
514C2×C42C22×D511yescharacteristic
515#107—54no—
516#107C22×D514yes—
517#106—54no—
518#106—54no—
519#103—54no—
520#103C22×D514yes—
521#102—54no—
522#102—54no—
523#102—54no—
524#102—54no—
525#102—54no—
526#102C22×D514yes—
527#97—54no—
528#97C22×D514yes—
529C4×C8—54no—
530C4×C8—54no—
531C22×C5—42no—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—84no—
535C22×C5#53212yes—
536C22×C5#57612yes—
537C22×C5#57712yes—
538C22×C5C23×D411yescharacteristic
539C2×D5—22no—
540C2×D5—22no—
541C2×D5—22no—
542C2×D5—44no—
543C2×D5—42no—
544C2×D5—42no—
545C2×D5—42no—
546C2×D5—42no—
547C2×D5—42no—
548C2×D5—42no—
549C2×D5—84no—
550C2×D5—84no—
551C4×C5—22no—
552C4×C5—22no—
553C4×C5—42no—
554C4×C5—42no—
555C4×C5—42no—
556C4×C5#53212yes—
557C4×C5C22×#4111yescharacteristic
558C4×C5C22×#4111yescharacteristic
559Dic5—22no—
560Dic5—22no—
561Dic5—22no—
562Dic5—42no—
563Dic5—42no—
564C24—21no—
565C24—51no—
566C24—101no—
567C24—101no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—104no—
572C2×Q8—402no—
573C2×Q8C23×D512yes—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—52no—
578C2×D4—52no—
579C2×D4—104no—
580C2×D4—104no—
581C2×D4—104no—
582C2×D4—104no—
583C2×D4—104no—
584C2×D4—102no—
585C2×D4—102no—
586C2×D4—101no—
587C2×D4—101no—
588C2×D4—102no—
589C2×D4—102no—
590C2×D4—402no—
591C2×D4—402no—
592C2×D4—402no—
593C2×D4—402no—
594C2×D4—402no—
595C2×D4C23×D512yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—51no—
601C22×C4—51no—
602C22×C4—51no—
603C22×C4—52no—
604C22×C4—52no—
605C22×C4—82no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—104no—
611C22×C4—104no—
612C22×C4—402no—
613C22×C4—402no—
614C22×C4D4×D511yescharacteristic
615C22×C4D4×D511yescharacteristic
616C22×C4C23×D511yescharacteristic
617SD16—28no—
618SD16—108no—
619D8—108no—
620D8—108no—
621M16—108no—
622C2×C8—22no—
623C2×C8—54no—
624C2×C8—52no—
625C2×C8—52no—
626C2×C8—102no—
627C2×C8—108no—
628C2×C8#70914yes—
629C2×C8C23×D512yes—
630C2×C8C23×D512yes—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—54no—
635C4⋊C4—54no—
636C4⋊C4—52no—
637C4⋊C4—52no—
638C4⋊C4—104no—
639C4⋊C4—104no—
640C4⋊C4—104no—
641C4⋊C4—104no—
642C4⋊C4—101no—
643C4⋊C4—101no—
644C4⋊C4C23×D512yes—
645C4⋊C4C23×D512yes—
646C22⋊C4—24no—
647C22⋊C4—54no—
648C22⋊C4—54no—
649C22⋊C4—104no—
650C22⋊C4—104no—
651C22⋊C4—104no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—104no—
655C22⋊C4—104no—
656C22⋊C4—104no—
657C42—24no—
658C42—52no—
659C42—52no—
660C42D4×D512yes—
661C42C23×D512yes—
662C2×C5—82no—
663C2×C5#317914yescomplemented
664C2×C5C2×#53211yescharacteristic
665C2×C5C2×#57611yescharacteristic
666C2×C5C2×#57711yescharacteristic
667D5—42no—
668D5—82no—
669D5—82no—
670C23—22no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—52no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—102no—
679C23—102no—
680C23—202no—
681C23—202no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23—202no—
686C23C2×D4×D511yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—42no—
690Q8—404no—
691D4—22no—
692D4—22no—
693D4—42no—
694D4—102no—
695D4—102no—
696D4—102no—
697D4—102no—
698D4—202no—
699D4—202no—
700D4—404no—
701D4—404no—
702D4—404no—
703D4—404no—
704D4—404no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—52no—
714C2×C4—52no—
715C2×C4—52no—
716C2×C4—84no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—104no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—404no—
728C2×C4—404no—
729C2×C4C2×#70912yes—
730C2×C4C2×D4×D512yes—
731C2×C4C2×D4×D512yes—
732C2×C4C2×D4×D511yescharacteristic
733C2×C4D5×#4112yes—
734C2×C4C24×D511yescharacteristic
735C8—22no—
736C8—54no—
737C8—102no—
738C8C2×#70914yes—
739C5C2×#317911yescharacteristic, complemented, Sylow
740C22—42no—
741C22—42no—
742C22—42no—
743C22—84no—
744C22—102no—
745C22—102no—
746C22—102no—
747C22—204no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—404no—
755C22—404no—
756C22#6588212yes—
757C22#6610812yes—
758C22#6611212yes—
759C22C22×D4×D511yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—102no—
766C4—102no—
767C4—102no—
768C4—202no—
769C4—202no—
770C4#6588212yes—
771C4C22×#70911yescharacteristic
772C4C2×D5×#4111yescharacteristic
773C2—82no—
774C2—202no—
775C2—402no—
776C2—402no—
777C2#1061150114yesdirect product factor
778C2C2×#6588211yescharacteristic
779C2C2×#6610811yescharacteristic
780C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#440C2
socleC23×C5C22×D4
hypercenterC2×#440D5
hypocenterC5C2×#3179
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#65916C2semidirect
2. C2×#65896C2semidirect
3. C2×C5×#440C2semidirect
4. C2×#65460C2semidirect
5. C2×#65465C2semidirect
6. C2×C4×#688C2semidirect
7. C2×C4×#686C2semidirect
8. #10611501C2direct (N × H)
9. C2×#65172C2semidirect
10. C2×#65165C2semidirect
11. C2×#65101C2semidirect
12. C2×#65089C2semidirect
13. C2×#65071C2semidirect
14. C2×#65049C2semidirect
15. C2×#65000C2semidirect
16. C2×#64997C2semidirect
32. #65916C22semidirect
34. #65896C22semidirect
48. C5×#440C22semidirect
55. #65465C22semidirect
56. #65460C22semidirect
62. C4×#688C22semidirect
63. C4×#686C22semidirect
69. #65172C22semidirect
70. #65165C22semidirect
71. #65101C22semidirect
72. #65089C22semidirect
73. #65071C22semidirect
74. #65049C22semidirect
75. #65000C22semidirect
76. #64997C22semidirect
195. C2×#440D5semidirect
337. #440C2×D5semidirect
663. C2×C5#3179semidirect
739. C5C2×#3179semidirect
777. C2#10611501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659162
C2×#658962
C2×C5×#4402
C2×#654602
C2×#654652
C2×C4×#6882
C2×C4×#6862
#106115012
C2×#651722
C2×#651652
C2×#651012
C2×#650892
C2×#650712
C2×#650492
C2×#650002
C2×#649972
C2×#31795