Finite Group Databasebeta

← C2×#10612383 #12977885

Subgroups — C2×#10612383 #12977885

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×#65969C211yesmaximal, characteristic, complemented
2C2×#65952C211yesmaximal, characteristic
3C2×C5×#465C211yesmaximal, characteristic, complemented
4C2×#65463C211yesmaximal, characteristic, complemented
5C2×#65453C211yesmaximal, characteristic, complemented
6C2×#65400C211yesmaximal, characteristic, complemented
7C22×#3950C211yesmaximal, characteristic, complemented
8C2×#65333C211yesmaximal, characteristic, complemented
9C2×#65323C211yesmaximal, characteristic, complemented
10#10612383C2116yesmaximal, direct product factor
11C2×#65150C211yesmaximal, characteristic, complemented
12C2×#65145C211yesmaximal, characteristic, complemented
13C2×#65103C211yesmaximal, characteristic, complemented
14C2×#65085C211yesmaximal, characteristic, complemented
15C2×#65063C211yesmaximal, characteristic, complemented
16C2×#65048C211yesmaximal, characteristic, complemented
17C22×C5×SD16C2211yescharacteristic
18C23×C5×C8C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21C2×#4092C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C2×#4085—21no—
24C2×#4084C2211yescharacteristic
25C2×D4×Dic5—21no—
26C2×D4×Dic5C2211yescharacteristic
27C2×C4×C22⋊D5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×#676C2211yescharacteristic
31#65969—24no—
32#65969C2218yescomplemented
33#65952—24no—
34#65952C2218yes—
35C2×#4043—21no—
36C2×#4038C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4036C2211yescharacteristic
39C2×#4035—21no—
40C2×#4034C2211yescharacteristic
41C2×#4032—21no—
42C2×#4027—21no—
43C2×#4025—21no—
44C2×#4024—21no—
45C5×#465C2218yescomplemented
46C2×C5×#106C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×C22⋊#168C2211yescharacteristic
54#65463C2218yescomplemented
55#65453C2218yescomplemented
56#65400C2218yescomplemented
57C2×#3952C2211yescharacteristic
58C2×#3950C2211yescharacteristic
59C2×#3950C2211yescharacteristic
60C2×#3950C2211yescharacteristic
61C2×#3950C2211yescharacteristic
62C2×#3950C2218yescomplemented
63C2×#3947C2211yescharacteristic
64C2×#3946C2211yescharacteristic
65#65333C2218yescomplemented
66#65323C2218yescomplemented
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65150C2218yescomplemented
72#65145C2218yescomplemented
73#65103C2218yescomplemented
74#65085C2218yescomplemented
75#65063C2218yescomplemented
76#65048C2218yescomplemented
77C2×#3346—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C23×Dic5—21no—
85C23×Dic5—21no—
86C23×Dic5—21no—
87C22×C4×D5—21no—
88C22×C4×D5C2311yescharacteristic
89C22×Dic10—21no—
90C2×C5×SD16—24no—
91C2×C5×SD16C2314yes—
92C22×C5×C8—24no—
93C22×C5×C8C2311yescharacteristic
94C22×C5×C8C2314yes—
95C22×C5×C8C2311yescharacteristic
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8C2314yes—
98C5×#121—22no—
99C5×#121C2314yes—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5D411yescharacteristic
108#4092—22no—
109#4092C2314yes—
110Q8×Dic5—22no—
111Q8×Dic5C2314yes—
112#4085—28no—
113#4084—22no—
114#4084C2314yes—
115D4×Dic5—28no—
116D4×Dic5—22no—
117D4×Dic5C2314yes—
118C4×C22⋊D5D414yes—
119C4×C22⋊D5C2314yes—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685D411yescharacteristic
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5—21no—
125C2×C4⋊Dic5—22no—
126C2×C4⋊Dic5—22no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2314yes—
