Finite Group Databasebeta

← C2×#10611076 #12967482

Subgroups — C2×#10611076 #12967482

Order 1280.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65813C211yesmaximal, characteristic, complemented
2C2×C4×#709C211yesmaximal, characteristic, complemented
3C2×C5×#432C211yesmaximal, characteristic, complemented
4#10611076C2116yesmaximal, direct product factor
5C2×#65118C211yesmaximal, characteristic, complemented
6C2×#65134C211yesmaximal, characteristic, complemented
7C2×#65136C211yesmaximal, characteristic, complemented
8C2×#65133C211yesmaximal, characteristic, complemented
9C2×#65022C211yesmaximal, characteristic, complemented
10C2×#65023C211yesmaximal, characteristic
11C2×#65012C211yesmaximal, characteristic, complemented
12C2×#65026C211yesmaximal, characteristic, complemented
13C2×#65005C211yesmaximal, characteristic, complemented
14C2×#65000C211yesmaximal, characteristic, complemented
15C2×#64999C211yesmaximal, characteristic, complemented
16C2×#64999C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C2×#4076C2211yescharacteristic
20C2×#4075—21no—
21C2×C4×C22⋊D5—21no—
22C2×C4×C22⋊D5—21no—
23C2×C4×C22⋊D5—21no—
24C2×#4072C2211yescharacteristic
25C2×#4070C2211yescharacteristic
26C22×Dic20C2211yescharacteristic
27C22×D40C2211yescharacteristic
28C22×#677C2211yescharacteristic
29C22×#677C2211yescharacteristic
30#65813—24no—
31#65813C2218yescomplemented
32C2×#4022—21no—
33C2×#4021C2211yescharacteristic
34C4×#709—24no—
35C4×#709C2218yescomplemented
36C2×C4×D20C2211yescharacteristic
37C2×C4×D20C2211yescharacteristic
38C2×C4×D20C2211yescharacteristic
39C2×#4018—21no—
40C2×#4018—21no—
41C2×C42×D5—21no—
42C2×#4016C2211yescharacteristic
43C2×C4×Dic10C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C5×#432C2218yescomplemented
47C2×C5×C4⋊C8C2211yescharacteristic
48C2×C5×C4⋊C8C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×C5×#97C2211yescharacteristic
52C2×C5×#97C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic
56C2×#3953C2211yescharacteristic
57C2×#3950C2211yescharacteristic
58C2×#3950C2211yescharacteristic
59C2×#3949C2211yescharacteristic
60C2×#3949C2211yescharacteristic
61C2×#3948C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3948C2211yescharacteristic
65#65136C2218yescomplemented
66#65134C2218yescomplemented
67#65133C2218yescomplemented
68#65118C2218yescomplemented
69#65026C2218yescomplemented
70#65023C2218yes—
71#65022C2218yescomplemented
72#65012C2218yescomplemented
73#65005C2218yescomplemented
74#65000C2218yescomplemented
75#64999C2218yescomplemented
76#64999C2218yescomplemented
77C2×#3111—51nomaximal, Sylow
78C23×C4×C5D411yescharacteristic
79C23×C4×C5D411yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C2×#709—22no—
84C2×#709—24no—
85C2×#709—24no—
86C2×#709C2314yes—
87C22×D20C2311yescharacteristic
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×Dic10C2311yescharacteristic
94C22×Dic10C2311yescharacteristic
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C2×C42×C5D411yescharacteristic
100C2×C42×C5D411yescharacteristic
101C2×C42×C5D414yes—
102C2×C42×C5C2311yescharacteristic
