Finite Group Databasebeta

← C2×#10610824 #12972212

Subgroups — C2×#10610824 #12972212

Order 1280.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65868C211yesmaximal, characteristic, complemented
2C2×#65869C211yesmaximal, characteristic, complemented
3C2×C5×#424C211yesmaximal, characteristic, complemented
4C2×#65424C211yesmaximal, characteristic, complemented
5C2×#65423C211yesmaximal, characteristic, complemented
6C2×#65404C211yesmaximal, characteristic, complemented
7C2×#65403C211yesmaximal, characteristic, complemented
8#10610824C2116yesmaximal, direct product factor
9C2×#65118C211yesmaximal, characteristic, complemented
10C2×#65137C211yesmaximal, characteristic, complemented
11C2×#65136C211yesmaximal, characteristic, complemented
12C2×#65131C211yesmaximal, characteristic, complemented
13C2×#65135C211yesmaximal, characteristic, complemented
14C2×#65133C211yesmaximal, characteristic, complemented
15C2×#65133C211yesmaximal, characteristic, complemented
16C2×#65132C211yesmaximal, characteristic, complemented
17C22×C5×M16C2211yescharacteristic
18C23×C5×C8C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C2×#4076C2211yescharacteristic
21C2×#4076C2211yescharacteristic
22C2×#4076C2211yescharacteristic
23C2×#4070C2211yescharacteristic
24C22×D40C2211yescharacteristic
25C22×D40C2211yescharacteristic
26C22×#677C2211yescharacteristic
27C22×#677C2211yescharacteristic
28#65869—24no—
29#65869C2218yescomplemented
30#65868—24no—
31#65868C2218yescomplemented
32C2×#4044—21no—
33C2×#4042—21no—
34C2×#4040—21no—
35C2×#4040—21no—
36C2×#4031—21no—
37C2×#4030—21no—
38C2×#4030—21no—
39C2×#4029—21no—
40C2×#4021C2211yescharacteristic
41C2×#4020C2211yescharacteristic
42C2×C4×D20C2211yescharacteristic
43C2×C4×D20C2211yescharacteristic
44C2×C4×D20C2211yescharacteristic
45C2×#4016C2211yescharacteristic
46C2×#4015C2211yescharacteristic
47C2×C4×Dic10C2211yescharacteristic
48C5×#424C2218yescomplemented
49C2×C5×C4⋊C8C2211yescharacteristic
50C2×C5×C4⋊C8C2211yescharacteristic
51C2×C5×C4⋊C8C2211yescharacteristic
52C2×C5×C4⋊C8C2211yescharacteristic
53#65424C2218yescomplemented
54#65423C2218yescomplemented
55#65404C2218yescomplemented
56#65403C2218yescomplemented
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic
62C2×#3953C2211yescharacteristic
63C2×#3950C2211yescharacteristic
64C2×#3950C2211yescharacteristic
65C2×#3949C2211yescharacteristic
66C2×#3949C2211yescharacteristic
67C2×#3948C2211yescharacteristic
68C2×#3948C2211yescharacteristic
69#65137C2218yescomplemented
70#65136C2218yescomplemented
71#65135C2218yescomplemented
72#65133C2218yescomplemented
73#65133C2218yescomplemented
74#65132C2218yescomplemented
75#65131C2218yescomplemented
76#65118C2218yescomplemented
77C2×#3257—51nomaximal, Sylow
78C23×C4×C5C2311yescharacteristic
79C22×C22⋊D5—21no—
80C22×C22⋊D5—21no—
81C22×C22⋊D5—21no—
82C22×D20—21no—
83C22×D20—21no—
84C22×D20C2311yescharacteristic
85C22×D20C2311yescharacteristic
86C22×D20C2311yescharacteristic
87C22×C4×D5—21no—
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×Dic10—21no—
91C22×Dic10C2311yescharacteristic
92C2×C5×M16—42no—
93C2×C5×M16C2314yes—
94C22×C5×C8—42no—
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2314yes—
100C5×#117D414yes—
