Finite Group Databasebeta

← C2×#10615400 #12979059

Subgroups — C2×#10615400 #12979059

Order 1280.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#556C211yesmaximal, characteristic, complemented
2C2×#65913C211yesmaximal, characteristic, complemented
3#10615400C2116yesmaximal, direct product factor
4C2×#65372C211yesmaximal, characteristic, complemented
5C2×#65371C211yesmaximal, characteristic, complemented
6C2×#65346C211yesmaximal, characteristic
7C2×#65346C211yesmaximal, characteristic
8C2×#65344C211yesmaximal, characteristic, complemented
9C2×#65345C211yesmaximal, characteristic, complemented
10C2×#65315C211yesmaximal, characteristic, complemented
11C2×#65313C211yesmaximal, characteristic, complemented
12C2×#65311C211yesmaximal, characteristic, complemented
13C2×#65309C211yesmaximal, characteristic, complemented
14C2×C4×#688C211yesmaximal, characteristic, complemented
15C2×#65298C211yesmaximal, characteristic, complemented
16C2×#65303C211yesmaximal, characteristic
17C5×#556—24no—
18C5×#556C2218yescomplemented
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#126—21no—
21C2×C5×#126—21no—
22C2×C5×#124C2211yescharacteristic
23C2×C5×#124C2211yescharacteristic
24C2×C5×C22⋊Q8—21no—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117—21no—
30C2×#4092—21no—
31C22×#688C2211yescharacteristic
32C22×#688C2211yescharacteristic
33C22×#686C2211yescharacteristic
34#65913—24no—
35#65913C2218yescomplemented
36C2×#4042—21no—
37C2×#4042—21no—
38C2×D5×C4⋊C4—21no—
39C2×C4×D20C2211yescharacteristic
40C2×C4×D20C2211yescharacteristic
41C2×C4×D20C2211yescharacteristic
42C2×#4016C2211yescharacteristic
43C2×#4016C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54#65372C2218yescomplemented
55#65371C2218yescomplemented
56#65346C2218yes—
57#65346C2218yes—
58#65345C2218yescomplemented
59#65344C2218yescomplemented
60#65315C2218yescomplemented
61C4×#688C2218yescomplemented
62#65313C2218yescomplemented
63#65311C2218yescomplemented
64#65309C2218yescomplemented
65#65303C2218yes—
66#65298C2218yescomplemented
67C2×#3941C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×C4⋊#168C2211yescharacteristic
72C2×C4⋊#168C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3376—51nomaximal, Sylow
78C22×C5×Q8D411yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C22×C5×Q8C2311yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C22×D20C2311yescharacteristic
84C22×C4×D5—21no—
85C22×C4×D5—21no—
86C22×C4×D5—21no—
87C22×Dic10—21no—
88C5×C4⋊Q8—22no—
89C5×C4⋊Q8C2314yes—
90C5×#126—28no—
91C5×#126—28no—
92C5×#124—22no—
93C5×#124—22no—
94C5×#124C2314yes—
95C5×#124C2314yes—
96C5×C22⋊Q8—28no—
97C4×C5×Q8—22no—
98C4×C5×Q8—22no—
99C4×C5×Q8D414yes—
100C4×C5×Q8C2314yes—
101C4×C5×Q8C2314yes—
102C4×C5×Q8C2314yes—
103C4×C5×D4—22no—
104C4×C5×D4C2314yes—
105C5×#117—28no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C42×C5—21no—
120C2×C42×C5—21no—
121C2×C42×C5C2311yescharacteristic