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2314yes—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683D411yescharacteristic
140C2×C4×Dic5—21no—
141C2×C4×Dic5—21no—
142C2×C4×Dic5C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C2×#676—24no—
146C2×#676C2314yes—
147#4043—28no—
148#4038—22no—
149#4038C2314yes—
150D5×C4⋊C4—22no—
151D5×C4⋊C4C2314yes—
152#4036—22no—
153#4036C2314yes—
154#4035—28no—
155#4034—22no—
156#4034C2314yes—
157#4032—28no—
158#4027—28no—
159#4025—28no—
160#4024—28no—
161C5×#106C2314yes—
162C5×#103C2314yes—
163C5×#102C2314yes—
164#3967C2314yes—
165#3967C2314yes—
166#3964C2314yes—
167#3964C2314yes—
168C22⋊#168C2314yes—
169#3952C2314yes—
170#3950C2314yes—
171#3950C2314yes—
172#3950C2314yes—
173#3950C2314yes—
174#3947C2314yes—
175#3946C2314yes—
176#3940C2314yes—
177#3940C2314yes—
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×#480—51no—
188C2×#479—51no—
189C2×#474—51no—
190C2×#468—51no—
191C2×#465D511yescharacteristic, complemented
192C2×#440—51no—
193C2×#435—51no—
194C2×#428—51no—
195C22×#107—51no—
196C24×C5—21no—
197C24×C5C2×D411yescharacteristic
198C23×D5C2×D411yescharacteristic
199C2×C5×Q8—21no—
200C2×C5×Q8—22no—
201C2×C5×Q8—22no—
202C2×C5×Q8C2412yes—
203C2×C5×D4—24no—
204C2×C5×D4—21no—
205C2×C5×D4—22no—
206C2×C5×D4—22no—
207C2×C5×D4—44no—
208C2×C5×D4C2412yes—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—82no—
221C2×C22⋊D5C2×D414yes—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—24no—
227C22×Dic5—24no—
228C22×Dic5—24no—
229C22×Dic5—82no—
230C22×Dic5—82no—
231C22×Dic5—82no—
232C22×Dic5C2×D411yescharacteristic
233C22×Dic5C2×D411yescharacteristic
234C22×Dic5C2×D411yescharacteristic
235C2×C4×D5—22no—
236C2×C4×D5—22no—
237C2×C4×D5—24no—
238C2×C4×D5—82no—
239C2×C4×D5C2×D412yes—
240C2×C4×D5C2412yes—
241C2×Dic10—24no—
242C2×Dic10—82no—
243C5×SD16—28no—
244C2×C5×C8—22no—
245C2×C5×C8—28no—
246C2×C5×C8#4114yes—
247C2×C5×C8C2412yes—
248C2×C5×C8C2412yes—
249C5×C4⋊C4—24no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4C2412yes—
253C5×C4⋊C4C2412yes—
254C5×C22⋊C4—24no—
255C5×C22⋊C4—24no—
256C22⋊Dic5—24no—
257C22⋊Dic5—24no—
258C22⋊Dic5C2×D414yes—
259#685—24no—
260#685—24no—
261#685C2×D414yes—
262C4⋊Dic5—24no—
263C4⋊Dic5—21no—
264C4⋊Dic5—24no—
265C4⋊Dic5—21no—
266C4⋊Dic5—21no—
267C4⋊Dic5—21no—
268C4⋊Dic5—24no—
269C4⋊Dic5—24no—
270C4⋊Dic5C2412yes—
271C4⋊Dic5C2412yes—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274#683—24no—
275#683—24no—
276#683—24no—
277#683—24no—
278#683C2×D414yes—
279C4×Dic5—24no—
280C4×Dic5—24no—
281C4×Dic5C2×D412yes—
282C4×Dic5C2412yes—
283C2×#168—22no—
284C2×#168—22no—
285C2×#168C2412yes—
286C2×#168C2412yes—
287#676—28no—
288C22×SD16C2×D511yescharacteristic
289C22×M16—51no—
290C23×C8C2×D511yescharacteristic
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—101no—
302C2×C22⋊Q8—101no—
303C2×C22⋊Q8C2×D511yescharacteristic
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⋊C4—51no—
316#501—58no—
317#485—58no—
318#484—58no—
319#481—58no—
320#480—58no—
321#479—58no—
322#474—58no—
323#468—58no—
324#465C2×D518yescomplemented
325#440—58no—
326#435—58no—
327#428—58no—
328C2×#107—51no—
329C2×#107—51no—
330C2×#107—58no—
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#106—51no—
336C2×#106—51no—
337C2×#106C2×D511yescharacteristic
338C2×C4⋊C8—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103C2×D511yescharacteristic
342C2×#102—51no—
343C2×#102—51no—
344C2×#102C2×D511yescharacteristic
