Finite Group Databasebeta

← C2×#10606517 #12265749

Subgroups — C2×#10606517 #12265749

Order 1280.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#386C211yesmaximal, characteristic
2C2×#65509C211yesmaximal, characteristic
3C2×#65509C211yesmaximal, characteristic
4C2×#65499C211yesmaximal, characteristic, complemented
5C22×#3963C211yesmaximal, characteristic, complemented
6C2×#65242C211yesmaximal, characteristic, complemented
7C2×#65241C211yesmaximal, characteristic, complemented
8C2×#65241C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×#65239C211yesmaximal, characteristic, complemented
11C2×#65235C211yesmaximal, characteristic, complemented
12#10606517C2116yesmaximal, direct product factor
13C2×C5⋊#401C211yesmaximal, characteristic, complemented
14C2×#64948C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64947C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C5×#386C2218yes—
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39#65509C2218yes—
40#65509C2218yes—
41#65499C2218yescomplemented
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2218yescomplemented
57#65242C2218yescomplemented
58#65241C2218yescomplemented
59#65241C2218yescomplemented
60#65239C2218yescomplemented
61#65237C2218yescomplemented
62#65235C2218yescomplemented
63C5⋊#401C2218yescomplemented
64#64949C2218yescomplemented
65#64948C2218yescomplemented
66#64947C2218yescomplemented
67C2×#2643—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C25×C5C2311yescharacteristic
70C22×C5×D4—24no—
71C22×C5×D4—24no—
72C22×C5×D4—24no—
73C22×C5×D4C2314yes—
74C23×C4×C5—24no—
75C23×C4×C5—42no—
76C23×C4×C5—42no—
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2314yes—
83C23×Dic5—24no—
84C23×Dic5—24no—
85C23×Dic5—42no—
86C23×Dic5—42no—
87C23×Dic5—42no—
88C23×Dic5—42no—
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2314yes—
98C23×Dic5C2314yes—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4—42no—
101C2×C5×C22⋊C4—42no—
102C2×C5×C22⋊C4C2314yes—
103C2×C5×C22⋊C4C2314yes—
104C2×C5×C22⋊C4C2314yes—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5—42no—
108C2×C22⋊Dic5—42no—
109C2×C22⋊Dic5—42no—
110C2×C22⋊Dic5—42no—
111C2×C22⋊Dic5C2314yes—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C2×C4⋊Dic5—42no—
118C2×C4⋊Dic5—42no—
119C2×C4⋊Dic5C2314yes—
120C2×C4⋊Dic5C2314yes—
121C2×#683—42no—
122C2×#683—42no—
123C2×#683—42no—
124C2×#683—42no—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C5×#95C2314yes—
130C5×#95C2314yes—
131#3963C2314yes—
132#3963C2314yes—
133#3963C2314yes—
134#3963C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2643—516no—
146C2×#401—51no—
147C2×#400—51no—
148C2×#400—51no—
149C2×#400—51no—
150C2×#397—51no—
151C2×#397—51no—
152C2×#397—51no—
153C2×#396—51no—
154C2×#386—51no—
155C2×#386—51no—
156C2×#386D511yescharacteristic
157C2×#385—51no—
158C2×#385—51no—
159C2×#385—51no—
160C22×#95—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5—22no—
168C24×C5—22no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5#4114yes—
173C24×C5#4114yes—
174C24×C5#4114yes—
175C24×C5C2412yes—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C2×C5×D4—28no—
179C2×C5×D4—28no—
180C2×C5×D4—28no—
181C2×C5×D4—416no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—28no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—44no—
199C22×C4×C5—44no—
200C22×C4×C5—416no—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—28no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—28no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—44no—
233C22×Dic5—44no—
234C22×Dic5—44no—
235C22×Dic5—44no—
236C22×Dic5—416no—
237C22×Dic5—416no—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C5×C22⋊C4—28no—
247C5×C22⋊C4—44no—
248C5×C22⋊C4—44no—
249C22⋊Dic5—28no—
250C22⋊Dic5—28no—
251C22⋊Dic5—44no—