103C2×C42×C5C2311yescharacteristic
104C2×C42×C5C2314yes—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107#4076—22no—
108#4076C2314yes—
109#4075—28no—
110C4×C22⋊D5—28no—
111C4×C22⋊D5—28no—
112C4×C22⋊D5—28no—
113C2×#685—21no—
114C2×#685—21no—
115C2×#685—21no—
116C2×#685—21no—
117C2×#685—21no—
118C2×#685—21no—
119#4072—22no—
120#4072C2314yes—
121C2×C4⋊Dic5C2311yescharacteristic
122C2×C4⋊Dic5C2311yescharacteristic
123C2×C4⋊Dic5C2311yescharacteristic
124C2×C4⋊Dic5C2311yescharacteristic
125#4070—22no—
126#4070C2314yes—
127C2×#683—21no—
128C2×#683—21no—
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×C4×Dic5—21no—
134C2×C4×Dic5—21no—
135C2×C4×Dic5—21no—
136C2×C4×Dic5—21no—
137C2×Dic20—24no—
138C2×Dic20C2314yes—
139C2×D40—24no—
140C2×D40C2314yes—
141C2×#677—24no—
142C2×#677—24no—
143C2×#677C2314yes—
144C2×#677C2314yes—
145#4022—28no—
146#4021—22no—
147#4021C2314yes—
148C4×D20—22no—
149C4×D20—22no—
150C4×D20—22no—
151C4×D20C2314yes—
152C4×D20C2314yes—
153C4×D20C2314yes—
154#4018—28no—
155#4018—28no—
156C42×D5—28no—
157#4016—22no—
158#4016C2314yes—
159C4×Dic10—22no—
160C4×Dic10—22no—
161C4×Dic10—22no—
162C4×Dic10C2314yes—
163C4×Dic10C2314yes—
164C4×Dic10C2314yes—
165C5×C4⋊C8C2314yes—
166C5×C4⋊C8C2314yes—
167C5×C22⋊C8C2314yes—
168C5×C22⋊C8C2314yes—
169C5×#97C2314yes—
170C5×#97C2314yes—
171#3953C2314yes—
172#3953C2314yes—
173#3953C2314yes—
174#3953C2314yes—
175#3950C2314yes—
176#3950C2314yes—
177#3949C2314yes—
178#3949C2314yes—
179#3948C2314yes—
180#3948C2314yes—
181#3948C2314yes—
182#3948C2314yes—
183C2×#529—51no—
184C2×C4×#41—51no—
185#3111—516no—
186C2×#485—51no—
187C2×#482—51no—
188C2×#479—51no—
189C2×#478—51no—
190C2×#464—51no—
191C2×#463—51no—
192C2×#452—51no—
193C2×#449—51no—
194C2×#442—51no—
195C2×#441—51no—
196C2×#440—51no—
197C2×#440—51no—
198C2×#432D511yescharacteristic, complemented
199C24×C5C2×D411yescharacteristic
200C23×D5—21no—
201C23×D5—21no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—42no—
205C22×C4×C5—42no—
206C22×C4×C5C2×D411yescharacteristic
207C22×C4×C5C2×D412yes—
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D414yes—
213C22×C4×C5C2×D414yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2411yescharacteristic
216C2×C22⋊D5—28no—
217C2×C22⋊D5—24no—
218C2×C22⋊D5—24no—
219C2×C22⋊D5—44no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226#709—216no—
227#709—28no—
228#709—28no—
229C2×D20—21no—
230C2×D20—22no—
231C2×D20—22no—
232C2×D20—22no—
233C2×D20—21no—
234C2×D20#4114yes—
235C2×D20C2412yes—
236C2×D20C2412yes—
237C2×C4×D5—28no—
238C2×C4×D5—24no—
239C2×C4×D5—24no—
240C2×C4×D5—24no—
241C2×C4×D5—24no—
242C2×C4×D5—44no—
243C2×C4×D5—44no—
244C2×C4×D5—44no—
245C2×Dic10—21no—
246C2×Dic10—22no—
247C2×Dic10—22no—
248C2×Dic10—22no—
249C2×Dic10—21no—
250C2×Dic10#4114yes—
251C2×Dic10C2412yes—
252C2×Dic10C2412yes—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8—22no—
256C2×C5×C8—22no—
257C2×C5×C8C2412yes—
258C2×C5×C8C2412yes—
259C2×C5×C8C2412yes—
260C2×C5×C8C2412yes—
261C42×C5C2×D412yes—
262C42×C5C2×D412yes—
263C42×C5C2×D414yes—
264C42×C5C2×D414yes—
265C42×C5C2412yes—
