Finite Group Databasebeta

← C2×#10613026 #12977882

Subgroups — C2×#10613026 #12977882

Order 1280.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65948C211yesmaximal, characteristic
2C2×#65845C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic, complemented
4C2×#65331C211yesmaximal, characteristic, complemented
5C2×#65253C211yesmaximal, characteristic, complemented
6#10613026C2116yesmaximal, direct product factor
7C2×#65166C211yesmaximal, characteristic, complemented
8C2×#65173C211yesmaximal, characteristic, complemented
9C2×D5×#107C211yesmaximal, characteristic, complemented
10C2×#65165C211yesmaximal, characteristic, complemented
11C2×#65066C211yesmaximal, characteristic, complemented
12C2×#65067C211yesmaximal, characteristic, complemented
13C2×#65048C211yesmaximal, characteristic, complemented
14C2×#65046C211yesmaximal, characteristic, complemented
15C2×#65017C211yesmaximal, characteristic, complemented
16C2×#65012C211yesmaximal, characteristic, complemented
17C2×C5×#121C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C2×#4084—21no—
20C2×#4084C2211yescharacteristic
21C2×#4081—21no—
22C2×D4×Dic5C2211yescharacteristic
23C22×#687C2211yescharacteristic
24C2×C4×C22⋊D5—21no—
25C2×C4×C22⋊D5C2211yescharacteristic
26C2×#4072C2211yescharacteristic
27C2×#4070—21no—
28C2×#4070C2211yescharacteristic
29C22×#681C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31#65948—24no—
32#65948C2218yes—
33#65845—24no—
34#65845C2218yescomplemented
35C2×#4043C2211yescharacteristic
36C2×#4042—21no—
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×D5×C4⋊C4C2211yescharacteristic
39C2×#4036C2211yescharacteristic
40C2×#4035—21no—
41C2×#4034C2211yescharacteristic
42C2×#4033C2211yescharacteristic
43C2×#4027—21no—
44C2×#4025—21no—
45C5×#480C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#107C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3952C2211yescharacteristic
53C2×#3950C2211yescharacteristic
54C2×#3949C2211yescharacteristic
55C2×#3948C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58C2×#3946C2211yescharacteristic
59#65331C2218yescomplemented
60C2×#3942C2211yescharacteristic
61#65253C2218yescomplemented
62C2×#3940C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3939C2211yescharacteristic
65C2×#3939C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67#65173C2218yescomplemented
68D5×#107C2218yescomplemented
69#65166C2218yescomplemented
70#65165C2218yescomplemented
71#65067C2218yescomplemented
72#65066C2218yescomplemented
73#65048C2218yescomplemented
74#65046C2218yescomplemented
75#65017C2218yescomplemented
76#65012C2218yescomplemented
77C2×#3346—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C23×Dic5—21no—
85C22×C4×D5—21no—
86C22×C4×D5—21no—
87C22×C4×D5C2311yescharacteristic
88C22×Dic10—21no—
89C22×Dic10C2311yescharacteristic
90C22×C5×C8C2311yescharacteristic
91C22×C5×C8C2311yescharacteristic
92C5×#121—22no—
93C5×#121C2314yes—
94C2×C5×C4⋊C4—21no—
95C2×C5×C4⋊C4—22no—
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2314yes—
100C2×C5×C22⋊C4—21no—
101C2×C22⋊Dic5—21no—
