Finite Group Databasebeta

← C2×#10613412 #12968545

Subgroups — C2×#10613412 #12968545

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66063C211yesmaximal, characteristic, complemented
2C2×#66009C211yesmaximal, characteristic
3C2×C5×#489C211yesmaximal, characteristic, complemented
4C2×#65382C211yesmaximal, characteristic, complemented
5C2×#65345C211yesmaximal, characteristic, complemented
6#10613412C2116yesmaximal, direct product factor
7C2×#65091C211yesmaximal, characteristic, complemented
8C2×D5×#103C211yesmaximal, characteristic, complemented
9C2×#65086C211yesmaximal, characteristic, complemented
10C2×#65081C211yesmaximal, characteristic, complemented
11C2×#65060C211yesmaximal, characteristic
12C2×#65061C211yesmaximal, characteristic
13C2×#65054C211yesmaximal, characteristic, complemented
14C2×#65057C211yesmaximal, characteristic, complemented
15C2×#64992C211yesmaximal, characteristic, complemented
16C2×#64997C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×#711C2211yescharacteristic
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#124C2211yescharacteristic
21C2×#4092—21no—
22C2×#4090—21no—
23C2×#4090C2211yescharacteristic
24C2×#4082C2211yescharacteristic
25C22×#676C2211yescharacteristic
26C22×C8×D5C2211yescharacteristic
27#66063—24no—
28#66063C2218yescomplemented
29#66009—24no—
30#66009C2218yes—
31C2×#4042—21no—
32C2×#4038C2211yescharacteristic
33C2×D5×C4⋊C4C2211yescharacteristic
34C2×#4036C2211yescharacteristic
35C2×#4035—21no—
36C2×#4034C2211yescharacteristic
37C2×#4029—21no—
38C2×#4029—21no—
39C2×#4024—21no—
40C2×#4024—21no—
41C2×#4018C2211yescharacteristic
42C2×#4016C2211yescharacteristic
43C2×#4015C2211yescharacteristic
44C5×#489C2218yescomplemented
45C2×C5×#103C2211yescharacteristic
46C2×C5×#103C2211yescharacteristic
47C2×C5×#102C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×#97C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54C2×#3948C2211yescharacteristic
55C2×#3948C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3948C2211yescharacteristic
58C2×#3947C2211yescharacteristic
59C2×C8×Dic5C2211yescharacteristic
60#65382C2218yescomplemented
61#65345C2218yescomplemented
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65C2×#3942C2211yescharacteristic
66C2×C4×#168C2211yescharacteristic
67#65091C2218yescomplemented
68D5×#103C2218yescomplemented
69#65086C2218yescomplemented
70#65081C2218yescomplemented
71#65061C2218yes—
72#65060C2218yes—
73#65057C2218yescomplemented
74#65054C2218yescomplemented
75#64997C2218yescomplemented
76#64992C2218yescomplemented
77C2×#3137—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C22×C22⋊D5—21no—
82C23×Dic5—21no—
83C2×Q8×D5—22no—
84C2×Q8×D5—24no—
85C2×Q8×D5—24no—
86C2×Q8×D5C2314yes—
87C2×#711—22no—
88C2×#711—24no—
89C2×#711—24no—
90C2×#711C2314yes—
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5C2311yescharacteristic
94C22×Dic10—21no—
95C22×Dic10—21no—
96C22×Dic10C2311yescharacteristic
97C22×Dic10C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2311yescharacteristic
100C5×C4⋊Q8—22no—
101C5×C4⋊Q8C2314yes—
102C5×#124—22no—
103C5×#124C2314yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C42×C5C2311yescharacteristic
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5—21no—
112#4092—28no—
113#4090—28no—
114#4090—22no—
115#4090C2314yes—
116#4082—22no—
117#4082C2314yes—
118C2×#685—21no—
119C2×#685D411yescharacteristic
120C2×#685D411yescharacteristic
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5—21no—
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5C2311yescharacteristic
125C2×C4⋊Dic5C2311yescharacteristic
126C2×#683—21no—
127C2×#683—21no—
128C2×#683—21no—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683D411yescharacteristic