266C42×C5C2412yes—
267C22⋊Dic5—24no—
268C22⋊Dic5—24no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273#685—24no—
274#685—24no—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5—21no—
278C4⋊Dic5—21no—
279C4⋊Dic5C2412yes—
280C4⋊Dic5C2412yes—
281C4⋊Dic5C2412yes—
282C4⋊Dic5C2412yes—
283#683—24no—
284#683—24no—
285#683—24no—
286#683—24no—
287#683—24no—
288#683—24no—
289C4×Dic5—24no—
290C4×Dic5—24no—
291C4×Dic5—24no—
292C4×Dic5—24no—
293Dic20—28no—
294D40—28no—
295#677—28no—
296#677—28no—
297C22×#41—51no—
298C22×Q16—51no—
299C22×SD16—51no—
300C22×SD16—51no—
301C22×D8—51no—
302#529—58no—
303#529—104no—
304C2×#126—101no—
305C2×#125—51no—
306C2×#124—51no—
307C2×#123—101no—
308C2×C22⋊Q8—51no—
309C2×#121—51no—
310C4×#41—58no—
311C4×#41—104no—
312C2×C4×Q8—51no—
313C2×C4×Q8—51no—
314C2×C4×Q8—51no—
315C2×C4×D4—51no—
316C2×C4×D4—51no—
317C2×C4×D4—51no—
318C2×C4×D4—101no—
319C2×C4×D4—101no—
320C2×C4×D4—101no—
321C2×#117—51no—
322C2×#117—101no—
323C2×#117—101no—
324C22×C42—101no—
325C22×C42C2×D511yescharacteristic
326#485—58no—
327#482—58no—
328#479—58no—
329#478—58no—
330#464—58no—
331#463—58no—
332#452—58no—
333#449—58no—
334#442—58no—
335#441—58no—
336#440—58no—
337#440—58no—
338#432C2×D518yescomplemented
339C2×#107—51no—
340C2×#107—51no—
341C2×#106—51no—
342C2×#106—51no—
343C2×C4⋊C8C2×D511yescharacteristic
344C2×C4⋊C8C2×D511yescharacteristic
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102—51no—
353C2×C22⋊C8C2×D511yescharacteristic
354C2×C22⋊C8C2×D511yescharacteristic
355C2×#97C2×D511yescharacteristic
356C2×#97C2×D511yescharacteristic
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5C22×D412yes—
361C23×C5C22×D411yescharacteristic
362C22×D5—24no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—42no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—24no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—44no—
379C2×C4×C5—44no—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D412yes—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D411yescharacteristic
386C2×C4×C5C2×#4112yes—
387C2×C4×C5C2×#4112yes—
388C2×C4×C5C2511yescharacteristic
389C22⋊D5—216no—
390C22⋊D5—48no—
391C2×Dic5—24no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403D20—24no—
404D20—22no—
405D20—22no—
406D20—22no—
407D20—42no—
408D20C2×#4114yes—
409C4×D5—216no—
410C4×D5—48no—
411C4×D5—48no—
412C4×D5—48no—
413Dic10—24no—
414Dic10—22no—
415Dic10—22no—
416Dic10—22no—
417Dic10—42no—
418Dic10C2×#4114yes—
419C5×C8—22no—
420C5×C8—22no—
421C5×C8—22no—
422C5×C8—22no—
423C2×#41—54no—
424C2×#41—104no—
425C2×#41—104no—
426C2×#41—102no—
427C22×Q8—51no—
428C22×Q8—51no—
429C22×D4—51no—
430C22×D4—51no—
431C22×D4—101no—
432C22×D4—101no—
433C23×C4—101no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4D2011yescharacteristic
438C23×C4D2011yescharacteristic
439C23×C4C22×D511yescharacteristic
440C2×Q16—54no—
441C2×Q16—104no—
442C2×SD16—54no—
443C2×SD16—54no—
444C2×SD16—104no—
445C2×SD16—104no—
446C2×D8—54no—
447C2×D8—104no—
448C22×C8C22×D511yescharacteristic
449C22×C8C22×D511yescharacteristic
450C22×C8C22×D511yescharacteristic
