Finite Group Databasebeta

← C2×#10610858 #12977859

Subgroups — C2×#10610858 #12977859

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65848C211yesmaximal, characteristic, complemented
2C2×#65841C211yesmaximal, characteristic, complemented
3C22×C5×#106C211yesmaximal, characteristic, complemented
4C2×#65404C211yesmaximal, characteristic, complemented
5C2×#65400C211yesmaximal, characteristic, complemented
6C2×#65257C211yesmaximal, characteristic, complemented
7C2×#65256C211yesmaximal, characteristic, complemented
8C2×#65160C211yesmaximal, characteristic, complemented
9C2×#65159C211yesmaximal, characteristic, complemented
10#10610858C2116yesmaximal, direct product factor
11C2×#65152C211yesmaximal, characteristic, complemented
12C2×#65155C211yesmaximal, characteristic, complemented
13C2×#65154C211yesmaximal, characteristic, complemented
14C2×#65150C211yesmaximal, characteristic, complemented
15C2×#65145C211yesmaximal, characteristic, complemented
16C2×#65158C211yesmaximal, characteristic, complemented
17C22×#709—21no—
18C23×C5×C8C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×#4076—21no—
22C2×#4076C2211yescharacteristic
23C2×#4076C2211yescharacteristic
24C2×#4075—21no—
25C2×C4×C22⋊D5—21no—
26C2×C4×C22⋊D5C2211yescharacteristic
27C22×D40C2211yescharacteristic
28C22×#676C2211yescharacteristic
29#65848—24no—
30#65848C2218yescomplemented
31C2×#4044—21no—
32C2×#4042—21no—
33#65841—24no—
34#65841C2218yescomplemented
35C2×#4041C2211yescharacteristic
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4040—21no—
39C2×#4039C2211yescharacteristic
40C2×#4039C2211yescharacteristic
41C2×#4038C2211yescharacteristic
42C2×D5×C4⋊C4C2211yescharacteristic
43C2×#4036C2211yescharacteristic
44C2×#4034C2211yescharacteristic
45C2×C5×#106C2211yescharacteristic
46C2×C5×#106C2211yescharacteristic
47C2×C5×#106C2211yescharacteristic
48C2×C5×#106C2211yescharacteristic
49C2×C5×#106C2218yescomplemented
50C2×C22⋊#168C2211yescharacteristic
51#65404C2218yescomplemented
52C2×#3953C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54#65400C2218yescomplemented
55C2×#3952C2211yescharacteristic
56C2×#3950C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58C2×#3946C2211yescharacteristic
59#65257C2218yescomplemented
60#65256C2218yescomplemented
61C2×#3941C2211yescharacteristic
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×#3939C2211yescharacteristic
69#65160C2218yescomplemented
70#65159C2218yescomplemented
71#65158C2218yescomplemented
72#65155C2218yescomplemented
73#65154C2218yescomplemented
74#65152C2218yescomplemented
75#65150C2218yescomplemented
76#65145C2218yescomplemented
77C2×#3345—51nomaximal, Sylow
78C23×C4×C5—21no—
79C23×C4×C5—21no—
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C2×#709—28no—
85C2×#709—48no—
86C22×D20—21no—
87C22×D20—21no—
88C22×D20C2311yescharacteristic
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5C2311yescharacteristic
94C22×Dic10—21no—
95C22×C5×C8—24no—
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2314yes—
98C22×C5×C8C2311yescharacteristic
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4—22no—
102C2×C5×C4⋊C4—22no—
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×C22⋊Dic5D411yescharacteristic
110#4076—22no—
111#4076—22no—
112#4076—28no—
113#4076C2314yes—
114#4076C2314yes—
115#4075—28no—
116C4×C22⋊D5—28no—
117C4×C22⋊D5D414yes—
118C4×C22⋊D5C2314yes—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685D411yescharacteristic
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5C2311yescharacteristic
129C2×C4⋊Dic5C2311yescharacteristic
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683D411yescharacteristic
134C2×C4×Dic5—21no—
135C2×C4×Dic5C2311yescharacteristic
136C22×#168C2311yescharacteristic
137C22×#168C2311yescharacteristic
138C2×D40—24no—
139C2×D40C2314yes—
140C2×#676—24no—
141C2×#676C2314yes—
142#4044—28no—
143#4042—28no—
144#4041—22no—