102C2×C22⋊Dic5—21no—
103C2×C22⋊Dic5—21no—
104C2×C22⋊Dic5—21no—
105C2×C22⋊Dic5D411yescharacteristic
106#4084—28no—
107#4084—22no—
108#4084C2314yes—
109#4081—28no—
110D4×Dic5—22no—
111D4×Dic5C2314yes—
112C2×#687—24no—
113C2×#687C2314yes—
114C4×C22⋊D5—28no—
115C4×C22⋊D5D414yes—
116C4×C22⋊D5C2314yes—
117C2×#685—21no—
118C2×#685D411yescharacteristic
119#4072—22no—
120#4072C2314yes—
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5—21no—
123C2×C4⋊Dic5C2311yescharacteristic
124C2×C4⋊Dic5C2311yescharacteristic
125C2×C4⋊Dic5C2311yescharacteristic
126#4070—22no—
127#4070—28no—
128#4070C2314yes—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683D411yescharacteristic
136C2×C4×Dic5—21no—
137C2×C4×Dic5—21no—
138C2×C4×Dic5C2311yescharacteristic
139C2×#681—24no—
140C2×#681C2314yes—
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C2×C8×D5—24no—
144C2×C8×D5C2314yes—
145#4043—22no—
146#4043C2314yes—
147#4042—28no—
148D5×C4⋊C4—22no—
149D5×C4⋊C4—22no—
150D5×C4⋊C4C2314yes—
151D5×C4⋊C4C2314yes—
152#4036—22no—
153#4036C2314yes—
154#4035—28no—
155#4034—22no—
156#4034C2314yes—
157#4033—22no—
158#4033C2314yes—
159#4027—28no—
160#4025—28no—
161C5×#107C2314yes—
162C5×#107C2314yes—
163C5×#102C2314yes—
164C5×#102C2314yes—
165C5×C22⋊C8C2314yes—
166#3964C2314yes—
167#3952C2314yes—
168#3950C2314yes—
169#3949C2314yes—
170#3948C2314yes—
171#3948C2314yes—
172#3947C2314yes—
173#3946C2314yes—
174#3942C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179#3939C2314yes—
180C2×#554—51no—
181C2×#553—51no—
182#3346—516no—
183C2×#501—51no—
184C2×#484—51no—
185C2×#481—51no—
186C2×#485—51no—
187C2×#480D511yescharacteristic, complemented
188C2×#479—51no—
189C2×#474—51no—
190C2×#468—51no—
191C2×#465—51no—
192C2×#440—51no—
193C2×#435—51no—
194C2×#428—51no—
195C22×#107—51no—
196C24×C5—21no—
197C24×C5C2×D411yescharacteristic
198C23×D5C2×D411yescharacteristic
199C2×C5×D4—24no—
200C2×C5×D4—21no—
201C2×C5×D4—22no—
202C2×C5×D4—22no—
203C2×C5×D4—82no—
204C2×C5×D4C2412yes—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—24no—
211C22×C4×C5—82no—
212C22×C4×C5C2×D411yescharacteristic
213C22×C4×C5C2×D412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2411yescharacteristic
216C2×C22⋊D5—24no—
217C2×C22⋊D5—24no—
218C2×C22⋊D5—44no—
219C2×C22⋊D5C2×D414yes—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—24no—
225C22×Dic5—82no—
226C22×Dic5C2×D411yescharacteristic
227C22×Dic5C2×D411yescharacteristic
228C22×Dic5C2×D411yescharacteristic
229C2×C4×D5—22no—
230C2×C4×D5—22no—
231C2×C4×D5—24no—
232C2×C4×D5—24no—
233C2×C4×D5—82no—
234C2×C4×D5—82no—
235C2×C4×D5C2×D412yes—
236C2×C4×D5C2412yes—
237C2×Dic10—22no—
238C2×Dic10—22no—
239C2×Dic10—21no—
240C2×Dic10—24no—
241C2×Dic10—82no—
242C2×Dic10C2412yes—
243C2×C5×C8—22no—
244C2×C5×C8—22no—
245C2×C5×C8C2412yes—
246C2×C5×C8C2412yes—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—24no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4C2412yes—
252C5×C4⋊C4C2412yes—
253C5×C4⋊C4C2412yes—
254C5×C22⋊C4—24no—
255C22⋊Dic5—24no—
256C22⋊Dic5—24no—
257C22⋊Dic5—24no—
258C22⋊Dic5—24no—
259C22⋊Dic5C2×D414yes—
260#687—28no—