101C5×#117C2314yes—
102C2×C5×C4⋊C4D411yescharacteristic
103C2×C5×C4⋊C4D411yescharacteristic
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C42×C5C2311yescharacteristic
107C2×C42×C5C2311yescharacteristic
108C2×C22⋊Dic5—21no—
109#4076—22no—
110#4076—22no—
111#4076—22no—
112#4076C2314yes—
113#4076C2314yes—
114#4076C2314yes—
115C2×#685—21no—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685—21no—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5C2311yescharacteristic
125C2×C4⋊Dic5C2311yescharacteristic
126C2×C4⋊Dic5C2311yescharacteristic
127C2×C4⋊Dic5C2311yescharacteristic
128#4070—22no—
129#4070C2314yes—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×C4×Dic5—21no—
135C2×D40—42no—
136C2×D40—42no—
137C2×D40C2314yes—
138C2×D40C2314yes—
139C2×#677—42no—
140C2×#677—42no—
141C2×#677C2314yes—
142C2×#677C2314yes—
143#4044—28no—
144#4042—28no—
145#4040—28no—
146#4040—28no—
147#4031—28no—
148#4030—28no—
149#4030—28no—
150#4029—28no—
151#4021—22no—
152#4021C2314yes—
153#4020—22no—
154#4020C2314yes—
155C4×D20—22no—
156C4×D20—22no—
157C4×D20—22no—
158C4×D20C2314yes—
159C4×D20C2314yes—
160C4×D20C2314yes—
161#4016—22no—
162#4016C2314yes—
163#4015—22no—
164#4015C2314yes—
165C4×Dic10—22no—
166C4×Dic10C2314yes—
167C5×C4⋊C8C2314yes—
168C5×C4⋊C8C2314yes—
169C5×C4⋊C8C2314yes—
170C5×C4⋊C8C2314yes—
171#3953C2314yes—
172#3953C2314yes—
173#3953C2314yes—
174#3953C2314yes—
175#3953C2314yes—
176#3953C2314yes—
177#3950C2314yes—
178#3950C2314yes—
179#3949C2314yes—
180#3949C2314yes—
181#3948C2314yes—
182#3948C2314yes—
183C2×#542—51no—
184C2×#540—51no—
185#3257—516no—
186C2×#479—51no—
187C2×#478—51no—
188C2×#476—51no—
189C2×#474—51no—
190C2×#469—51no—
191C2×#468—51no—
192C2×#466—51no—
193C2×#465—51no—
194C2×#460—51no—
195C2×#463—51no—
196C2×#463—51no—
197C2×#459—51no—
198C2×#424D511yescharacteristic, complemented
199C24×C5C2×D411yescharacteristic
200C23×D5—21no—
201C23×D5—21no—
202C23×D5—21no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5C2×D411yescharacteristic
206C22×C4×C5C2×D411yescharacteristic
207C22×C4×C5C2×D411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2411yescharacteristic
213C2×C22⋊D5—24no—
214C2×C22⋊D5—24no—
215C2×C22⋊D5—24no—
216C2×C22⋊D5—82no—
217C2×C22⋊D5—82no—
218C2×C22⋊D5—82no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C2×D20—22no—
225C2×D20—22no—
226C2×D20—22no—
227C2×D20—22no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20—21no—
232C2×D20—21no—
233C2×D20—24no—
234C2×D20—24no—
235C2×D20—82no—
236C2×D20—82no—
237C2×D20C2412yes—
238C2×D20C2412yes—
239C2×D20C2412yes—
240C2×C4×D5—24no—
241C2×C4×D5—24no—
242C2×C4×D5—24no—
243C2×C4×D5—82no—
244C2×C4×D5—82no—
245C2×C4×D5—82no—
246C2×Dic10—22no—
247C2×Dic10—22no—
248C2×Dic10—21no—
249C2×Dic10—24no—
250C2×Dic10—82no—
251C2×Dic10C2412yes—
252C5×M16—44no—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8—22no—
256C2×C5×C8—22no—
257C2×C5×C8—44no—
258C2×C5×C8C2412yes—
259C2×C5×C8C2412yes—
260C2×C5×C8C2412yes—
261C2×C5×C8C2412yes—
262C5×C4⋊C4C2×D414yes—
263C5×C4⋊C4C2×D414yes—
264C5×C22⋊C4C2×D414yes—
265C5×C22⋊C4C2×D414yes—
266C42×C5C2×D412yes—
267C42×C5C2×D412yes—
268C42×C5C2412yes—
269C42×C5C2412yes—
270C22⋊Dic5—24no—
271#685—24no—
272#685—24no—