134C2×#683D411yescharacteristic
135C2×C4×Dic5—21no—
136C2×C4×Dic5C2311yescharacteristic
137C22×#168C2311yescharacteristic
138C22×#168C2311yescharacteristic
139C2×#676—24no—
140C2×#676C2314yes—
141C2×C8×D5—24no—
142C2×C8×D5C2314yes—
143#4042—28no—
144#4038—22no—
145#4038C2314yes—
146D5×C4⋊C4—22no—
147D5×C4⋊C4C2314yes—
148#4036—22no—
149#4036C2314yes—
150#4035—28no—
151#4034—22no—
152#4034C2314yes—
153#4029—28no—
154#4029—28no—
155#4024—28no—
156#4024—28no—
157#4018D414yes—
158#4018C2314yes—
159#4016—22no—
160#4016C2314yes—
161#4015—22no—
162#4015C2314yes—
163C5×#103C2314yes—
164C5×#103C2314yes—
165C5×#102C2314yes—
166C5×#102C2314yes—
167C5×#97C2314yes—
168#3967C2314yes—
169#3967C2314yes—
170#3964C2314yes—
171#3964C2314yes—
172#3948C2314yes—
173#3948C2314yes—
174#3948C2314yes—
175#3948C2314yes—
176#3947C2314yes—
177C8×Dic5C2314yes—
178#3942C2314yes—
179#3942C2314yes—
180#3942C2314yes—
181#3942C2314yes—
182C4×#168C2314yes—
183C2×#544—51no—
184C2×#536—51no—
185#3137—516no—
186C2×#491—51no—
187C2×#491—51no—
188C2×#489—51no—
189C2×#489D511yescharacteristic, complemented
190C2×#488—51no—
191C2×#488—51no—
192C2×#487—51no—
193C2×#487—51no—
194C2×#417—51no—
195C2×#419—51no—
196C2×#416—51no—
197C22×#103—51no—
198C2×#405—51no—
199C24×C5—21no—
200C23×D5C2×D411yescharacteristic
201C2×C5×Q8—21no—
202C2×C5×Q8—24no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8—82no—
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×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2411yescharacteristic
217C2×C22⋊D5—24no—
218C2×C22⋊D5—44no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—24no—
224C22×Dic5—44no—
225C22×Dic5C2×D411yescharacteristic
226C22×Dic5C2×D411yescharacteristic
227C22×Dic5C2×D411yescharacteristic
228Q8×D5—28no—
229Q8×D5—28no—
230Q8×D5—48no—
231#711—28no—
232#711—28no—
233#711—48no—
234C2×C4×D5—24no—
235C2×C4×D5—24no—
236C2×C4×D5—44no—
237C2×C4×D5—82no—
238C2×C4×D5C2×D412yes—
239C2×C4×D5#4114yes—
240C2×C4×D5#4114yes—
241C2×C4×D5C2412yes—
242C2×Dic10—22no—
243C2×Dic10—22no—
244C2×Dic10—22no—
245C2×Dic10—22no—
246C2×Dic10—21no—
247C2×Dic10—21no—
248C2×Dic10—24no—
249C2×Dic10—24no—
250C2×Dic10—44no—
251C2×Dic10—82no—
252C2×Dic10C2412yes—
253C2×Dic10C2412yes—
254C2×C5×C8—22no—
255C2×C5×C8—22no—
256C2×C5×C8C2412yes—
257C2×C5×C8C2412yes—
258C5×C4⋊C4—24no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4C2412yes—
262C5×C4⋊C4C2412yes—
263C5×C22⋊C4—24no—
264C5×C22⋊C4—24no—
265C42×C5C2×D412yes—
266C42×C5C2412yes—
267C22⋊Dic5—24no—
268C22⋊Dic5—24no—
269#685—24no—
270#685C2×D414yes—
271#685C2×D414yes—
272C4⋊Dic5—24no—
273C4⋊Dic5—24no—
274C4⋊Dic5—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5—24no—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279#683—24no—
280#683—24no—
281#683—24no—
282#683—24no—
283#683—24no—
284#683—24no—
285#683—24no—
286#683C2×D414yes—
287#683C2×D414yes—
288C4×Dic5—24no—
289C4×Dic5C2×D412yes—
290C4×Dic5C2412yes—
291C2×#168—22no—
292C2×#168—22no—
293C2×#168C2412yes—
294C2×#168C2412yes—
295#676—28no—
296C8×D5—28no—
297C22×#41—51no—
298C23×Q8—51no—
299C22×M16—51no—
300C23×C8—51no—
301#544—58no—
302#544—104no—
303#536—58no—
304#536—104no—
305C2×C4⋊Q8—51no—
306C2×C4⋊Q8—51no—
307C2×C4⋊Q8—51no—
308C2×C4⋊Q8—101no—
309C2×C4⋊Q8C2×D511yescharacteristic
310C2×#125—51no—
311C2×#125—51no—
312C2×#125—101no—
313C2×#124—51no—
314C2×#124C2×D511yescharacteristic
315C2×#123—101no—
316C2×#123—101no—
317C2×C22⋊Q8—101no—
318C2×C22⋊Q8—101no—
319C2×C22⋊Q8—101no—
320C2×C22⋊Q8—101no—
321C2×#117—51no—
322C2×#117—51no—
323C22×C4⋊C4—51no—
324#491—58no—
325#491—58no—
326#489—58no—
327#489C2×D518yescomplemented
328#488—58no—
329#488—58no—
330#487—58no—
331#487—58no—
332#419—58no—
333#417—58no—
334#416—58no—
335C2×#103—51no—
336C2×#103—51no—
337C2×#103—51no—