145#4041—22no—
146#4041C2314yes—
147#4041C2314yes—
148#4040—28no—
149#4040—28no—
150#4039—22no—
151#4039—22no—
152#4039C2314yes—
153#4039C2314yes—
154#4038—22no—
155#4038C2314yes—
156D5×C4⋊C4—22no—
157D5×C4⋊C4C2314yes—
158#4036—22no—
159#4036C2314yes—
160#4034—22no—
161#4034C2314yes—
162C5×#106C2314yes—
163C5×#106C2314yes—
164C5×#106C2314yes—
165C5×#106C2314yes—
166C22⋊#168C2314yes—
167#3953C2314yes—
168#3953C2314yes—
169#3952C2314yes—
170#3950C2314yes—
171#3947C2314yes—
172#3946C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3941C2314yes—
176#3941C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3939C2314yes—
180#3939C2314yes—
181C2×#553—51no—
182C2×#547—51no—
183#3345—516no—
184C2×#501—51no—
185C2×#481—51no—
186C2×#481—51no—
187C2×#482—51no—
188C2×#480—51no—
189C2×#478—51no—
190C2×#476—51no—
191C2×#469—51no—
192C2×#466—51no—
193C2×#442—51no—
194C2×#435—51no—
195C2×#428—51no—
196C22×#106D511yescharacteristic, complemented
197C24×C5C2×D411yescharacteristic
198C23×D5—21no—
199C23×D5—21no—
200C23×D5C2×D411yescharacteristic
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—24no—
208C22×C4×C5—24no—
209C22×C4×C5—44no—
210C22×C4×C5—82no—
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2×D412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2411yescharacteristic
215C2×C22⋊D5—24no—
216C2×C22⋊D5—24no—
217C2×C22⋊D5—24no—
218C2×C22⋊D5—44no—
219C2×C22⋊D5—44no—
220C2×C22⋊D5C2×D414yes—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5C2×D411yescharacteristic
224C22×Dic5C2×D411yescharacteristic
225C22×Dic5C2×D411yescharacteristic
226#709—432no—
227C2×D20—22no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—22no—
231C2×D20—24no—
232C2×D20—21no—
233C2×D20—21no—
234C2×D20—24no—
235C2×D20—44no—
236C2×D20—82no—
237C2×D20C2412yes—
238C2×D20C2412yes—
239C2×C4×D5—22no—
240C2×C4×D5—22no—
241C2×C4×D5—24no—
242C2×C4×D5—24no—
243C2×C4×D5—24no—
244C2×C4×D5—44no—
245C2×C4×D5—44no—
246C2×C4×D5—82no—
247C2×C4×D5C2×D412yes—
248C2×C4×D5C2412yes—
249C2×Dic10—24no—
250C2×Dic10—44no—
251C2×C5×C8—22no—
252C2×C5×C8—28no—
253C2×C5×C8#4114yescomplemented
254C2×C5×C8C2412yes—
255C2×C5×C8C2412yes—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—24no—
261C5×C4⋊C4—24no—
262C5×C4⋊C4C2412yes—
263C5×C4⋊C4C2412yes—
264C5×C4⋊C4C2412yes—
265C5×C4⋊C4C2412yes—
266C22⋊Dic5C2×D414yes—
267#685—24no—
268#685—24no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273#685—24no—
274#685C2×D414yes—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5—24no—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280#683—24no—
281#683—24no—
282#683—24no—
283#683C2×D414yes—
284C4×Dic5—24no—
285C4×Dic5C2×D412yes—
286C4×Dic5C2412yes—
287C2×#168—22no—
288C2×#168—22no—
289C2×#168C2412yes—
290C2×#168C2412yes—
291D40—28no—
292#676—28no—
293C22×#41—101no—
294C22×D8—51no—
295C22×M16—51no—
296C23×C8C2×D511yescharacteristic
297#553—58no—
298#553—104no—
299#547—58no—
300#547—104no—
301C2×C4⋊Q8—51no—
302C2×#126—101no—
303C2×#125—51no—
304C2×#123—101no—
305C2×#123—101no—
306C2×#123—101no—
307C2×C22⋊Q8—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×#121—51no—
311C2×#121—51no—
312C2×#121—101no—
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—51no—
316C2×C4×D4—101no—
317C2×#117—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4C2×D511yescharacteristic
320C22×C4⋊C4C2×D511yescharacteristic
321#501—58no—
322#482—58no—
323#481—58no—
324#481—58no—
325#480—58no—
326#478—58no—
327#476—58no—
328#469—58no—
329#466—58no—
330#442—58no—
331#435—58no—
332#428—58no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#106C2×D511yescharacteristic
339C2×#106C2×D511yescharacteristic
340C2×#106C2×D511yescharacteristic
341C2×#106C2×D511yescharacteristic
342C2×#106C2×D518yescomplemented
343C2×C4⋊C8—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×C22⋊C8—51no—
351C2×C22⋊C8—51no—
352C2×#97—51no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5AGL(1,ℤ/8)14yes—