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124#4092—28no—
125C2×#688—24no—
126C2×#688—24no—
127C2×#688C2314yes—
128C2×#688C2314yes—
129C2×#686—24no—
130C2×#686C2314yes—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134C2×C4⋊Dic5—21no—
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137C2×C4⋊Dic5C2311yescharacteristic
138C2×#683—21no—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C22×#168C2311yescharacteristic
146#4042—28no—
147#4042—28no—
148D5×C4⋊C4—28no—
149C4×D20—22no—
150C4×D20—22no—
151C4×D20—22no—
152C4×D20C2314yes—
153C4×D20C2314yes—
154C4×D20C2314yes—
155#4016—22no—
156#4016—22no—
157#4016C2314yes—
158#4016C2314yes—
159#4015—22no—
160#4015C2314yes—
161#3967C2314yes—
162#3967C2314yes—
163#3967C2314yes—
164#3967C2314yes—
165#3967C2314yes—
166#3967C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169#3964C2314yes—
170#3941C2314yes—
171#3940C2314yes—
172#3940C2314yes—
173#3939C2314yes—
174C4⋊#168C2314yes—
175C4⋊#168C2314yes—
176C4⋊#168C2314yes—
177#3935C2314yes—
178#3935C2314yes—
179C4×#168C2314yes—
180C2×#556D511yescharacteristic, complemented
181C2×#554—51no—
182#3376—516no—
183C2×#491—51no—
184C2×#489—51no—
185C2×#488—51no—
186C2×#479—51no—
187C2×#475—51no—
188C2×#478—51no—
189C2×#463—51no—
190C2×#463—51no—
191C2×#461—51no—
192C2×#446—51no—
193C2×#442—51no—
194C2×#440—51no—
195C2×C4×SD16—51no—
196C24×C5—21no—
197C23×D5—21no—
198C2×C5×Q8—21no—
199C2×C5×Q8—21no—
200C2×C5×Q8—22no—
201C2×C5×Q8—22no—
202C2×C5×Q8—22no—
203C2×C5×Q8—22no—
204C2×C5×Q8—42no—
205C2×C5×Q8C2×D414yes—
206C2×C5×Q8C2412yes—
207C2×C5×Q8C2412yes—
208C2×C5×D4—21no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4C2412yes—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—24no—
216C22×C4×C5—44no—
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2411yescharacteristic
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C2×D20—21no—
228C2×D20—22no—
229C2×D20#4114yes—
230C2×D20C2412yes—
231C2×C4×D5—24no—
232C2×C4×D5—24no—
233C2×C4×D5—24no—
234C2×C4×D5—44no—
235C2×C4×D5—82no—
236C2×C4×D5—82no—
237C2×Dic10—24no—
238C2×Dic10—82no—
239C5×C4⋊C4—24no—
240C5×C4⋊C4—24no—
241C5×C4⋊C4—24no—
242C5×C4⋊C4—24no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4C2×D414yes—
245C5×C4⋊C4C2×D414yes—
246C5×C4⋊C4C2×D414yes—
247C5×C4⋊C4C2412yes—
248C5×C22⋊C4—24no—
249C5×C22⋊C4—24no—
250C5×C22⋊C4—24no—
251C5×C22⋊C4—24no—
252C5×C22⋊C4—24no—
253C42×C5—24no—
254C42×C5—24no—
255C42×C5C2×D412yes—
256C42×C5C2×D412yes—
257C42×C5C2×D412yes—
258C42×C5C2412yes—
259C42×C5C2412yes—
260C42×C5C2412yes—
261#688—28no—
262#688—28no—
263#686—28no—
264#685—24no—
265#685—24no—
266#685—24no—
267C4⋊Dic5—21no—
268C4⋊Dic5—21no—
269C4⋊Dic5—24no—
270C4⋊Dic5—21no—
271C4⋊Dic5C2412yes—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274#683—24no—
275#683—24no—
276#683—24no—
277#683—24no—
278C2×#168—22no—
279C2×#168—22no—
280C2×#168—22no—
281C2×#168—22no—