338C2×#103—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#103—58no—
346C2×#103C2×D511yescharacteristic
347C2×#103C2×D511yescharacteristic
348C2×#102—51no—
349C2×#102—51no—
350C2×#102C2×D511yescharacteristic
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#12414yes—
365C22×D5C22×D412yes—
366C5×Q8—22no—
367C5×Q8—22no—
368C5×Q8—42no—
369C5×Q8—84no—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—42no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
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×C5C2×#4112yes—
386C2×C4×C5C2511yescharacteristic
387C22⋊D5—48no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—48no—
399C2×Dic5#12414yes—
400C2×Dic5C22×D412yes—
401C2×Dic5C22×D412yes—
402C2×Dic5C22×D412yes—
403C4×D5—48no—
404C4×D5—84no—
405C4×D5#12418yes—
406C4×D5C2×#4114yes—
407C4×D5C2×#4114yes—
408Dic10—22no—
409Dic10—22no—
410Dic10—22no—
411Dic10—22no—
412Dic10—42no—
413Dic10—42no—
414Dic10—48no—
415Dic10—84no—
416C5×C8—22no—
417C5×C8—22no—
418#168—22no—
419#168—22no—
420C2×#41—54no—
421C2×#41—102no—
422C2×#41—104no—
423C2×#41—104no—
424C22×Q8—21no—
425C22×Q8—54no—
426C22×Q8—51no—
427C22×Q8—51no—
428C22×Q8—101no—
429C22×Q8—101no—
430C22×Q8—102no—
431C22×Q8—104no—
432C22×Q8—104no—
433C22×Q8C22×D511yescharacteristic
434C22×D4—101no—
435C22×D4C22×D511yescharacteristic
436C23×C4—51no—
437C23×C4—101no—
438C23×C4—101no—
439C23×C4—101no—
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⋊Q8—54no—
450C4⋊Q8—54no—
451C4⋊Q8—54no—
452C4⋊Q8—102no—
453C4⋊Q8—102no—
454C4⋊Q8—108no—
455C4⋊Q8—102no—
456C4⋊Q8C22×D514yes—
457#125—54no—
458#125—54no—
459#125—102no—
460#125—108no—
461#125—102no—
462#124—22no—
463#124—54no—
464#124—102no—
465#124C22×D514yes—
466#123—108no—
467#123—108no—
468C22⋊Q8—108no—
469C22⋊Q8—108no—
470C22⋊Q8—108no—
471C22⋊Q8—108no—
472#117—54no—
473#117—54no—
474#117—54no—
475#117—102no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—51no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—102no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4C22×D511yescharacteristic
494C2×C4⋊C4C22×D511yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4—101no—
502C2×C42—51no—
503C2×C42—101no—
504C2×C42C22×D511yescharacteristic
505#103—54no—
506#103—54no—
507#103—54no—
508#103—54no—
509#103—54no—
510#103—54no—
511#103—54no—
512#103—54no—
513#103—54no—
514#103—54no—
515#103C22×D514yes—
516#103C22×D514yes—
517#102—54no—
518#102—54no—
519#102C22×D514yes—
520#102C22×D514yes—
521#97—54no—
522#97C22×D514yes—
523C4×C8—54no—
524C4×C8—54no—
525C22×C5—42no—
526C22×C5—42no—
527C22×C5—42no—
528C22×C5—84no—
529C22×C5C2×#12412yes—
530C22×C5#57712yes—
531C22×C5#57812yes—
532C22×C5C23×D411yescharacteristic
533C2×D5—28no—
534C2×D5—22no—
535C2×D5—22no—
536C2×D5C2×#12414yes—
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5—42no—
542C4×C5C2×#12412yes—
543C4×C5C22×#4111yescharacteristic
544C4×C5C22×#4111yescharacteristic
545Dic5—22no—
546Dic5—22no—
547Dic5—42no—
548Dic5—42no—
549Dic5—42no—
550Dic5—42no—
551Dic5C2×#12414yes—
552C24—21no—
553C24—51no—
554#41—108no—
555#41—108no—
556#41—208no—
557C2×Q8—21no—
558C2×Q8—24no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—52no—
562C2×Q8—52no—
563C2×Q8—82no—
564C2×Q8—104no—
565C2×Q8—104no—
566C2×Q8—108no—
567C2×Q8—108no—
568C2×Q8—101no—
569C2×Q8—101no—
570C2×Q8—102no—
571C2×Q8—102no—
572C2×Q8—102no—
573C2×Q8—102no—
574C2×Q8—204no—
575C2×Q8—208no—
576C2×Q8—402no—
577C2×Q8C23×D512yes—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—104no—
582C2×D4—204no—
583C2×D4C23×D512yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—51no—
588C22×C4—52no—
589C22×C4—54no—
590C22×C4—54no—
591C22×C4—52no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—104no—
595C22×C4—104no—