356C23×C5C22×D412yes—
357C23×C5C22×D411yescharacteristic
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—22no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5—42no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5C22×D412yes—
370C2×C4×C5—22no—
371C2×C4×C5—24no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—48no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—84no—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D411yescharacteristic
386C2×C4×C5C2×#4112yes—
387C2×C4×C52−1+412yes—
388C2×C4×C5C2511yescharacteristic
389C22⋊D5—28no—
390C22⋊D5—48no—
391C22⋊D5—48no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5C22×D412yes—
400C2×Dic5C22×D412yes—
401C2×Dic5C22×D412yes—
402D20—22no—
403D20—22no—
404D20—22no—
405D20—22no—
406D20—48no—
407D20—42no—
408D20—42no—
409D20—84no—
410C4×D5—24no—
411C4×D5—22no—
412C4×D5—22no—
413C4×D5—48no—
414C4×D5—48no—
415C4×D5—84no—
416Dic10—48no—
417C5×C8—22no—
418C5×C8C2×#4114yescomplemented
419#168—22no—
420#168—22no—
421C2×#41—108no—
422C2×#41—208no—
423C22×Q8—101no—
424C22×D4—51no—
425C22×D4—51no—
426C22×D4—51no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4—101no—
430C22×D4—101no—
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—51no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4C22×D511yescharacteristic
438C2×D8—54no—
439C2×D8—104no—
440C2×M16—54no—
441C2×M16—104no—
442C22×C8—24no—
443C22×C8—51no—
444C22×C8—51no—
445C22×C8C22×D511yescharacteristic
446C22×C8C22×D514yes—
447C22×C8C22×D511yescharacteristic
448C4⋊Q8—54no—
449C4⋊Q8—102no—
450#126—108no—
451#125—54no—
452#125—102no—
453#123—108no—
454#123—108no—
455#123—108no—
456C22⋊Q8—108no—
457#121—54no—
458#121—54no—
459#121—54no—
460#121—54no—
461#121—102no—
462#121—102no—
463#121—108no—
464#121—102no—
465#121—102no—
466C4×D4—54no—
467C4×D4—54no—
468C4×D4—54no—
469C4×D4—54no—
470C4×D4—102no—
471C4×D4—102no—
472C4×D4—108no—
473#117—54no—
474#117—102no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—102no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C4⋊C4C22×D511yescharacteristic
492C2×C4⋊C4C22×D514yes—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—51no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C42—51no—
504C2×C42—101no—
505#107—54no—
506#107—54no—
507#107—54no—
508#106—54no—
509#106—54no—
510#106C22×D514yes—
511#106C22×D514yes—
512#106C22×D514yes—
513#106C22×D514yes—
514C4⋊C8—54no—
515#102—54no—
516#102—54no—
517#102—54no—
518#102—54no—
519#102—54no—
520#102—54no—
521C22⋊C8—54no—
522C22⋊C8—54no—
523#97—54no—
524C22×C5—28no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5#54712yes—
528C22×C5C2×AGL(1,ℤ/8)14yes—
529C22×C5C2×AGL(1,ℤ/8)12yes—
530C22×C5#57712yes—
531C22×C5C23×D411yescharacteristic
532C2×D5—22no—
533C2×D5—22no—
534C2×D5—22no—
535C2×D5—44no—
536C2×D5—42no—
537C2×D5—42no—
538C2×D5—42no—
539C2×D5—42no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—84no—
543C2×D5—84no—
544C4×C5—22no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5—42no—
549C4×C5#54712yes—
550C4×C5C22×#4111yescharacteristic
551C4×C5C2×2−1+411yescharacteristic
552Dic5—22no—
553Dic5—22no—
554Dic5—22no—
555Dic5—42no—
556Dic5—42no—
557C24—51no—
558C24—101no—
559C24—101no—
560C24D4×D511yescharacteristic
561#41—2032no—
562C2×Q8—104no—
563C2×Q8—204no—
564C2×D4—54no—
565C2×D4—52no—
566C2×D4—52no—
567C2×D4—104no—
568C2×D4—104no—
569C2×D4—104no—
570C2×D4—104no—
571C2×D4—104no—
572C2×D4—102no—
573C2×D4—102no—
574C2×D4—101no—
575C2×D4—101no—
576C2×D4—102no—
577C2×D4—102no—
578C2×D4—204no—
579C2×D4—204no—
580C2×D4—204no—
581C2×D4—402no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—44no—
591C22×C4—51no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—52no—
595C22×C4—52no—
596C22×C4—82no—
597C22×C4—104no—
598C22×C4—104no—
599C22×C4—104no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—204no—
605C22×C4—204no—