282C2×#168C2412yes—
283C2×#168C2412yes—
284C2×#168C2412yes—
285C2×#168C2412yes—
286C22×SD16—51no—
287C22×SD16—51no—
288C22×D8—51no—
289#556—24no—
290#556C2×D518yescomplemented
291#554—58no—
292#554—104no—
293C2×C4⋊Q8—51no—
294C2×C4⋊Q8C2×D511yescharacteristic
295C2×#126—21no—
296C2×#126—21no—
297C2×#125—51no—
298C2×#125—51no—
299C2×#124C2×D511yescharacteristic
300C2×#124C2×D511yescharacteristic
301C2×C22⋊Q8—21no—
302C2×C22⋊Q8—101no—
303C2×C22⋊Q8—101no—
304C2×C22⋊Q8—101no—
305C2×C4×Q8C2×D511yescharacteristic
306C2×C4×Q8C2×D511yescharacteristic
307C2×C4×Q8C2×D511yescharacteristic
308C2×C4×D4—51no—
309C2×C4×D4—51no—
310C2×C4×D4—51no—
311C2×C4×D4C2×D511yescharacteristic
312C2×#117—21no—
313C22×C4⋊C4—101no—
314#491—58no—
315#489—58no—
316#488—58no—
317#479—58no—
318#478—58no—
319#475—58no—
320#463—58no—
321#463—58no—
322#461—58no—
323#446—58no—
324#442—58no—
325#440—58no—
326C4×SD16—58no—
327C2×#107—51no—
328C2×#106—51no—
329C2×#106—51no—
330C2×C4⋊C8—51no—
331C2×C4⋊C8—51no—
332C2×C4⋊C8—51no—
333C2×#103—51no—
334C2×#103—51no—
335C2×#103—51no—
336C2×#103—51no—
337C2×#103—51no—
338C2×#103—51no—
339C2×#102—51no—
340C2×#102—51no—
341C2×#102—51no—
342C2×#102—51no—
343C2×#97—51no—
344C2×#97—51no—
345C2×C4×C8—51no—
346C23×C5—22no—
347C23×C5—42no—
348C23×C5—42no—
349C23×C5—42no—
350C23×C5C22×D411yescharacteristic
351C22×D5—24no—
352C22×D5—22no—
353C22×D5—42no—
354C22×D5—42no—
355C5×Q8—22no—
356C5×Q8—22no—
357C5×Q8—22no—
358C5×Q8—22no—
359C5×Q8—44no—
360C5×Q8—42no—
361C5×Q8—42no—
362C5×D4—22no—
363C5×D4—22no—
364C5×D4—42no—
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—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—48no—
375C2×C4×C5—42no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5C22×D412yes—
379C2×C4×C5C22×D412yes—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D412yes—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D411yescharacteristic
385C2×C4×C5C2×#4112yes—
386C2×C4×C52−1+412yes—
387C2×C4×C5C2511yescharacteristic
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394D20—24no—
395D20—22no—
396D20C2×#4114yes—
397C4×D5—48no—
398C4×D5—84no—
399C4×D5—84no—
400Dic10—84no—
401#168—22no—
402#168—22no—
403#168—22no—
404#168—22no—
405C22×Q8—101no—
406C22×Q8C22⋊D511yescharacteristic
407C22×Q8C22×D511yescharacteristic
408C22×Q8C22×D511yescharacteristic
409C22×D4—51no—
410C22×D4C22×D511yescharacteristic
411C23×C4—21no—
412C23×C4—101no—
413C23×C4—101no—
414C23×C4—101no—
415C2×SD16—54no—
416C2×SD16—54no—
417C2×SD16—104no—
418C2×SD16—104no—
419C2×D8—54no—
420C2×D8—104no—
421C22×C8—51no—
422C22×C8—51no—
423C22×C8—51no—
424C22×C8—51no—
425C4⋊Q8—22no—
426C4⋊Q8—54no—
427C4⋊Q8—102no—
428C4⋊Q8C22×D514yes—
429#126—28no—
430#126—28no—
431#125—54no—
432#125—54no—
433#125—102no—
434#125—102no—
435#124—22no—
436#124—22no—
437#124C22×D514yes—
438#124C22×D514yes—
439C22⋊Q8—28no—
440C22⋊Q8—108no—
441C22⋊Q8—108no—
