Finite Group Databasebeta

← C2×#10610954 #12977832

Subgroups — C2×#10610954 #12977832

Order 1280.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65863C211yesmaximal, characteristic, complemented
2C2×#65841C211yesmaximal, characteristic
3C2×C5×#428C211yesmaximal, characteristic, complemented
4C2×#65423C211yesmaximal, characteristic, complemented
5C2×#65416C211yesmaximal, characteristic, complemented
6C2×#65292C211yesmaximal, characteristic, complemented
7C2×#65259C211yesmaximal, characteristic, complemented
8#10610954C2116yesmaximal, direct product factor
9C2×#65164C211yesmaximal, characteristic, complemented
10C2×#65171C211yesmaximal, characteristic, complemented
11C2×D5×#107C211yesmaximal, characteristic, complemented
12C2×#65178C211yesmaximal, characteristic, complemented
13C2×#65160C211yesmaximal, characteristic, complemented
14C2×#65151C211yesmaximal, characteristic, complemented
15C2×#65153C211yesmaximal, characteristic, complemented
16C2×#65145C211yesmaximal, characteristic, complemented
17C22×#709—21no—
18C22×C5×M16C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×#4076C2211yescharacteristic
22C2×#4075—21no—
23C2×C4×C22⋊D5C2211yescharacteristic
24C2×#4070C2211yescharacteristic
25C22×#677C2211yescharacteristic
26C22×C8×D5C2211yescharacteristic
27#65863—24no—
28#65863C2218yescomplemented
29C2×#4043C2211yescharacteristic
30C2×#4042—21no—
31#65841—24no—
32#65841C2218yes—
33C2×#4041C2211yescharacteristic
34C2×#4040—21no—
35C2×#4039C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4036C2211yescharacteristic
39C2×#4034C2211yescharacteristic
40C2×#4033C2211yescharacteristic
41C2×#4029—21no—
42C2×#4025—21no—
43C2×#4018—21no—
44C2×#4016—21no—
45C5×#428C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#107C2211yescharacteristic
48C2×C5×#106C2211yescharacteristic
49C2×C5×#106C2211yescharacteristic
50C2×C22⋊#168C2211yescharacteristic
51#65423C2218yescomplemented
52#65416C2218yescomplemented
53C2×#3953C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3950C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58C2×#3946C2211yescharacteristic
59#65292C2218yescomplemented
60#65259C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×#3939C2211yescharacteristic
69#65178C2218yescomplemented
70#65171C2218yescomplemented
71D5×#107C2218yescomplemented
72#65164C2218yescomplemented
73#65160C2218yescomplemented
74#65153C2218yescomplemented
75#65151C2218yescomplemented
76#65145C2218yescomplemented
77C2×#3343—51nomaximal, Sylow
78C23×C4×C5—21no—
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—21no—
81C22×C22⋊D5D411yescharacteristic
82C2×#709—28no—
83C2×#709—48no—
84C22×D20—21no—
85C22×D20C2311yescharacteristic
86C22×C4×D5—21no—
87C22×C4×D5—21no—
88C22×C4×D5—21no—
89C22×C4×D5C2311yescharacteristic
90C22×Dic10—21no—
91C22×Dic10C2311yescharacteristic
92C2×C5×M16—24no—
93C2×C5×M16C2314yes—
94C22×C5×C8C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C5×#117—22no—
97C5×#117C2314yes—
98C2×C5×C4⋊C4—21no—
99C2×C5×C4⋊C4—22no—
100C2×C5×C4⋊C4C2311yescharacteristic