261#685—24no—
262#685C2×D414yes—
263C4⋊Dic5—21no—
264C4⋊Dic5—21no—
265C4⋊Dic5—21no—
266C4⋊Dic5—24no—
267C4⋊Dic5—24no—
268C4⋊Dic5C2412yes—
269C4⋊Dic5C2412yes—
270C4⋊Dic5C2412yes—
271#683—24no—
272#683—24no—
273#683—24no—
274#683—24no—
275#683—24no—
276#683—24no—
277#683C2×D414yes—
278C4×Dic5—24no—
279C4×Dic5—24no—
280C4×Dic5C2×D412yes—
281C4×Dic5C2412yes—
282#681—28no—
283C2×#168—22no—
284C2×#168#4114yes—
285C2×#168C2412yes—
286C2×#168C2412yes—
287C8×D5—28no—
288C22×SD16—51no—
289C22×M16—51no—
290C23×C8—51no—
291#554—58no—
292#554—104no—
293#553—58no—
294#553—104no—
295C2×C4⋊Q8—51no—
296C2×#126—101no—
297C2×#125—51no—
298C2×#125—101no—
299C2×#123—101no—
300C2×C22⋊Q8—51no—
301C2×C22⋊Q8—51no—
302C2×C22⋊Q8—101no—
303C2×C22⋊Q8—101no—
304C2×#121—51no—
305C2×#121—101no—
306C2×#121C2×D511yescharacteristic
307C2×C4×Q8—51no—
308C2×C4×D4—51no—
309C2×C4×D4—51no—
310C2×C4×D4—101no—
311C2×C4×D4—101no—
312C2×#117—51no—
313C22×C4⋊C4—51no—
314C22×C4⋊C4—51no—
315C22×C4⋊C4C2×D511yescharacteristic
316#501—58no—
317#485—58no—
318#484—58no—
319#481—58no—
320#480C2×D518yescomplemented
321#479—58no—
322#474—58no—
323#468—58no—
324#465—58no—
325#440—58no—
326#435—58no—
327#428—58no—
328C2×#107—51no—
329C2×#107—51no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#107—58no—
333C2×#107C2×D511yescharacteristic
334C2×#107C2×D511yescharacteristic
335C2×#106—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×C4⋊C8—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×#102—51no—
343C2×#102C2×D511yescharacteristic
344C2×#102C2×D511yescharacteristic
345C2×C22⋊C8—51no—
346C2×C22⋊C8C2×D511yescharacteristic
347C2×#97—51no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—42no—
353C23×C5—42no—
354C23×C5—42no—
355C23×C5C22×D412yes—
356C23×C5C22×D411yescharacteristic
357C22×D5—22no—
358C22×D5—22no—
359C22×D5#13714yes—
360C22×D5C22×D412yes—
361C5×D4—22no—
362C5×D4—22no—
363C5×D4—42no—
364C5×D4—84no—
365C2×C4×C5—22no—
366C2×C4×C5—24no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—42no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5—84no—
376C2×C4×C5C22×D412yes—
377C2×C4×C5C22×D411yescharacteristic
378C2×C4×C5C2×#4112yes—
379C2×C4×C52−1+412yes—
380C2×C4×C5C2511yescharacteristic
381C22⋊D5—28no—
382C22⋊D5—48no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5—84no—
395C2×Dic5C22×D412yes—
396C2×Dic5C22×D412yes—
397C2×Dic5C22×D412yes—
398C4×D5—24no—
399C4×D5—22no—
400C4×D5—22no—
401C4×D5—84no—
402C4×D5—84no—
403Dic10—22no—
404Dic10—22no—
405Dic10—42no—
406Dic10—84no—
407C5×C8—22no—
408C5×C8—22no—
409#168—22no—
410#168C2×#4114yes—
411C22×Q8—51no—
412C22×Q8—101no—
413C22×D4—21no—
414C22×D4—51no—
415C22×D4—101no—
416C22×D4C22×D511yescharacteristic
417C23×C4—21no—
418C23×C4—51no—
419C23×C4—101no—
420C23×C4—101no—
421C23×C4—101no—
422C23×C4C22×D511yescharacteristic
423C2×SD16—54no—
424C2×SD16—104no—
425C2×M16—54no—
426C2×M16—104no—
427C22×C8—51no—
428C22×C8—51no—
429C22×C8—54no—
430C22×C8—104no—
431C22×C8C22×D511yescharacteristic
432C22×C8C22×D511yescharacteristic
433C4⋊Q8—54no—
434C4⋊Q8—102no—
435#126—108no—
436#125—54no—