345C2×C22⋊C8—51no—
346C2×C22⋊C8—51no—
347C2×#97—51no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—42no—
352C23×C5—42no—
353C23×C5—42no—
354C23×C5#13714yes—
355C23×C5C22×D412yes—
356C23×C5C22×D411yescharacteristic
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5C22×D412yes—
361C5×Q8—22no—
362C5×Q8—22no—
363C5×Q8—42no—
364C5×D4—22no—
365C5×D4—22no—
366C5×D4—48no—
367C5×D4—42no—
368C2×C4×C5—22no—
369C2×C4×C5—24no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—42no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5C22×D412yes—
379C2×C4×C5C22×D411yescharacteristic
380C2×C4×C5C2×#4112yes—
381C2×C4×C52−1+412yes—
382C2×C4×C5C2511yescharacteristic
383C22⋊D5—28no—
384C22⋊D5—84no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5—84no—
397C2×Dic5—84no—
398C2×Dic5—84no—
399C2×Dic5C22×D412yes—
400C2×Dic5C22×D412yes—
401C2×Dic5C22×D412yes—
402C4×D5—24no—
403C4×D5—22no—
404C4×D5—22no—
405C4×D5—84no—
406Dic10—84no—
407C5×C8—22no—
408C5×C8C2×#4114yes—
409#168—22no—
410#168—22no—
411C22×Q8—101no—
412C22×Q8C22×D511yescharacteristic
413C22×D4—21no—
414C22×D4—51no—
415C22×D4—101no—
416C22×D4C22×D511yescharacteristic
417C23×C4—51no—
418C23×C4—101no—
419C23×C4—101no—
420C23×C4—101no—
421C23×C4—101no—
422C23×C4C22×D511yescharacteristic
423C2×SD16—24no—
424C2×SD16C22×D514yes—
425C2×M16—54no—
426C2×M16—104no—
427C22×C8—24no—
428C22×C8—51no—
429C22×C8—51no—
430C22×C8C22×D511yescharacteristic
431C22×C8C22×D514yes—
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—22no—
441C22⋊Q8—54no—
442C22⋊Q8—108no—
443C22⋊Q8—108no—
444C22⋊Q8—102no—
445C22⋊Q8C22×D514yes—
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—51no—
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—54no—
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⋊C4—102no—
480C2×C4⋊C4—102no—
481C2×C4⋊C4C22×D511yescharacteristic
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C22⋊C4—21no—
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×C42—51no—
492C2×C42—101no—
493C2×C42—101no—
494#107—54no—
495#107—54no—
496#107—54no—
497#107—54no—
498#107—54no—
499#107—54no—
500#106—54no—
501#106—54no—
502#106C22×D514yes—
503C4⋊C8—54no—
504#103—54no—
505#103—54no—
506#103C22×D514yes—
507#102—54no—
508#102—54no—
509#102C22×D514yes—
510C22⋊C8—54no—
511C22⋊C8—54no—
512#97—54no—
513C22×C5—28no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5—42no—
517C22×C5—42no—
518C22×C5—42no—
519C22×C5—84no—
520C22×C5#54712yes—
521C22×C5C2×#13714yes—
522C22×C5C2×#13712yes—
523C22×C5#57612yes—
524C22×C5C23×D411yescharacteristic
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—22no—
528C2×D5—44no—
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—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—104no—
550C2×Q8—402no—
551C2×Q8C23×D512yes—
552C2×D4—24no—
553C2×D4—21no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—44no—
557C2×D4—54no—
558C2×D4—104no—
559C2×D4—104no—
560C2×D4—402no—
561C2×D4C23×D512yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—51no—
568C22×C4—51no—
569C22×C4—51no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—104no—
573C22×C4—104no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—104no—
581C22×C4—104no—
582C22×C4—402no—
583C22×C4—402no—
584C22×C4—402no—
585C22×C4—402no—
586C22×C4D4×D512yes—
587C22×C4D4×D511yescharacteristic
588C22×C4C23×D512yes—
589C22×C4C23×D511yescharacteristic
590SD16—28no—
591M16—108no—
592C2×C8—22no—