596C22×C4—104no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—204no—
602C22×C4—204no—
603C22×C4—402no—
604C22×C4D4×D511yescharacteristic
605C22×C4D4×D511yescharacteristic
606C22×C4C23×D511yescharacteristic
607M16—108no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—52no—
611C2×C8—52no—
612C2×C8—108no—
613C2×C8—102no—
614C2×C8—102no—
615C2×C8C23×D512yes—
616C2×C8C23×D512yes—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—54no—
621C4⋊C4—54no—
622C4⋊C4—52no—
623C4⋊C4—52no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—104no—
628C4⋊C4—104no—
629C4⋊C4—104no—
630C4⋊C4—101no—
631C4⋊C4—101no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—104no—
636C4⋊C4C23×D512yes—
637C4⋊C4C23×D512yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—54no—
641C22⋊C4—54no—
642C22⋊C4—104no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C42—52no—
646C42—52no—
647C42—104no—
648C42D4×D512yes—
649C42C23×D512yes—
650C2×C5—82no—
651C2×C5#313714yescomplemented
652C2×C5C22×#12411yescharacteristic
653C2×C5C2×#57711yescharacteristic
654C2×C5C2×#57811yescharacteristic
655D5—24no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—54no—
661C23—52no—
662C23—102no—
663C23—102no—
664C23C2×D4×D511yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—84no—
669Q8—102no—
670Q8—102no—
671Q8—102no—
672Q8—102no—
673Q8—208no—
674Q8—202no—
675Q8—202no—
676Q8—404no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—208no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—54no—
690C2×C4—52no—
691C2×C4—58no—
692C2×C4—54no—
693C2×C4—54no—
694C2×C4—52no—
695C2×C4—52no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—208no—
703C2×C4—208no—
704C2×C4—202no—
705C2×C4—202no—
706C2×C4—202no—
707C2×C4—202no—
708C2×C4—404no—
709C2×C4C2×D4×D512yes—
710C2×C4C2×D4×D512yes—
711C2×C4C2×D4×D511yescharacteristic
712C2×C4D5×#4112yes—
713C2×C4D5×#4112yes—
714C2×C4C24×D511yescharacteristic
715C8—22no—
716C8—22no—
717C8—102no—
718C8—102no—
719C5C2×#313711yescharacteristic, complemented, Sylow
720C22—42no—
721C22—42no—
722C22—42no—
723C22—54no—
724C22—84no—
725C22—108no—
726C22—102no—
727C22—102no—
728C22D5×#12412yes—
729C22#6610912yes—
730C22#6611312yes—
731C22C22×D4×D511yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—54no—
738C4—102no—
739C4—102no—
740C4—202no—
741C4—202no—
742C4—202no—
743C4—202no—
744C4D5×#12412yes—
745C4C2×D5×#4111yescharacteristic
746C4C2×D5×#4111yescharacteristic
747C2—82no—
748C2—104no—
749C2#1061341214yesdirect product factor
750C2C2×D5×#12411yescharacteristic
751C2C2×#6610911yescharacteristic
752C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#489C2
socleC23×C5C22×D4
prime radicalC22×#711C22
hypercenterC2×#489D5
hypocenterC5C2×#3137
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#66063C2semidirect
3. C2×C5×#489C2semidirect
4. C2×#65382C2semidirect
5. C2×#65345C2semidirect
6. #10613412C2direct (N × H)
7. C2×#65091C2semidirect
8. C2×D5×#103C2semidirect
9. C2×#65086C2semidirect
10. C2×#65081C2semidirect
13. C2×#65054C2semidirect
14. C2×#65057C2semidirect
15. C2×#64992C2semidirect
16. C2×#64997C2semidirect
28. #66063C22semidirect
44. C5×#489C22semidirect
60. #65382C22semidirect
61. #65345C22semidirect
67. #65091C22semidirect
68. D5×#103C22semidirect
69. #65086C22semidirect
70. #65081C22semidirect
73. #65057C22semidirect
74. #65054C22semidirect
75. #64997C22semidirect
76. #64992C22semidirect
189. C2×#489D5semidirect
327. #489C2×D5semidirect
651. C2×C5#3137semidirect
719. C5C2×#3137semidirect
749. C2#10613412direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660632
C2×#660092
C2×C5×#4892
C2×#653822
C2×#653452
#106134122
C2×#650912
C2×D5×#1032
C2×#650862
C2×#650812
C2×#650602
C2×#650612
C2×#650542
C2×#650572
C2×#649922
C2×#649972
C2×#31375