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C22⋊C4—21no—
106C2×C42×C5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5D411yescharacteristic
109#4076—22no—
110#4076C2314yes—
111#4075—28no—
112C4×C22⋊D5D414yes—
113C4×C22⋊D5C2314yes—
114C2×#685—21no—
115C2×#685—21no—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685D411yescharacteristic
119C2×C4⋊Dic5—21no—
120C2×C4⋊Dic5—21no—
121C2×C4⋊Dic5C2311yescharacteristic
122C2×C4⋊Dic5C2311yescharacteristic
123#4070—22no—
124#4070C2314yes—
125C2×#683—21no—
126C2×#683—21no—
127C2×#683—21no—
128C2×#683—21no—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683D411yescharacteristic
132C2×C4×Dic5—21no—
133C2×C4×Dic5C2311yescharacteristic
134C22×#168C2311yescharacteristic
135C22×#168C2311yescharacteristic
136C2×#677—24no—
137C2×#677C2314yes—
138C2×C8×D5—24no—
139C2×C8×D5C2314yes—
140#4043—22no—
141#4043C2314yes—
142#4042—28no—
143#4041—22no—
144#4041C2314yes—
145#4040—28no—
146#4039—22no—
147#4039C2314yes—
148D5×C4⋊C4—22no—
149D5×C4⋊C4—22no—
150D5×C4⋊C4C2314yes—
151D5×C4⋊C4C2314yes—
152#4036—22no—
153#4036C2314yes—
154#4034—22no—
155#4034C2314yes—
156#4033—22no—
157#4033C2314yes—
158#4029—28no—
159#4025—28no—
160#4018—28no—
161#4016—28no—
162C5×#107C2314yes—
163C5×#107C2314yes—
164C5×#106C2314yes—
165C5×#106C2314yes—
166C22⋊#168C2314yes—
167#3953C2314yes—
168#3952C2314yes—
169#3950C2314yes—
170#3948C2314yes—
171#3947C2314yes—
172#3946C2314yes—
173#3942C2314yes—
174#3942C2314yes—
175#3941C2314yes—
176#3941C2314yes—
177#3940C2314yes—
178#3939C2314yes—
179#3939C2314yes—
180#3939C2314yes—
181C2×#552—51no—
182C2×#547—51no—
183#3343—516no—
184C2×#501—51no—
185C2×#484—51no—
186C2×#482—51no—
187C2×#483—51no—
188C2×#480—51no—
189C2×#477—51no—
190C2×#478—51no—
191C2×#468—51no—
192C2×#465—51no—
193C2×#440—51no—
194C2×#435—51no—
195C2×#428D511yescharacteristic, complemented
196C22×#107—51no—
197C24×C5C2×D411yescharacteristic
198C23×D5—21no—
199C23×D5C2×D411yescharacteristic
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—24no—
207C22×C4×C5—44no—
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2411yescharacteristic
212C2×C22⋊D5—24no—
213C2×C22⋊D5—24no—
214C2×C22⋊D5—44no—
215C2×C22⋊D5C2×D414yes—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5C2×D411yescharacteristic
220C22×Dic5C2×D411yescharacteristic
221C22×Dic5C2×D411yescharacteristic
222#709—432no—
223C2×D20—22no—
224C2×D20—22no—
225C2×D20—24no—
226C2×D20—21no—
227C2×D20—44no—
228C2×D20C2412yes—
229C2×C4×D5—22no—
230C2×C4×D5—22no—
231C2×C4×D5—24no—
232C2×C4×D5—24no—
233C2×C4×D5—24no—
234C2×C4×D5—44no—
235C2×C4×D5—44no—
236C2×C4×D5—44no—
237C2×C4×D5C2×D412yes—
238C2×C4×D5C2412yes—
239C2×Dic10—22no—
240C2×Dic10—22no—
241C2×Dic10—21no—
242C2×Dic10—24no—
243C2×Dic10—44no—
244C2×Dic10C2412yes—
245C5×M16—28no—
246C2×C5×C8—22no—
247C2×C5×C8#4114yescomplemented
248C2×C5×C8C2412yes—
249C2×C5×C8C2412yes—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—24no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4C2412yes—
256C5×C4⋊C4C2412yes—
257C5×C4⋊C4C2412yes—
258C5×C4⋊C4C2412yes—
259C5×C22⋊C4—24no—