273#685—24no—
274#685—24no—
275#685—24no—
276#685—24no—
277#685—24no—
278#685—24no—
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5—24no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5C2412yes—
285C4⋊Dic5C2412yes—
286C4⋊Dic5C2412yes—
287C4⋊Dic5C2412yes—
288#683—24no—
289#683—24no—
290#683—24no—
291#683—24no—
292C4×Dic5—24no—
293D40—44no—
294D40—44no—
295#677—44no—
296#677—44no—
297C22×SD16—51no—
298C22×SD16—51no—
299C22×D8—51no—
300C22×D8—51no—
301C22×M16C2×D511yescharacteristic
302C23×C8C2×D511yescharacteristic
303#542—58no—
304#542—104no—
305#540—58no—
306#540—104no—
307C2×C4⋊Q8—51no—
308C2×#127—51no—
309C2×#126—101no—
310C2×#125—51no—
311C2×#124—51no—
312C2×#124—101no—
313C2×#123—101no—
314C2×#123—101no—
315C2×#123—101no—
316C2×C22⋊Q8—51no—
317C2×C22⋊Q8—101no—
318C2×#121—51no—
319C2×#121—51no—
320C2×#121—51no—
321C2×#121—101no—
322C2×#121—101no—
323C2×C4×Q8—51no—
324C2×C4×D4—51no—
325C2×C4×D4—51no—
326C2×C4×D4—51no—
327C2×#117C2×D511yescharacteristic
328#479—58no—
329#478—58no—
330#476—58no—
331#474—58no—
332#469—58no—
333#468—58no—
334#466—58no—
335#465—58no—
336#463—58no—
337#463—58no—
338#460—58no—
339#459—58no—
340C2×#107—51no—
341C2×#107—51no—
342C2×#106—51no—
343C2×#106—51no—
344#424C2×D518yescomplemented
345C2×C4⋊C8C2×D511yescharacteristic
346C2×C4⋊C8C2×D511yescharacteristic
347C2×C4⋊C8C2×D511yescharacteristic
348C2×C4⋊C8C2×D511yescharacteristic
349C2×#103—51no—
350C2×#103—51no—
351C2×#102—51no—
352C2×#102—51no—
353C2×#102—51no—
354C2×#102—51no—
355C2×#102—51no—
356C2×#102—51no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5C22×D412yes—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—42no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C22×D5—42no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5—42no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—24no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5H(5,𝔽2)12yes—
389C2×C4×C52−1+412yes—
390C2×C4×C5C2511yescharacteristic
391C22⋊D5—84no—
392C22⋊D5—84no—
393C22⋊D5—84no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5—42no—
404D20—22no—
405D20—22no—
406D20—22no—
407D20—22no—
408D20—22no—
409D20—22no—
410D20—42no—
411D20—42no—
412D20—42no—
413D20—84no—
414D20—84no—
415C4×D5—84no—
416C4×D5—84no—
417C4×D5—84no—
418Dic10—22no—
419Dic10—22no—
420Dic10—42no—
421Dic10—84no—
422C5×C8—22no—
423C5×C8—22no—
424C5×C8—22no—
425C5×C8—22no—
426C22×Q8—51no—
427C22×Q8—101no—
428C22×D4—51no—
429C22×D4—51no—
430C22×D4—51no—
431C22×D4—101no—
432C22×D4—101no—
433C22×D4—101no—
434C22×D4—101no—
435C22×D4—101no—
436C23×C4—101no—
437C23×C4—101no—
438C23×C4—101no—
439C23×C4C22×D511yescharacteristic
440C2×SD16—54no—
441C2×SD16—54no—
442C2×SD16—202no—
443C2×SD16—202no—
444C2×D8—54no—
445C2×D8—54no—
446C2×D8—202no—
447C2×D8—202no—
448C2×M16—42no—
449C2×M16C22×D514yes—
450C22×C8—42no—
451C22×C8C22×D511yescharacteristic
452C22×C8C22×D511yescharacteristic
453C22×C8C22×D511yescharacteristic
454C22×C8C22×D511yescharacteristic
455C22×C8C22×D514yes—
456C4⋊Q8—54no—
457C4⋊Q8—102no—
458#127—54no—
459#127—102no—
460#126—108no—
461#125—54no—
462#125—102no—
463#124—54no—
464#124—108no—
465#124—102no—
466#123—108no—
467#123—108no—
468#123—108no—
469C22⋊Q8—54no—
470C22⋊Q8—102no—