451C22×C8C22×D511yescharacteristic
452#126—108no—
453#125—54no—
454#125—102no—
455#124—54no—
456#124—102no—
457#123—108no—
458C22⋊Q8—54no—
459C22⋊Q8—102no—
460#121—54no—
461#121—102no—
462C4×Q8—54no—
463C4×Q8—54no—
464C4×Q8—54no—
465C4×Q8—102no—
466C4×Q8—102no—
467C4×Q8—102no—
468C4×D4—54no—
469C4×D4—54no—
470C4×D4—54no—
471C4×D4—108no—
472C4×D4—108no—
473C4×D4—108no—
474C4×D4—102no—
475C4×D4—102no—
476C4×D4—102no—
477#117—54no—
478#117—102no—
479#117—108no—
480#117—108no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—101no—
500C2×C42—101no—
501C2×C42—101no—
502C2×C42—101no—
503C2×C42—108no—
504C2×C42D2011yescharacteristic
505C2×C42D2014yes—
506C2×C42D2011yescharacteristic
507C2×C42C22×D511yescharacteristic
508C2×C42C22×D511yescharacteristic
509C2×C42C22×D514yes—
510#107—54no—
511#107—54no—
512#106—54no—
513#106—54no—
514C4⋊C8C22×D514yes—
515C4⋊C8C22×D514yes—
516#103—54no—
517#103—54no—
518#103—54no—
519#103—54no—
520#102—54no—
521#102—54no—
522#102—54no—
523#102—54no—
524C22⋊C8C22×D514yes—
525C22⋊C8C22×D514yes—
526#97C22×D514yes—
527#97C22×D514yes—
528C22×C5—22no—
529C22×C5—22no—
530C22×C5—22no—
531C22×C5—44no—
532C22×C5#52512yes—
533C22×C5#57512yes—
534C22×C5#57512yes—
535C22×C5C23×D411yescharacteristic
536C2×D5—24no—
537C2×D5—48no—
538C2×D5—42no—
539C2×D5—42no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—84no—
544C4×C5—22no—
545C4×C5—22no—
546C4×C5—22no—
547C4×C5—22no—
548C4×C5—22no—
549C4×C5#52512yes—
550C4×C5C22×#4111yescharacteristic
551C4×C5C22×#4111yescharacteristic
552Dic5—24no—
553Dic5—42no—
554Dic5—42no—
555Dic5—42no—
556Dic5—42no—
557Dic5—42no—
558C24—101no—
559C24—101no—
560C24C2×D2011yescharacteristic
561#41—108no—
562#41—108no—
563#41—1016no—
564C2×Q8—54no—
565C2×Q8—52no—
566C2×Q8—52no—
567C2×Q8—101no—
568C2×Q8—101no—
569C2×Q8—102no—
570C2×Q8—102no—
571C2×Q8—102no—
572C2×D4—54no—
573C2×D4—52no—
574C2×D4—52no—
575C2×D4—108no—
576C2×D4—104no—
577C2×D4—104no—
578C2×D4—101no—
579C2×D4—101no—
580C2×D4—102no—
581C2×D4—102no—
582C2×D4—102no—
583C2×D4—204no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—108no—
589C22×C4—101no—
590C22×C4—104no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—104no—
597C22×C4—104no—
598C22×C4—104no—
599C22×C4—204no—
600C22×C4—204no—
601C22×C4—204no—
602C22×C4C2×D2012yes—
603C22×C4C2×D2011yescharacteristic
604C22×C4C2×D2011yescharacteristic
605C22×C4C2×D2011yescharacteristic
606C22×C4C2×D2011yescharacteristic
607C22×C4C2×D2011yescharacteristic
608C22×C4C2×D2014yes—
609C22×C4C2×D2014yes—
610C22×C4C23×D512yes—
611C22×C4C23×D511yescharacteristic
612Q16—108no—
613SD16—108no—
614SD16—108no—
615D8—108no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C2×C8C23×D512yes—
623C2×C8C23×D512yes—
624C4⋊C4—52no—
625C4⋊C4—52no—
626C4⋊C4—52no—
627C4⋊C4—52no—
628C4⋊C4—101no—
629C4⋊C4—101no—
630C4⋊C4—101no—
631C4⋊C4—101no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—104no—
636C4⋊C4—104no—
637C4⋊C4—104no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C22⋊C4—104no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C42—104no—
647C42—104no—
648C42—104no—
649C42—104no—