260C42×C5—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5C2×D414yes—
263#685—24no—
264#685—24no—
265#685—24no—
266#685—24no—
267#685C2×D414yes—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—24no—
271C4⋊Dic5—24no—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274#683—24no—
275#683—24no—
276#683—24no—
277#683—24no—
278#683—24no—
279#683—24no—
280#683C2×D414yes—
281C4×Dic5—24no—
282C4×Dic5C2×D412yes—
283C4×Dic5C2412yes—
284C2×#168—22no—
285C2×#168—22no—
286C2×#168C2412yes—
287C2×#168C2412yes—
288#677—28no—
289C8×D5—28no—
290C22×#41—101no—
291C22×SD16—51no—
292C22×M16C2×D511yescharacteristic
293C23×C8—51no—
294#552—58no—
295#552—104no—
296#547—58no—
297#547—104no—
298C2×C4⋊Q8—51no—
299C2×#126—101no—
300C2×#125—51no—
301C2×#125—101no—
302C2×#123—101no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—51no—
306C2×C22⋊Q8—51no—
307C2×C22⋊Q8—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×C4×Q8—51no—
311C2×C4×D4—51no—
312C2×C4×D4—51no—
313C2×#117—101no—
314C2×#117C2×D511yescharacteristic
315C22×C4⋊C4—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4C2×D511yescharacteristic
318#501—58no—
319#484—58no—
320#483—58no—
321#482—58no—
322#480—58no—
323#478—58no—
324#477—58no—
325#468—58no—
326#465—58no—
327#440—58no—
328#435—58no—
329#428C2×D518yescomplemented
330C2×#107—51no—
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—58no—
335C2×#107C2×D511yescharacteristic
336C2×#107C2×D511yescharacteristic
337C2×#106—51no—
338C2×#106C2×D511yescharacteristic
339C2×#106C2×D511yescharacteristic
340C2×C4⋊C8—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×C22⋊C8—51no—
348C2×C22⋊C8—51no—
349C2×#97—51no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5C22×D412yes—
354C23×C5C22×D411yescharacteristic
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—42no—
359C22×D5—42no—
360C22×D5—42no—
361C22×D5AGL(1,ℤ/8)14yes—
362C22×D5C22×D412yes—
363C2×C4×C5—22no—
364C2×C4×C5—24no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—48no—
372C2×C4×C5—42no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5—42no—
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—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5C22×D412yes—
393C2×Dic5C22×D412yes—
394C2×Dic5C22×D412yes—
395D20—22no—
396D20—22no—
397D20—48no—
398D20—42no—
399C4×D5—24no—
400C4×D5—22no—
401C4×D5—22no—
402C4×D5—48no—
403C4×D5—48no—
404C4×D5—48no—
405Dic10—22no—
406Dic10—22no—
407Dic10—48no—
408Dic10—42no—
409C5×C8—22no—
410C5×C8C2×#4114yescomplemented
411#168—22no—
412#168—22no—
413C2×#41—108no—
414C2×#41—208no—
415C22×Q8—51no—
416C22×Q8—101no—
417C22×D4—51no—
418C22×D4—51no—
419C22×D4—101no—
420C22×D4—101no—
421C23×C4—21no—
422C23×C4—51no—
423C23×C4—101no—
424C23×C4—101no—
425C23×C4—101no—
426C23×C4C22×D511yescharacteristic
427C2×SD16—54no—
428C2×SD16—104no—
429C2×M16—24no—
430C2×M16C22×D514yes—
431C22×C8—51no—
432C22×C8—51no—
433C22×C8—54no—
434C22×C8—104no—
435C22×C8C22×D511yescharacteristic
436C22×C8C22×D511yescharacteristic
437C4⋊Q8—54no—
438C4⋊Q8—102no—
439#126—108no—
440#125—54no—
441#125—108no—
442#125—102no—