471C22⋊Q8—108no—
472#121—54no—
473#121—54no—
474#121—54no—
475#121—102no—
476#121—102no—
477#121—102no—
478#121—108no—
479#121—108no—
480C4×Q8—54no—
481C4×Q8—102no—
482C4×D4—54no—
483C4×D4—54no—
484C4×D4—54no—
485C4×D4—102no—
486C4×D4—102no—
487C4×D4—102no—
488#117D2014yes—
489#117C22×D514yes—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—51no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—101no—
495C2×C4⋊C4—101no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4—101no—
499C2×C4⋊C4D2011yescharacteristic
500C2×C4⋊C4D2011yescharacteristic
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C22⋊C4—101no—
504C2×C22⋊C4—101no—
505C2×C22⋊C4—101no—
506C2×C22⋊C4—101no—
507C2×C22⋊C4—101no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C22⋊C4D2011yescharacteristic
511C2×C22⋊C4D2011yescharacteristic
512C2×C42—101no—
513C2×C42C22×D511yescharacteristic
514C2×C42C22×D511yescharacteristic
515#107—54no—
516#107—54no—
517#106—54no—
518#106—54no—
519C4⋊C8C22×D514yes—
520C4⋊C8C22×D514yes—
521C4⋊C8C22×D514yes—
522C4⋊C8C22×D514yes—
523#103—54no—
524#103—54no—
525#102—54no—
526#102—54no—
527#102—54no—
528#102—54no—
529#102—54no—
530#102—54no—
531C22×C5—22no—
532C22×C5—22no—
533C22×C5—22no—
534C22×C5—44no—
535C22×C5#53712yes—
536C22×C5#57612yes—
537C22×C5#57712yes—
538C22×C5C23×D411yescharacteristic
539C2×D5—42no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—42no—
544C2×D5—42no—
545C2×D5—42no—
546C2×D5—42no—
547C2×D5—42no—
548C2×D5—84no—
549C2×D5—84no—
550C2×D5—84no—
551C4×C5—22no—
552C4×C5—22no—
553C4×C5—22no—
554C4×C5—22no—
555C4×C5—22no—
556C4×C5#53712yes—
557C4×C5C2×H(5,𝔽2)11yescharacteristic
558C4×C5C2×2−1+411yescharacteristic
559Dic5—42no—
560Dic5—42no—
561Dic5—42no—
562Dic5—42no—
563Dic5—42no—
564C24—101no—
565C24—101no—
566C24—101no—
567C24C2×D2011yescharacteristic
568C2×Q8—52no—
569C2×Q8—101no—
570C2×Q8—104no—
571C2×Q8—102no—
572C2×Q8—102no—
573C2×Q8—402no—
574C2×D4—52no—
575C2×D4—52no—
576C2×D4—52no—
577C2×D4—104no—
578C2×D4—104no—
579C2×D4—104no—
580C2×D4—101no—
581C2×D4—101no—
582C2×D4—101no—
583C2×D4—104no—
584C2×D4—104no—
585C2×D4—102no—
586C2×D4—102no—
587C2×D4—102no—
588C2×D4—102no—
589C2×D4—102no—
590C2×D4—102no—
591C2×D4—402no—
592C2×D4—402no—
593C2×D4—402no—
594C2×D4—402no—
595C2×D4—402no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—104no—
604C22×C4—104no—
605C22×C4—104no—
606C22×C4—402no—
607C22×C4—402no—
608C22×C4—402no—
609C22×C4C2×D2012yes—
610C22×C4C2×D2011yescharacteristic
611C22×C4C2×D2011yescharacteristic
612C22×C4C2×D2011yescharacteristic
613C22×C4C2×D2011yescharacteristic
614C22×C4C2×D2011yescharacteristic
615C22×C4C23×D512yes—
616C22×C4C23×D511yescharacteristic
617SD16—204no—
618SD16—204no—
619D8—204no—
620D8—204no—
621M16—44no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—44no—
627C2×C8C23×D512yes—
628C2×C8C23×D512yes—
629C2×C8C23×D512yes—
630C2×C8C23×D512yes—
631C4⋊C4—52no—
632C4⋊C4—52no—
633C4⋊C4—52no—
634C4⋊C4—52no—
635C4⋊C4—101no—
636C4⋊C4—101no—
637C4⋊C4—101no—
638C4⋊C4—101no—
639C4⋊C4—104no—
640C4⋊C4—104no—
641C4⋊C4—104no—
642C4⋊C4—104no—
643C4⋊C4—104no—
644C4⋊C4C2×D2014yes—
645C4⋊C4C2×D2014yes—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C22⋊C4—104no—
650C22⋊C4—104no—