650C42C2×D2014yes—
651C42C2×D2014yes—
652C42C2×D2012yes—
653C42C2×D2012yes—
654C42C23×D512yes—
655C42C23×D512yes—
656C2×C5—42no—
657C2×C5#311114yescomplemented
658C2×C5C2×#52511yescharacteristic
659C2×C5C2×#57511yescharacteristic
660C2×C5C2×#57511yescharacteristic
661D5—44no—
662D5—82no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—104no—
667C23—102no—
668C23—102no—
669C23—202no—
670C23—202no—
671C23—202no—
672C23—202no—
673C23—202no—
674C23C22×D2012yes—
675C23C22×D2011yescharacteristic
676Q8—54no—
677Q8—104no—
678Q8—102no—
679Q8—102no—
680Q8—102no—
681Q8—202no—
682D4—54no—
683D4—1016no—
684D4—104no—
685D4—102no—
686D4—102no—
687D4—102no—
688D4—208no—
689D4—202no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—1016no—
701C2×C4—104no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—208no—
709C2×C4—208no—
710C2×C4—208no—
711C2×C4—202no—
712C2×C4—202no—
713C2×C4—202no—
714C2×C4—202no—
715C2×C4—202no—
716C2×C4C22×D2012yes—
717C2×C4C22×D2012yes—
718C2×C4C22×D2012yes—
719C2×C4C22×D2012yes—
720C2×C4C22×D2012yes—
721C2×C4C22×D2011yescharacteristic
722C2×C4D5×#4112yes—
723C2×C4D5×#4112yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8—22no—
729C5C2×#311111yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—104no—
735C22—208no—
736C22—202no—
737C22—202no—
738C22—202no—
739C22—202no—
740C22—202no—
741C22—404no—
742C22#6585812yes—
743C22#6608212yes—
744C22#6608212yes—
745C22C23×D2011yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—104no—
752C4—202no—
753C4—202no—
754C4—202no—
755C4—202no—
756C4—202no—
757C4#6585812yes—
758C4C2×D5×#4111yescharacteristic
759C4C2×D5×#4111yescharacteristic
760C2—42no—
761C2—204no—
762C2—402no—
763C2#1061107614yesdirect product factor
764C2C2×#6585811yescharacteristic
765C2C2×#6608211yescharacteristic
766C2C2×#6608211yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#432C2
socleC23×C5C22×D4
prime radicalC2×#65023C2
hypercenterC2×#432D5
hypocenterC5C2×#3111
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#65813C2semidirect
2. C2×C4×#709C2semidirect
3. C2×C5×#432C2semidirect
4. #10611076C2direct (N × H)
5. C2×#65118C2semidirect
6. C2×#65134C2semidirect
7. C2×#65136C2semidirect
8. C2×#65133C2semidirect
9. C2×#65022C2semidirect
11. C2×#65012C2semidirect
12. C2×#65026C2semidirect
13. C2×#65005C2semidirect
14. C2×#65000C2semidirect
15. C2×#64999C2semidirect
16. C2×#64999C2semidirect
31. #65813C22semidirect
35. C4×#709C22semidirect
46. C5×#432C22semidirect
65. #65136C22semidirect
66. #65134C22semidirect
67. #65133C22semidirect
68. #65118C22semidirect
69. #65026C22semidirect
71. #65022C22semidirect
72. #65012C22semidirect
73. #65005C22semidirect
74. #65000C22semidirect
75. #64999C22semidirect
76. #64999C22semidirect
198. C2×#432D5semidirect
338. #432C2×D5semidirect
657. C2×C5#3111semidirect
729. C5C2×#3111semidirect
763. C2#10611076direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658132
C2×C4×#7092
C2×C5×#4322
#106110762
C2×#651182
C2×#651342
C2×#651362
C2×#651332
C2×#650222
C2×#650232
C2×#650122
C2×#650262
C2×#650052
C2×#650002
C2×#649992
C2×#31115