442C22⋊Q8—108no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×Q8C22⋊D514yes—
446C4×Q8C22×D514yes—
447C4×Q8C22×D514yes—
448C4×Q8C22×D514yes—
449C4×D4—22no—
450C4×D4—54no—
451C4×D4—54no—
452C4×D4—54no—
453C4×D4—102no—
454C4×D4—102no—
455C4×D4—102no—
456C4×D4C22×D514yes—
457#117—28no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—51no—
463C2×C4⋊C4—51no—
464C2×C4⋊C4—51no—
465C2×C4⋊C4—101no—
466C2×C4⋊C4—101no—
467C2×C4⋊C4—101no—
468C2×C4⋊C4—101no—
469C2×C4⋊C4—101no—
470C2×C4⋊C4—108no—
471C2×C4⋊C4C22⋊D511yescharacteristic
472C2×C4⋊C4C22⋊D511yescharacteristic
473C2×C4⋊C4C22⋊D511yescharacteristic
474C2×C4⋊C4C22×D511yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—101no—
481C2×C22⋊C4—101no—
482C2×C22⋊C4—101no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C22×D511yescharacteristic
486C2×C42C22×D511yescharacteristic
487C2×C42C22×D511yescharacteristic
488#107—54no—
489#106—54no—
490#106—54no—
491C4⋊C8—54no—
492C4⋊C8—54no—
493C4⋊C8—54no—
494#103—54no—
495#103—54no—
496#103—54no—
497#103—54no—
498#103—54no—
499#103—54no—
500#102—54no—
501#102—54no—
502#102—54no—
503#102—54no—
504#97—54no—
505#97—54no—
506C4×C8—54no—
507C22×C5—42no—
508C22×C5—42no—
509C22×C5—42no—
510C22×C5—84no—
511C22×C5#54812yes—
512C22×C5#57512yes—
513C22×C5#57712yes—
514C22×C5C23×D411yescharacteristic
515C2×D5—24no—
516C2×D5—48no—
517C2×D5—42no—
518C2×D5—42no—
519C4×C5—22no—
520C4×C5—22no—
521C4×C5—22no—
522C4×C5—22no—
523C4×C5—22no—
524C4×C5—22no—
525C4×C5—42no—
526C4×C5—42no—
527C4×C5—42no—
528C4×C5#54812yes—
529C4×C5C22×#4111yescharacteristic
530C4×C5C2×2−1+411yescharacteristic
531Dic5—42no—
532Dic5—42no—
533Dic5—42no—
534C24—21no—
535C24—101no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—42no—
543C2×Q8—104no—
544C2×Q8—402no—
545C2×Q8C2×C22⋊D514yes—
546C2×Q8C23×D512yes—
547C2×Q8C23×D512yes—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—54no—
552C2×D4—52no—
553C2×D4—102no—
554C2×D4—101no—
555C2×D4C23×D512yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—44no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—104no—
565C22×C4—104no—
566C22×C4—104no—
567C22×C4—204no—
568C22×C4—402no—
569C22×C4—402no—
570C22×C4C2×C22⋊D511yescharacteristic
571C22×C4C2×C22⋊D511yescharacteristic
572C22×C4C2×C22⋊D511yescharacteristic
573C22×C4C2×C22⋊D511yescharacteristic
574C22×C4C2×C22⋊D511yescharacteristic
575C22×C4C2×C22⋊D511yescharacteristic
576C22×C4C23×D511yescharacteristic
577SD16—108no—
578SD16—108no—
579D8—108no—
580C2×C8—52no—
581C2×C8—52no—
582C2×C8—52no—
583C2×C8—52no—
584C2×C8—102no—
585C2×C8—102no—
586C2×C8—102no—
587C2×C8—102no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—52no—
594C4⋊C4—52no—
595C4⋊C4—52no—
596C4⋊C4—101no—
597C4⋊C4—101no—
598C4⋊C4—101no—
599C4⋊C4—104no—
600C4⋊C4—104no—
601C4⋊C4—104no—
602C4⋊C4—104no—
603C4⋊C4—104no—
604C4⋊C4C2×C22⋊D514yes—
605C4⋊C4C2×C22⋊D514yes—
606C4⋊C4C2×C22⋊D514yes—