443#123—108no—
444#123—108no—
445#123—108no—
446C22⋊Q8—54no—
447C22⋊Q8—54no—
448C22⋊Q8—108no—
449C22⋊Q8—102no—
450C22⋊Q8—102no—
451#121—54no—
452#121—54no—
453#121—102no—
454#121—102no—
455C4×Q8—54no—
456C4×Q8—102no—
457C4×D4—54no—
458C4×D4—54no—
459C4×D4—54no—
460C4×D4—102no—
461#117—22no—
462#117—108no—
463#117C22×D514yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—102no—
472C2×C4⋊C4—102no—
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⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4C22×D511yescharacteristic
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C4⋊C4C22×D511yescharacteristic
484C2×C4⋊C4C22×D514yes—
485C2×C4⋊C4C22×D511yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—51no—
488C2×C22⋊C4—51no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C42—21no—
495C2×C42—51no—
496C2×C42—101no—
497#107—54no—
498#107—54no—
499#107—54no—
500#107—54no—
501#107C22×D514yes—
502#107C22×D514yes—
503#106—54no—
504#106C22×D514yes—
505#106C22×D514yes—
506C4⋊C8—54no—
507#103—54no—
508#103—54no—
509#103—54no—
510#102—54no—
511#102—54no—
512#102—54no—
513C22⋊C8—54no—
514C22⋊C8—54no—
515#97—54no—
516C22×C5—22no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—44no—
520C22×C5#54712yes—
521C22×C5C2×AGL(1,ℤ/8)12yes—
522C22×C5#57812yes—
523C22×C5C23×D411yescharacteristic
524C2×D5—28no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—42no—
528C2×D5—42no—
529C2×D5—42no—
530C2×D5—84no—
531C2×D5C2×AGL(1,ℤ/8)14yes—
532C4×C5—22no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5#54712yes—
538C4×C5C22×#4111yescharacteristic
539C4×C5C2×2−1+411yescharacteristic
540Dic5—22no—
541Dic5—22no—
542Dic5—22no—
543Dic5—42no—
544Dic5—42no—
545Dic5—42no—
546C24—51no—
547C24—101no—
548C24D4×D511yescharacteristic
549#41—2032no—
550C2×Q8—52no—
551C2×Q8—104no—
552C2×Q8—101no—
553C2×Q8—102no—
554C2×Q8—102no—
555C2×Q8—204no—
556C2×D4—54no—
557C2×D4—52no—
558C2×D4—104no—
559C2×D4—104no—
560C2×D4—104no—
561C2×D4—102no—
562C2×D4—101no—
563C2×D4—102no—
564C2×D4—204no—
565C2×D4—204no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—44no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—104no—
580C22×C4—104no—
581C22×C4—104no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—204no—
588C22×C4—204no—
589C22×C4—204no—
590C22×C4D4×D512yes—
591C22×C4D4×D511yescharacteristic
592C22×C4C23×D512yes—
593C22×C4C23×D511yescharacteristic
594SD16—108no—
595M16—28no—
596C2×C8—22no—
597C2×C8—52no—
598C2×C8—52no—
599C2×C8—102no—
600C2×C8—102no—
601C2×C8—108no—
602C2×C8#70914yescomplemented
603C2×C8C23×D512yes—
604C2×C8C23×D512yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—54no—
611C4⋊C4—52no—
612C4⋊C4—52no—
613C4⋊C4—104no—
614C4⋊C4—104no—
615C4⋊C4—104no—
616C4⋊C4—104no—
617C4⋊C4—104no—
618C4⋊C4—104no—
619C4⋊C4—104no—
620C4⋊C4—101no—
621C4⋊C4—101no—
622C4⋊C4—104no—
623C4⋊C4C23×D512yes—
624C4⋊C4C23×D512yes—
625C4⋊C4C23×D512yes—
626C4⋊C4C23×D512yes—
627C22⋊C4—24no—
628C22⋊C4—54no—
629C22⋊C4—54no—
630C22⋊C4—104no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4—104no—
634C22⋊C4—104no—