651C22⋊C4—104no—
652C22⋊C4—104no—
653C22⋊C4—104no—
654C22⋊C4—104no—
655C22⋊C4C2×D2014yes—
656C22⋊C4C2×D2014yes—
657C42—104no—
658C42C2×D2012yes—
659C42C2×D2012yes—
660C42C23×D512yes—
661C42C23×D512yes—
662C2×C5—42no—
663C2×C5#325714yescomplemented
664C2×C5C2×#53711yescharacteristic
665C2×C5C2×#57611yescharacteristic
666C2×C5C2×#57711yescharacteristic
667D5—82no—
668D5—82no—
669D5—82no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—202no—
677C23—202no—
678C23—202no—
679C23—202no—
680C23—202no—
681C23—202no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23C22×D2012yes—
686C23C22×D2011yescharacteristic
687Q8—102no—
688Q8—102no—
689Q8—202no—
690Q8—404no—
691D4—102no—
692D4—102no—
693D4—102no—
694D4—102no—
695D4—102no—
696D4—102no—
697D4—202no—
698D4—202no—
699D4—202no—
700D4—404no—
701D4—404no—
702D4—404no—
703D4—404no—
704D4—404no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—202no—
719C2×C4—202no—
720C2×C4—202no—
721C2×C4—202no—
722C2×C4—202no—
723C2×C4—404no—
724C2×C4—404no—
725C2×C4—404no—
726C2×C4C22×D2012yes—
727C2×C4C22×D2012yes—
728C2×C4C22×D2012yes—
729C2×C4C22×D2012yes—
730C2×C4C22×D2012yes—
731C2×C4C22×D2011yescharacteristic
732C2×C4#414412yes—
733C2×C4#414712yes—
734C2×C4C24×D511yescharacteristic
735C8—22no—
736C8—22no—
737C8—22no—
738C8—22no—
739C5C2×#325711yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—202no—
745C22—202no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—404no—
754C22—404no—
755C22—404no—
756C22#6584412yes—
757C22#6608512yes—
758C22#6608612yes—
759C22C23×D2011yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—202no—
766C4—202no—
767C4—202no—
768C4—202no—
769C4—202no—
770C4#6584412yes—
771C4C2×#414411yescharacteristic
772C4C2×#414711yescharacteristic
773C2—42no—
774C2—402no—
775C2—402no—
776C2—402no—
777C2#1061082414yesdirect product factor
778C2C2×#6584411yescharacteristic
779C2C2×#6608611yescharacteristic
780C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#424C2
socleC23×C5C22×D4
hypercenterC2×#424D5
hypocenterC5C2×#3257
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#65868C2semidirect
2. C2×#65869C2semidirect
3. C2×C5×#424C2semidirect
4. C2×#65424C2semidirect
5. C2×#65423C2semidirect
6. C2×#65404C2semidirect
7. C2×#65403C2semidirect
8. #10610824C2direct (N × H)
9. C2×#65118C2semidirect
10. C2×#65137C2semidirect
11. C2×#65136C2semidirect
12. C2×#65131C2semidirect
13. C2×#65135C2semidirect
14. C2×#65133C2semidirect
15. C2×#65133C2semidirect
16. C2×#65132C2semidirect
29. #65869C22semidirect
31. #65868C22semidirect
48. C5×#424C22semidirect
53. #65424C22semidirect
54. #65423C22semidirect
55. #65404C22semidirect
56. #65403C22semidirect
69. #65137C22semidirect
70. #65136C22semidirect
71. #65135C22semidirect
72. #65133C22semidirect
73. #65133C22semidirect
74. #65132C22semidirect
75. #65131C22semidirect
76. #65118C22semidirect
198. C2×#424D5semidirect
344. #424C2×D5semidirect
663. C2×C5#3257semidirect
739. C5C2×#3257semidirect
777. C2#10610824direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658682
C2×#658692
C2×C5×#4242
C2×#654242
C2×#654232
C2×#654042
C2×#654032
#106108242
C2×#651182
C2×#651372
C2×#651362
C2×#651312
C2×#651352
C2×#651332
C2×#651322
C2×#32575