593C2×C8—28no—
594C2×C8—52no—
595C2×C8—52no—
596C2×C8—102no—
597C2×C8—102no—
598C2×C8#71114yes—
599C2×C8C23×D512yes—
600C2×C8C23×D512yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—54no—
605C4⋊C4—52no—
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—101no—
616C4⋊C4—101no—
617C4⋊C4—101no—
618C4⋊C4—104no—
619C4⋊C4—101no—
620C4⋊C4—104no—
621C4⋊C4C23×D512yes—
622C4⋊C4C23×D512yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—54no—
626C22⋊C4—54no—
627C22⋊C4—104no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C42—52no—
632C42—52no—
633C42—104no—
634C42—104no—
635C2×C5—24no—
636C2×C5—82no—
637C2×C5#334614yescomplemented
638C2×C5C2×#54711yescharacteristic
639C2×C5C22×#13711yescharacteristic
640C2×C5C2×#57611yescharacteristic
641D5—42no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—52no—
649C23—102no—
650C23—102no—
651C23—102no—
652C23#406114yes—
653C23C2×D4×D512yes—
654C23C2×D4×D511yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—404no—
659D4—22no—
660D4—22no—
661D4—48no—
662D4—42no—
663D4—108no—
664D4—404no—
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—102no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—104no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—202no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—202no—
692C2×C4—404no—
693C2×C4—404no—
694C2×C4—404no—
695C2×C4—404no—
696C2×C4C2×D4×D512yes—
697C2×C4C2×D4×D511yescharacteristic
698C2×C4C2×#71112yes—
699C2×C4#415012yes—
700C2×C4C24×D511yescharacteristic
701C8—22no—
702C8—102no—
703C8—102no—
704C8C2×#71114yes—
705C5C2×#334611yescharacteristic, complemented, Sylow
706C22—28no—
707C22—22no—
708C22—22no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—84no—
713C22—102no—
714C22—102no—
715C22—102no—
716C22—204no—
717C22#6594512yes—
718C22C2×#406114yes—
719C22C2×#406112yes—
720C22#6610312yes—
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#6594512yes—
734C4C22×#71111yescharacteristic
735C4C2×#415011yescharacteristic
736C2—24no—
737C2—82no—
738C2—202no—
739C2#1061238314yesdirect product factor
740C2C2×#6594511yescharacteristic
741C2C22×#406111yescharacteristic
742C2C2×#6610311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#465C2
socleC23×C5C22×D4
prime radicalC2×#65952C2
hypercenterC2×#465D5
hypocenterC5C2×#3346
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#65969C2semidirect
3. C2×C5×#465C2semidirect
4. C2×#65463C2semidirect
5. C2×#65453C2semidirect
6. C2×#65400C2semidirect
7. C22×#3950C2semidirect
8. C2×#65333C2semidirect
9. C2×#65323C2semidirect
10. #10612383C2direct (N × H)
11. C2×#65150C2semidirect
12. C2×#65145C2semidirect
13. C2×#65103C2semidirect
14. C2×#65085C2semidirect
15. C2×#65063C2semidirect
16. C2×#65048C2semidirect
32. #65969C22semidirect
45. C5×#465C22semidirect
54. #65463C22semidirect
55. #65453C22semidirect
56. #65400C22semidirect
62. C2×#3950C22semidirect
65. #65333C22semidirect
66. #65323C22semidirect
71. #65150C22semidirect
72. #65145C22semidirect
73. #65103C22semidirect
74. #65085C22semidirect
75. #65063C22semidirect
76. #65048C22semidirect
191. C2×#465D5semidirect
324. #465C2×D5semidirect
637. C2×C5#3346semidirect
705. C5C2×#3346semidirect
739. C2#10612383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659692
C2×#659522
C2×C5×#4652
C2×#654632
C2×#654532
C2×#654002
C22×#39502
C2×#653332
C2×#653232
#106123832
C2×#651502
C2×#651452
C2×#651032
C2×#650852
C2×#650632
C2×#650482
C2×#33465