252C22⋊Dic5—44no—
253C22⋊Dic5—44no—
254C22⋊Dic5—44no—
255C4⋊Dic5—44no—
256C4⋊Dic5—44no—
257#683—44no—
258#683—44no—
259#683—44no—
260#683—44no—
261C23×D4C2×D511yescharacteristic
262C24×C4—51no—
263C24×C4—51no—
264C24×C4C2×D511yescharacteristic
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4—51no—
268C22×C4⋊C4—51no—
269C22×C4⋊C4—51no—
270C22×C4⋊C4—51no—
271C22×C22⋊C4—51no—
272C22×C22⋊C4—51no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4—51no—
275C22×C22⋊C4—51no—
276C22×C22⋊C4—51no—
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C22⋊C4C2×D511yescharacteristic
279C22×C22⋊C4C2×D511yescharacteristic
280#401—58no—
281#400—58no—
282#400—58no—
283#400—58no—
284#397—58no—
285#397—58no—
286#397—58no—
287#396—58no—
288#386—58no—
289#386—58no—
290#386C2×D518yes—
291#385—58no—
292#385—58no—
293#385—58no—
294C2×#95—58no—
295C2×#95—51no—
296C2×#95—51no—
297C2×#95—51no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95—51no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95C2×D511yescharacteristic
310C2×#95C2×D511yescharacteristic
311C23×C5—28no—
312C23×C5—28no—
313C23×C5—28no—
314C23×C5—28no—
315C23×C5—28no—
316C23×C5—28no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—44no—
329C23×C5—44no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5#126116yes—
336C23×C5C2×#4114yes—
337C23×C5C2×#4112yes—
338C23×C5C2×#4114yes—
339C23×C5C2×#4114yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5H(5,𝔽2)12yes—
343C23×C5H(5,𝔽2)12yes—
344C23×C5H(5,𝔽2)12yes—
345C23×C52−1+412yes—
346C23×C5C2511yescharacteristic
347C5×D4—416no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—416no—
364C2×C4×C5—44no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—416no—
394C2×Dic5—416no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5—44no—
399C2×Dic5—44no—
400C2×Dic5—44no—
401C2×Dic5—44no—
402C2×Dic5—44no—
403C25C22×D511yescharacteristic
404C25C22×D511yescharacteristic
405C22×D4—24no—
406C22×D4—24no—
407C22×D4—24no—
408C22×D4C22×D514yes—
409C23×C4—24no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—54no—
421C23×C4—54no—
422C23×C4—104no—
423C23×C4—104no—
424C23×C4—202no—
425C23×C4—202no—
426C23×C4—202no—
427C23×C4—202no—
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D514yes—
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—202no—
441C2×C4⋊C4—202no—
442C2×C4⋊C4—202no—
443C2×C4⋊C4—202no—
444C2×C4⋊C4—202no—
445C2×C4⋊C4—202no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—54no—
450C2×C22⋊C4—54no—
451C2×C22⋊C4—54no—
452C2×C22⋊C4—54no—
453C2×C22⋊C4—54no—
454C2×C22⋊C4—54no—
455C2×C22⋊C4—104no—
456C2×C22⋊C4—104no—
457C2×C22⋊C4—202no—
458C2×C22⋊C4—202no—
459C2×C22⋊C4—202no—
460C2×C22⋊C4—202no—
461C2×C22⋊C4C22×D514yes—
462C2×C22⋊C4C22×D514yes—
463C2×C22⋊C4C22×D514yes—
464#95—54no—
465#95—54no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95—54no—
473#95—54no—
474#95—54no—
475#95—54no—
476#95—54no—
477#95—54no—
478#95C22×D514yes—
479#95C22×D514yes—
480C22×C5—232no—
481C22×C5—24no—
482C22×C5—24no—
483C22×C5—24no—
484C22×C5—24no—
485C22×C5—24no—
486C22×C5—24no—
487C22×C5—42no—
488C22×C5—42no—
489C22×C5—42no—
490C22×C5—42no—
491C22×C5—42no—
492C22×C5—42no—
493C22×C5—42no—
494C22×C5—88no—
495C22×C5C2×#12618yes—
496C22×C5C2×#12614yes—
497C22×C5#53814yes—
498C22×C5#53814yes—
499C22×C5#53814yes—
500C22×C5#53914yes—
501C22×C5#53914yes—
502C22×C5#53914yes—
503C22×C5C22×#4111yescharacteristic
504C22×C5C22×#4111yescharacteristic
505C22×C5C22×#4111yescharacteristic
506C22×C5C2×H(5,𝔽2)11yescharacteristic
507C22×C5C2×H(5,𝔽2)11yescharacteristic
508C22×C5C2×H(5,𝔽2)11yescharacteristic
509C22×C5C2×2−1+411yescharacteristic
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514C4×C5—42no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521Dic5—42no—
