Finite Group Databasebeta

← C2×#10610965 #12978000

Subgroups — C2×#10610965 #12978000

Order 1280.

2082 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×#65867C211yesmaximal, characteristic, complemented
2C2×#65841C211yesmaximal, characteristic
3C2×C5×#428C211yesmaximal, characteristic, complemented
4C2×#65423C211yesmaximal, characteristic, complemented
5C2×#65417C211yesmaximal, characteristic, complemented
6C2×#65292C211yesmaximal, characteristic, complemented
7C2×#65259C211yesmaximal, characteristic, complemented
8#10610965C2116yesmaximal, direct product factor
9C2×#65179C211yesmaximal, characteristic, complemented
10C2×#65173C211yesmaximal, characteristic, complemented
11C2×#65175C211yesmaximal, characteristic, complemented
12C2×#65163C211yesmaximal, characteristic, complemented
13C2×#65143C211yesmaximal, characteristic, complemented
14C2×#65155C211yesmaximal, characteristic, complemented
15C2×#65150C211yesmaximal, characteristic, complemented
16C2×#65141C211yesmaximal, 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×#676C2211yescharacteristic
27#65867—24no—
28#65867C2218yescomplemented
29C2×#4043C2211yescharacteristic
30C2×#4042—21no—
31#65841—24no—
32#65841C2218yes—
33C2×#4041C2211yescharacteristic
34C2×#4040—21no—
35C2×#4039C2211yescharacteristic
36C2×#4038C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4034C2211yescharacteristic
39C2×#4034C2211yescharacteristic
40C2×#4033C2211yescharacteristic
41C2×#4031—21no—
42C2×#4025—21no—
43C2×#4022—21no—
44C2×C4×Dic10—21no—
45C5×#428C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#107C2211yescharacteristic
48C2×C5×#106C2211yescharacteristic
49C2×C5×#106C2211yescharacteristic
50C2×C22⋊#168C2211yescharacteristic
51#65423C2218yescomplemented
52#65417C2218yescomplemented
53C2×#3953C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3950C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3946C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65292C2218yescomplemented
60#65259C2218yescomplemented
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×#3939C2211yescharacteristic
69#65179C2218yescomplemented
70#65175C2218yescomplemented
71#65173C2218yescomplemented
72#65163C2218yescomplemented
73#65155C2218yescomplemented
74#65150C2218yescomplemented
75#65143C2218yescomplemented
76#65141C2218yescomplemented
77C2×#3353—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×D5C2311yescharacteristic
89C22×Dic10—21no—
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×#685—21no—
119C2×#685D411yescharacteristic
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×#683D411yescharacteristic
131C2×C4×Dic5—21no—
132C2×C4×Dic5—21no—
133C2×C4×Dic5C2311yescharacteristic
134C22×#168C2311yescharacteristic
135C22×#168C2311yescharacteristic
136C2×#677—24no—
137C2×#677C2314yes—
138C2×#676—24no—
139C2×#676C2314yes—
140#4043—22no—
141#4043C2314yes—
142#4042—28no—
143#4041—22no—
144#4041C2314yes—
145#4040—28no—
146#4039—22no—
147#4039C2314yes—
148#4038—22no—
149#4038C2314yes—
150D5×C4⋊C4—22no—
151D5×C4⋊C4C2314yes—
152#4034—22no—
153#4034—22no—
154#4034C2314yes—
155#4034C2314yes—
156#4033—22no—
157#4033C2314yes—
158#4031—28no—
159#4025—28no—
160#4022—28no—
161C4×Dic10—28no—
162C5×#107C2314yes—
163C5×#107C2314yes—
164C5×#106C2314yes—
165C5×#106C2314yes—
166C22⋊#168C2314yes—
167#3953C2314yes—
168#3952C2314yes—
169#3950C2314yes—
170#3948C2314yes—
171#3946C2314yes—
172C8×Dic5C2314yes—
173#3942C2314yes—
174#3942C2314yes—
175#3941C2314yes—
176#3941C2314yes—
177#3940C2314yes—
178#3939C2314yes—
179#3939C2314yes—
180#3939C2314yes—
181C2×#556—51no—
182C2×#547—51no—