437#125—102no—
438#125—108no—
439#123—108no—
440C22⋊Q8—54no—
441C22⋊Q8—54no—
442C22⋊Q8—108no—
443C22⋊Q8—108no—
444C22⋊Q8—102no—
445C22⋊Q8—102no—
446#121—22no—
447#121—54no—
448#121—102no—
449#121—108no—
450#121C22×D514yes—
451C4×Q8—54no—
452C4×Q8—102no—
453C4×D4—54no—
454C4×D4—54no—
455C4×D4—54no—
456C4×D4—102no—
457C4×D4—108no—
458C4×D4—108no—
459#117—54no—
460#117—102no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—51no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—54no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—102no—
470C2×C4⋊C4—102no—
471C2×C4⋊C4—101no—
472C2×C4⋊C4—101no—
473C2×C4⋊C4—101no—
474C2×C4⋊C4—101no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4—101no—
479C2×C4⋊C4C22×D511yescharacteristic
480C2×C4⋊C4C22×D511yescharacteristic
481C2×C4⋊C4C22×D511yescharacteristic
482C2×C4⋊C4C22×D514yes—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—51no—
485C2×C22⋊C4—51no—
486C2×C22⋊C4—101no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C42—51no—
492C2×C42—101no—
493C2×C42—101no—
494#107—54no—
495#107—54no—
496#107—54no—
497#107—54no—
498#107C22×D514yes—
499#107C22×D514yes—
500#106—54no—
501#106—54no—
502#106—54no—
503C4⋊C8—54no—
504#103—54no—
505#103—54no—
506#103—54no—
507#102—54no—
508#102C22×D514yes—
509#102C22×D514yes—
510C22⋊C8—54no—
511C22⋊C8C22×D514yes—
512#97—54no—
513C22×C5—22no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5—44no—
517C22×C5—42no—
518C22×C5—42no—
519C22×C5—42no—
520C22×C5—84no—
521C22×C5#54712yes—
522C22×C5C2×#13712yes—
523C22×C5#57612yes—
524C22×C5C23×D411yescharacteristic
525C2×D5—28no—
526C2×D5—22no—
527C2×D5—22no—
528C2×D5C2×#13714yes—
529C4×C5—22no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5#54712yes—
534C4×C5C22×#4111yescharacteristic
535C4×C5C2×2−1+411yescharacteristic
536Dic5—22no—
537Dic5—22no—
538Dic5—22no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—21no—
544C24—51no—
545C24D4×D511yescharacteristic
546C2×Q8—52no—
547C2×Q8—104no—
548C2×Q8—101no—
549C2×Q8—102no—
550C2×Q8—102no—
551C2×Q8—402no—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—54no—
557C2×D4—82no—
558C2×D4—104no—
559C2×D4—104no—
560C2×D4—204no—
561C2×D4C23×D512yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—51no—
569C22×C4—51no—
570C22×C4—51no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—82no—
574C22×C4—104no—
575C22×C4—104no—
576C22×C4—104no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—402no—
584C22×C4—402no—
585C22×C4—402no—
586C22×C4D4×D512yes—
587C22×C4D4×D511yescharacteristic
588C22×C4C23×D512yes—
589C22×C4C23×D511yescharacteristic
590SD16—108no—
591M16—108no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—54no—
595C2×C8—52no—
596C2×C8—52no—
597C2×C8—108no—
598C2×C8—102no—
599C2×C8C23×D512yes—
600C2×C8C23×D512yes—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—54no—
606C4⋊C4—52no—
607C4⋊C4—52no—
608C4⋊C4—52no—
609C4⋊C4—104no—
610C4⋊C4—104no—
611C4⋊C4—104no—
612C4⋊C4—104no—
613C4⋊C4—104no—
614C4⋊C4—104no—
615C4⋊C4—104no—
616C4⋊C4—101no—
617C4⋊C4—101no—
618C4⋊C4—101no—
619C4⋊C4—104no—
620C4⋊C4C23×D512yes—