522Dic5—42no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24#70914yes—
535C24#71114yes—
536C24#71114yes—
537C24C23×D512yes—
538C24C23×D512yes—
539C24C23×D511yescharacteristic
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—28no—
543C2×D4—416no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—416no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—108no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—108no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—204no—
598C22×C4—204no—
599C22×C4—204no—
600C22×C4—204no—
601C22×C4—2016no—
602C22×C4—2016no—
603C22×C4C23×D512yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C4⋊C4—204no—
609C4⋊C4—204no—
610C4⋊C4—204no—
611C4⋊C4—204no—
612C4⋊C4—204no—
613C4⋊C4—204no—
614C22⋊C4—28no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—108no—
618C22⋊C4—108no—
619C22⋊C4—204no—
620C22⋊C4—204no—
621C22⋊C4—204no—
622C22⋊C4—204no—
623C2×C5—28no—
624C2×C5—82no—
625C2×C5#264318yescomplemented
626C2×C5C22×#12611yescharacteristic
627C2×C5C2×#53811yescharacteristic
628C2×C5C2×#53811yescharacteristic
629C2×C5C2×#53811yescharacteristic
630C2×C5C2×#53911yescharacteristic
631C2×C5C2×#53911yescharacteristic
632C2×C5C2×#53911yescharacteristic
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23#4025116yes—
658C23C2×#70914yes—
659C23C2×#70912yes—
660C23C2×#71114yes—
661C23C2×#71114yes—
662C23C2×#71112yes—
663C23C2×#71112yes—
664C23#414412yes—
665C23#414412yes—
666C23#414912yes—
667C23#415012yes—
668C23C24×D511yescharacteristic
669D4—416no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—2016no—
716C2×C4—2016no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4—204no—
721C2×C4—204no—
722C2×C4—204no—
723C2×C4—204no—
724C2×C4—204no—
725C5C2×#264311yescharacteristic, complemented, Sylow
726C22—24no—
727C22—24no—
728C22—24no—
729C22—232no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—88no—
741C22C2×#402518yes—
742C22C2×#402514yes—
743C22#6589414yes—
744C22#6589814yes—
745C22#6592714yes—
746C22#6593614yes—
747C22#6595114yes—
748C22#6599914yes—
749C22C22×#70911yescharacteristic
750C22C22×#71111yescharacteristic
751C22C22×#71111yescharacteristic
752C22C2×#414411yescharacteristic
753C22C2×#414411yescharacteristic
754C22C2×#414911yescharacteristic
755C22C2×#415011yescharacteristic
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—202no—
762C4—202no—
763C4—202no—
764C4—202no—
765C4—202no—
766C4—202no—
767C4—202no—
768C4—202no—
769C2—28no—
770C2—82no—
771C2#1060651718yesdirect product factor
772C2C22×#402511yescharacteristic
773C2C2×#6589811yescharacteristic
774C2C2×#6589411yescharacteristic
775C2C2×#6592711yescharacteristic
776C2C2×#6593611yescharacteristic
777C2C2×#6595111yescharacteristic
778C2C2×#6599911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC2×#386D5
hypocenterC5C2×#2643
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×#65499C2semidirect
5. C22×#3963C2semidirect
6. C2×#65242C2semidirect
7. C2×#65241C2semidirect
8. C2×#65241C2semidirect
9. C2×#65237C2semidirect
10. C2×#65239C2semidirect
11. C2×#65235C2semidirect
12. #10606517C2direct (N × H)
13. C2×C5⋊#401C2semidirect
14. C2×#64948C2semidirect
15. C2×#64949C2semidirect
16. C2×#64947C2semidirect
41. #65499C22semidirect
56. C2×#3963C22semidirect
57. #65242C22semidirect
58. #65241C22semidirect
59. #65241C22semidirect
60. #65239C22semidirect
61. #65237C22semidirect
62. #65235C22semidirect
63. C5⋊#401C22semidirect
64. #64949C22semidirect
65. #64948C22semidirect
66. #64947C22semidirect
625. C2×C5#2643semidirect
725. C5C2×#2643semidirect
771. C2#10606517direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3862
C2×#655092
C2×#654992
C22×#39632
C2×#652422
C2×#652412
C2×#652372
C2×#652392
C2×#652352
#106065172
C2×C5⋊#4012
C2×#649482
C2×#649492
C2×#649472
C2×#26435