183#3353—516no—
184C2×#500—51no—
185C2×#484—51no—
186C2×#484—51no—
187C2×#482—51no—
188C2×#482—51no—
189C2×#475—51no—
190C2×#474—51no—
191C2×#468—51no—
192C2×#468—51no—
193C2×C4×SD16—51no—
194C2×#436—51no—
195C2×#428—51no—
196C2×#428D511yescharacteristic, complemented
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—44no—
234C2×C4×D5—44no—
235C2×C4×D5C2×D412yes—
236C2×C4×D5C2412yes—
237C2×Dic10—22no—
238C2×Dic10—22no—
239C2×Dic10—21no—
240C2×Dic10—24no—
241C2×Dic10—24no—
242C2×Dic10—44no—
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#685—24no—
268#685C2×D414yes—
269C4⋊Dic5—21no—
270C4⋊Dic5—21no—
271C4⋊Dic5—24no—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274#683—24no—
275#683—24no—
276#683—24no—
277#683—24no—
278#683—24no—
279#683C2×D414yes—
280C4×Dic5—24no—
281C4×Dic5—24no—
282C4×Dic5C2×D412yes—
283C4×Dic5C2412yes—
284C2×#168—22no—
285C2×#168—22no—
286C2×#168C2412yes—
287C2×#168C2412yes—
288#677—28no—
289#676—28no—
290C22×#41—101no—
291C22×SD16—51no—
292C22×M16—51no—
293C22×M16C2×D511yescharacteristic
294#556—58no—
295#556—104no—
296#547—58no—
297#547—104no—
298C2×C4⋊Q8—51no—
299C2×C4⋊Q8—51no—
300C2×#126—101no—
301C2×#126—101no—
302C2×#124—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×Q8—101no—
312C2×C4×D4—51no—
313C2×C4×D4—51no—
314C2×#117—51no—
315C2×#117C2×D511yescharacteristic
316C22×C4⋊C4—51no—
317C22×C4⋊C4C2×D511yescharacteristic
318#500—58no—
319#484—58no—
320#484—58no—
321#482—58no—
322#482—58no—
323#475—58no—
324#474—58no—
325#468—58no—
326#468—58no—
327C4×SD16—58no—
328#436—58no—
329#428—58no—
330#428C2×D518yescomplemented
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—51no—
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×C4×C8—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—22no—
359C22×D5—42no—
360C22×D5—42no—
361C22×D5—42no—
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—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5AGL(1,ℤ/8)14yes—
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—
404Dic10—22no—
405Dic10—22no—
406Dic10—42no—
407Dic10—48no—
408Dic10—48no—
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×Q8—101no—
418C22×D4—51no—
419C22×D4—51no—
420C22×D4—101no—
421C22×D4—101no—
422C23×C4—21no—
423C23×C4—51no—
424C23×C4—101no—
425C23×C4—101no—
426C23×C4C22×D511yescharacteristic
427C2×SD16—54no—
428C2×SD16—104no—
429C2×M16—24no—
430C2×M16—54no—
431C2×M16—104no—
432C2×M16C22×D514yes—
433C22×C8—51no—
434C22×C8—51no—
435C22×C8C22×D511yescharacteristic
436C22×C8C22×D511yescharacteristic
437C4⋊Q8—54no—
438C4⋊Q8—54no—
439C4⋊Q8—102no—
440C4⋊Q8—102no—
441#126—108no—
442#126—108no—
443#124—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—108no—
457C4×Q8—102no—
458C4×D4—54no—
459C4×D4—54no—
460C4×D4—54no—
461C4×D4—102no—
462#117—22no—
463#117—54no—
464#117—102no—
465#117C22×D514yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—54no—
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⋊C4C22×D511yescharacteristic
480C2×C4⋊C4C22×D511yescharacteristic
481C2×C4⋊C4C22×D514yes—
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C4⋊C4C22×D511yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—51no—
486C2×C22⋊C4—51no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C42—21no—
494C2×C42—51no—
495C2×C42—101no—
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—
515C4×C8—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—22no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—44no—
528C2×D5—42no—
529C2×D5—42no—
530C2×D5—42no—
531C2×D5—84no—
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—42no—
543Dic5—42no—