635C42—24no—
636C42—52no—
637C42—52no—
638C42—104no—
639C2×C5—42no—
640C2×C5#334314yescomplemented
641C2×C5C2×#54711yescharacteristic
642C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
643C2×C5C2×#57811yescharacteristic
644D5—24no—
645D5—82no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—54no—
650C23—52no—
651C23—102no—
652C23—102no—
653C23—102no—
654C23—202no—
655C23—202no—
656C23—202no—
657C23C2×D4×D512yes—
658C23C2×D4×D511yescharacteristic
659Q8—102no—
660Q8—102no—
661Q8—208no—
662Q8—202no—
663D4—108no—
664D4—102no—
665D4—102no—
666D4—208no—
667D4—208no—
668D4—202no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—52no—
683C2×C4—52no—
684C2×C4—52no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—104no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—208no—
695C2×C4—208no—
696C2×C4—208no—
697C2×C4—202no—
698C2×C4—202no—
699C2×C4—202no—
700C2×C4C2×#70912yes—
701C2×C4C2×D4×D512yes—
702C2×C4C2×D4×D511yescharacteristic
703C2×C4#414712yes—
704C2×C4C24×D511yescharacteristic
705C8—22no—
706C8—102no—
707C8—102no—
708C8C2×#70914yescomplemented
709C5C2×#334311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—54no—
715C22—108no—
716C22—102no—
717C22—102no—
718C22—202no—
719C22—202no—
720C22—202no—
721C22—404no—
722C22#6584112yes—
723C22D5×AGL(1,ℤ/8)12yes—
724C22#6611312yes—
725C22C22×D4×D511yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—102no—
732C4—102no—
733C4—102no—
734C4—202no—
735C4—202no—
736C4—202no—
737C4#6584112yes—
738C4C22×#70911yescharacteristic
739C4C2×#414711yescharacteristic
740C2—42no—
741C2—104no—
742C2—402no—
743C2#1061095414yesdirect product factor
744C2C2×#6584111yescharacteristic
745C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#428C2
socleC23×C5C22×D4
prime radicalC2×#65841C2
hypercenterC2×#428D5
hypocenterC5C2×#3343
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#65863C2semidirect
3. C2×C5×#428C2semidirect
4. C2×#65423C2semidirect
5. C2×#65416C2semidirect
6. C2×#65292C2semidirect
7. C2×#65259C2semidirect
8. #10610954C2direct (N × H)
9. C2×#65164C2semidirect
10. C2×#65171C2semidirect
11. C2×D5×#107C2semidirect
12. C2×#65178C2semidirect
13. C2×#65160C2semidirect
14. C2×#65151C2semidirect
15. C2×#65153C2semidirect
16. C2×#65145C2semidirect
28. #65863C22semidirect
45. C5×#428C22semidirect
51. #65423C22semidirect
52. #65416C22semidirect
59. #65292C22semidirect
60. #65259C22semidirect
69. #65178C22semidirect
70. #65171C22semidirect
71. D5×#107C22semidirect
72. #65164C22semidirect
73. #65160C22semidirect
74. #65153C22semidirect
75. #65151C22semidirect
76. #65145C22semidirect
195. C2×#428D5semidirect
247. C2×C5×C8#41semidirect
329. #428C2×D5semidirect
410. C5×C8C2×#41semidirect
602. C2×C8#709semidirect
640. C2×C5#3343semidirect
708. C8C2×#709semidirect
709. C5C2×#3343semidirect
743. C2#10610954direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658632
C2×#658412
C2×C5×#4282
C2×#654232
C2×#654162
C2×#652922
C2×#652592
#106109542
C2×#651642
C2×#651712
C2×D5×#1072
C2×#651782
C2×#651602
C2×#651512
C2×#651532
C2×#651452
C2×#33435