607C4⋊C4C23×D512yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—104no—
614C22⋊C4—104no—
615C22⋊C4—104no—
616C42—24no—
617C42—24no—
618C42C2×C22⋊D512yes—
619C42C2×C22⋊D512yes—
620C42C2×C22⋊D512yes—
621C42C23×D512yes—
622C42C23×D512yes—
623C42C23×D512yes—
624C2×C5—82no—
625C2×C5#337614yescomplemented
626C2×C5C2×#54811yescharacteristic
627C2×C5C2×#57511yescharacteristic
628C2×C5C2×#57711yescharacteristic
629D5—44no—
630C23—22no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—104no—
635C23—102no—
636C23—202no—
637C23—202no—
638C23C22×C22⋊D511yescharacteristic
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—44no—
644Q8—42no—
645Q8—42no—
646Q8—404no—
647D4—22no—
648D4—22no—
649D4—42no—
650D4—54no—
651D4—104no—
652D4—102no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—102no—
669C2×C4—208no—
670C2×C4—202no—
671C2×C4—202no—
672C2×C4—202no—
673C2×C4—404no—
674C2×C4—404no—
675C2×C4D5×#4112yes—
676C2×C4#415012yes—
677C2×C4C22×C22⋊D512yes—
678C2×C4C22×C22⋊D512yes—
679C2×C4C22×C22⋊D512yes—
680C2×C4C22×C22⋊D512yes—
681C2×C4C22×C22⋊D512yes—
682C2×C4C22×C22⋊D512yes—
683C2×C4C22×C22⋊D511yescharacteristic
684C2×C4C24×D511yescharacteristic
685C8—102no—
686C8—102no—
687C8—102no—
688C8—102no—
689C5C2×#337611yescharacteristic, complemented, Sylow
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—104no—
695C22—202no—
696C22—202no—
697C22—208no—
698C22#6615612yes—
699C22#6616512yes—
700C22#6617112yes—
701C22C23×C22⋊D511yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—202no—
712C4—202no—
713C4—202no—
714C4#6616512yes—
715C4C2×D5×#4111yescharacteristic
716C4C2×#415011yescharacteristic
717C2—82no—
718C2—204no—
719C2#1061540014yesdirect product factor
720C2C2×#6615611yescharacteristic
721C2C2×#6616511yescharacteristic
722C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#556C2
socleC23×C5C22×D4
prime radicalC22×#686C22
hypercenterC2×#556D5
hypocenterC5C2×#3376
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×C5×#556C2semidirect
2. C2×#65913C2semidirect
3. #10615400C2direct (N × H)
4. C2×#65372C2semidirect
5. C2×#65371C2semidirect
8. C2×#65344C2semidirect
9. C2×#65345C2semidirect
10. C2×#65315C2semidirect
11. C2×#65313C2semidirect
12. C2×#65311C2semidirect
13. C2×#65309C2semidirect
14. C2×C4×#688C2semidirect
15. C2×#65298C2semidirect
18. C5×#556C22semidirect
35. #65913C22semidirect
54. #65372C22semidirect
55. #65371C22semidirect
58. #65345C22semidirect
59. #65344C22semidirect
60. #65315C22semidirect
61. C4×#688C22semidirect
62. #65313C22semidirect
63. #65311C22semidirect
64. #65309C22semidirect
66. #65298C22semidirect
180. C2×#556D5semidirect
290. #556C2×D5semidirect
625. C2×C5#3376semidirect
689. C5C2×#3376semidirect
719. C2#10615400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5562
C2×#659132
#106154002
C2×#653722
C2×#653712
C2×#653462
C2×#653442
C2×#653452
C2×#653152
C2×#653132
C2×#653112
C2×#653092
C2×C4×#6882
C2×#652982
C2×#653032
C2×#33765