606C22×C4—402no—
607C22×C4D4×D512yes—
608C22×C4D4×D511yescharacteristic
609C22×C4C23×D512yes—
610C22×C4C23×D511yescharacteristic
611D8—108no—
612M16—108no—
613C2×C8—22no—
614C2×C8—28no—
615C2×C8—52no—
616C2×C8—52no—
617C2×C8—102no—
618C2×C8—102no—
619C2×C8#70914yescomplemented
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—54no—
629C4⋊C4—52no—
630C4⋊C4—52no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—101no—
636C4⋊C4—101no—
637C4⋊C4C23×D512yes—
638C4⋊C4C23×D512yes—
639C4⋊C4C23×D512yes—
640C4⋊C4C23×D512yes—
641C22⋊C4—54no—
642C22⋊C4—54no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C22⋊C4—104no—
650C42—52no—
651C42—52no—
652C42—104no—
653C2×C5—24no—
654C2×C5#334514yescomplemented
655C2×C5C2×#54711yescharacteristic
656C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
657C2×C5C2×#57711yescharacteristic
658D5—42no—
659D5—82no—
660D5—82no—
661C23—22no—
662C23—22no—
663C23—52no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—202no—
670C23—202no—
671C23—202no—
672C23—202no—
673C23—202no—
674C23—202no—
675C23#406014yes—
676C23C2×D4×D512yes—
677C23C2×D4×D511yescharacteristic
678Q8—208no—
679D4—108no—
680D4—102no—
681D4—102no—
682D4—102no—
683D4—102no—
684D4—208no—
685D4—208no—
686D4—208no—
687D4—202no—
688D4—202no—
689D4—404no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—52no—
706C2×C4—84no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—104no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—208no—
716C2×C4—208no—
717C2×C4—202no—
718C2×C4—202no—
719C2×C4—404no—
720C2×C4C2×#70912yes—
721C2×C4C2×D4×D512yes—
722C2×C4C2×D4×D511yescharacteristic
723C2×C4#414712yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—102no—
727C8—102no—
728C8C2×#70914yescomplemented
729C5C2×#334511yescharacteristic, complemented, Sylow
730C22—22no—
731C22—28no—
732C22—22no—
733C22—102no—
734C22—102no—
735C22—102no—
736C22—204no—
737C22—202no—
738C22—202no—
739C22—202no—
740C22—202no—
741C22—202no—
742C22—202no—
743C22—404no—
744C22—404no—
745C22#6584112yes—
746C22C2×#406014yes—
747C22C2×#406012yes—
748C22#6609612yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—102no—
756C4—102no—
757C4—102no—
758C4—202no—
759C4—202no—
760C4#6584112yes—
761C4C22×#70911yescharacteristic
762C4C2×#414711yescharacteristic
763C2—24no—
764C2—202no—
765C2—402no—
766C2—402no—
767C2#1061085814yesdirect product factor
768C2C2×#6584111yescharacteristic
769C2C22×#406011yescharacteristic
770C2C2×#6609611yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC22×C5×#106C2
socleC23×C5C22×D4
hypercenterC22×#106D5
hypocenterC5C2×#3345
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#65848C2semidirect
2. C2×#65841C2semidirect
3. C22×C5×#106C2semidirect
4. C2×#65404C2semidirect
5. C2×#65400C2semidirect
6. C2×#65257C2semidirect
7. C2×#65256C2semidirect
8. C2×#65160C2semidirect
9. C2×#65159C2semidirect
10. #10610858C2direct (N × H)
11. C2×#65152C2semidirect
12. C2×#65155C2semidirect
13. C2×#65154C2semidirect
14. C2×#65150C2semidirect
15. C2×#65145C2semidirect
16. C2×#65158C2semidirect
30. #65848C22semidirect
34. #65841C22semidirect
49. C2×C5×#106C22semidirect
51. #65404C22semidirect
54. #65400C22semidirect
59. #65257C22semidirect
60. #65256C22semidirect
69. #65160C22semidirect
70. #65159C22semidirect
71. #65158C22semidirect
72. #65155C22semidirect
73. #65154C22semidirect
74. #65152C22semidirect
75. #65150C22semidirect
76. #65145C22semidirect
196. C22×#106D5semidirect
253. C2×C5×C8#41semidirect
342. C2×#106C2×D5semidirect
418. C5×C8C2×#41semidirect
619. C2×C8#709semidirect
654. C2×C5#3345semidirect
728. C8C2×#709semidirect
729. C5C2×#3345semidirect
767. C2#10610858direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658482
C2×#658412
C22×C5×#1062
C2×#654042
C2×#654002
C2×#652572
C2×#652562
C2×#651602
C2×#651592
#106108582
C2×#651522
C2×#651552
C2×#651542
C2×#651502
C2×#651452
C2×#651582
C2×#33455