544Dic5—42no—
545Dic5C2×AGL(1,ℤ/8)14yes—
546C24—51no—
547C24—101no—
548C24D4×D511yescharacteristic
549#41—2032no—
550C2×Q8—52no—
551C2×Q8—104no—
552C2×Q8—104no—
553C2×Q8—101no—
554C2×Q8—102no—
555C2×Q8—102no—
556C2×Q8—204no—
557C2×Q8—204no—
558C2×D4—54no—
559C2×D4—52no—
560C2×D4—104no—
561C2×D4—104no—
562C2×D4—104no—
563C2×D4—102no—
564C2×D4—101no—
565C2×D4—102no—
566C2×D4—204no—
567C2×D4—204no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—44no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—104no—
582C22×C4—104no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—101no—
588C22×C4—204no—
589C22×C4—204no—
590C22×C4D4×D512yes—
591C22×C4D4×D511yescharacteristic
592C22×C4C23×D512yes—
593C22×C4C23×D511yescharacteristic
594SD16—108no—
595M16—28no—
596M16—108no—
597C2×C8—22no—
598C2×C8—52no—
599C2×C8—52no—
600C2×C8—102no—
601C2×C8—102no—
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—101no—
619C4⋊C4—101no—
620C4⋊C4—104no—
621C4⋊C4C23×D512yes—
622C4⋊C4C23×D512yes—
623C4⋊C4C23×D512yes—
624C4⋊C4C23×D512yes—
625C22⋊C4—24no—
626C22⋊C4—54no—
627C22⋊C4—54no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4—104no—
634C42—24no—
635C42—52no—
636C42—52no—
637C42—104no—
638C42—104no—
639C2×C5—42no—
640C2×C5#335314yescomplemented
641C2×C5C2×#54711yescharacteristic
642C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
643C2×C5C2×#57811yescharacteristic
644D5—42no—
645D5—82no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—52no—
650C23—102no—
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—208no—
663Q8—202no—
664D4—108no—
665D4—102no—
666D4—102no—
667D4—208no—
668D4—208no—
669D4—202no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—54no—
684C2×C4—52no—
685C2×C4—52no—
686C2×C4—52no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—104no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
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×#335311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—102no—
715C22—102no—
716C22—102no—
717C22—204no—
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—54no—
732C4—102no—
733C4—102no—
734C4—202no—
735C4—202no—
736C4—202no—
737C4#6584112yes—
738C4C22×#70911yescharacteristic
739C4C2×#414711yescharacteristic
740C2—42no—
741C2—202no—
742C2—402no—
743C2#1061096514yesdirect 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×#3353
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×#65867C2semidirect
3. C2×C5×#428C2semidirect
4. C2×#65423C2semidirect
5. C2×#65417C2semidirect
6. C2×#65292C2semidirect
7. C2×#65259C2semidirect
8. #10610965C2direct (N × H)
9. C2×#65179C2semidirect
10. C2×#65173C2semidirect
11. C2×#65175C2semidirect
12. C2×#65163C2semidirect
13. C2×#65143C2semidirect
14. C2×#65155C2semidirect
15. C2×#65150C2semidirect
16. C2×#65141C2semidirect
28. #65867C22semidirect
45. C5×#428C22semidirect
51. #65423C22semidirect
52. #65417C22semidirect
59. #65292C22semidirect
60. #65259C22semidirect
69. #65179C22semidirect
70. #65175C22semidirect
71. #65173C22semidirect
72. #65163C22semidirect
73. #65155C22semidirect
74. #65150C22semidirect
75. #65143C22semidirect
76. #65141C22semidirect
196. C2×#428D5semidirect
247. C2×C5×C8#41semidirect
330. #428C2×D5semidirect
410. C5×C8C2×#41semidirect
602. C2×C8#709semidirect
640. C2×C5#3353semidirect
708. C8C2×#709semidirect
709. C5C2×#3353semidirect
743. C2#10610965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658672
C2×#658412
C2×C5×#4282
C2×#654232
C2×#654172
C2×#652922
C2×#652592
#106109652
C2×#651792
C2×#651732
C2×#651752
C2×#651632
C2×#651432
C2×#651552
C2×#651502
C2×#651412
C2×#33535