621C4⋊C4C23×D512yes—
622C4⋊C4C23×D512yes—
623C22⋊C4—24no—
624C22⋊C4—54no—
625C22⋊C4—54no—
626C22⋊C4—104no—
627C22⋊C4—104no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C42—52no—
632C42—52no—
633C42—104no—
634C42—104no—
635C2×C5—42no—
636C2×C5—82no—
637C2×C5#334614yescomplemented
638C2×C5C2×#54711yescharacteristic
639C2×C5C22×#13711yescharacteristic
640C2×C5C2×#57611yescharacteristic
641D5—24no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—54no—
650C23—52no—
651C23—102no—
652C23—102no—
653C23C2×D4×D512yes—
654C23C2×D4×D511yescharacteristic
655Q8—102no—
656Q8—102no—
657Q8—202no—
658Q8—404no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—84no—
663D4—108no—
664D4—208no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—52no—
676C2×C4—52no—
677C2×C4—52no—
678C2×C4—84no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—104no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—202no—
692C2×C4—202no—
693C2×C4—404no—
694C2×C4—404no—
695C2×C4—404no—
696C2×C4C2×D4×D512yes—
697C2×C4C2×D4×D511yescharacteristic
698C2×C4D5×#4112yes—
699C2×C4#415012yes—
700C2×C4C24×D511yescharacteristic
701C8—22no—
702C8—22no—
703C8—54no—
704C8—102no—
705C5C2×#334611yescharacteristic, complemented, Sylow
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—54no—
714C22—84no—
715C22—108no—
716C22—102no—
717C22—102no—
718C22#6598912yes—
719C22#6609112yes—
720C22D5×#13712yes—
721C22C22×D4×D511yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—102no—
727C4—102no—
728C4—102no—
729C4—202no—
730C4—202no—
731C4—202no—
732C4—202no—
733C4#6598912yes—
734C4C2×D5×#4111yescharacteristic
735C4C2×#415011yescharacteristic
736C2—42no—
737C2—82no—
738C2—104no—
739C2#1061302614yesdirect product factor
740C2C2×#6598911yescharacteristic
741C2C2×#6609111yescharacteristic
742C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#480C2
socleC23×C5C22×D4
prime radicalC2×#65948C2
hypercenterC2×#480D5
hypocenterC5C2×#3346
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#65845C2semidirect
3. C2×C5×#480C2semidirect
4. C2×#65331C2semidirect
5. C2×#65253C2semidirect
6. #10613026C2direct (N × H)
7. C2×#65166C2semidirect
8. C2×#65173C2semidirect
9. C2×D5×#107C2semidirect
10. C2×#65165C2semidirect
11. C2×#65066C2semidirect
12. C2×#65067C2semidirect
13. C2×#65048C2semidirect
14. C2×#65046C2semidirect
15. C2×#65017C2semidirect
16. C2×#65012C2semidirect
34. #65845C22semidirect
45. C5×#480C22semidirect
59. #65331C22semidirect
61. #65253C22semidirect
67. #65173C22semidirect
68. D5×#107C22semidirect
69. #65166C22semidirect
70. #65165C22semidirect
71. #65067C22semidirect
72. #65066C22semidirect
73. #65048C22semidirect
74. #65046C22semidirect
75. #65017C22semidirect
76. #65012C22semidirect
187. C2×#480D5semidirect
320. #480C2×D5semidirect
637. C2×C5#3346semidirect
705. C5C2×#3346semidirect
739. C2#10613026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659482
C2×#658452
C2×C5×#4802
C2×#653312
C2×#652532
#106130262
C2×#651662
C2×#651732
C2×D5×#1072
C2×#651652
C2×#650662
C2×#650672
C2×#650482
C2×#650462
C2×#650172
C2×#650122
C2×#33465