Finite Group Databasebeta

← C2×#10606817 #12269758

Subgroups — C2×#10606817 #12269758

Order 1280.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#387C211yesmaximal, characteristic, complemented
2C2×#65283C211yesmaximal, characteristic, complemented
3C2×#65280C211yesmaximal, characteristic
4C2×#65279C211yesmaximal, characteristic, complemented
5C2×#65266C211yesmaximal, characteristic, complemented
6C2×#65229C211yesmaximal, characteristic, complemented
7C2×C4×#685C211yesmaximal, characteristic, complemented
8#10606817C2116yesmaximal, direct product factor
9C2×#64964C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic
11C2×#64954C211yesmaximal, characteristic
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×#64953C211yesmaximal, characteristic, complemented
14C2×C5⋊#401C211yesmaximal, characteristic, complemented
15C2×#64941C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C5×#387C2218yescomplemented
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65283C2218yescomplemented
54#65280C2218yes—
55#65279C2218yescomplemented
56#65266C2218yescomplemented
57#65229C2218yescomplemented
58C4×#685C2218yescomplemented
59#64964C2218yescomplemented
60#64957C2218yescomplemented
61#64955C2218yescomplemented
62#64954C2218yes—
63#64954C2218yes—
64#64953C2218yescomplemented
65C5⋊#401C2218yescomplemented
66#64941C2218yescomplemented
67C2×#2576—51nomaximal, Sylow
68C24×D5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C22×D20—24no—
84C22×D20—24no—
85C22×D20—42no—
86C22×D20C2314yes—
87C22×C4×D5—24no—
88C22×C4×D5—24no—
89C22×C4×D5—24no—
90C22×C4×D5—42no—
91C22×C4×D5—42no—
92C22×C4×D5—42no—
93C22×C4×D5C2314yes—
94C22×C4×D5C2314yes—
95C2×C5×C4⋊C4—24no—
96C2×C5×C4⋊C4—42no—
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C4⋊C4C2314yes—
99C2×C42×C5—42no—
100C2×C42×C5C2314yes—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—24no—
108C2×#685—42no—
109C2×#685—42no—
110C2×#685—42no—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—42no—
122C2×C4⋊Dic5C2314yes—
123C2×#683—24no—
124C2×#683—42no—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×C4×Dic5—24no—
128C2×C4×Dic5—42no—
129C2×C4×Dic5C2314yes—
130C2×C4×Dic5C2314yes—
131C5×#95C2314yes—
132C5×#95C2314yes—
133C5×#95C2314yes—
134C5×#95C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2576—516no—
146C2×#401—51no—
147C2×#397—51no—
148C2×#396—51no—
149C2×#394—51no—
150C2×#388—51no—
151C2×#388—51no—
152C2×#387—51no—
153C2×#387D511yescharacteristic, complemented
154C2×#386—51no—
155C2×#386—51no—
156C2×#385—51no—
157C2×#382—51no—
158C2×#381—51no—
159C2×C4×C22⋊C4—51no—
160C2×C4×C22⋊C4—51no—
161C24×C5C2411yescharacteristic
162C23×D5—22no—
163C23×D5—22no—
164C23×D5—22no—
165C23×D5—22no—
166C23×D5—22no—
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5#4114yes—
175C23×D5#4114yes—
176C23×D5C2412yes—
177C23×D5C2412yes—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
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#4114yes—
198C22×C4×C5#4114yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
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—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
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#4114yes—
224C22×Dic5C2412yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C2×D20—28no—
231C2×D20—28no—
232C2×D20—44no—
233C2×D20—416no—
234C2×C4×D5—28no—
235C2×C4×D5—28no—
236C2×C4×D5—28no—
237C2×C4×D5—44no—
238C2×C4×D5—44no—
239C2×C4×D5—44no—
240C2×C4×D5—416no—
241C2×C4×D5—416no—
242C5×C4⋊C4—28no—
243C5×C4⋊C4—44no—
244C42×C5—44no—
245#685—28no—
246#685—28no—
247#685—28no—
248#685—28no—
249#685—28no—
250#685—28no—
251#685—28no—
252#685—44no—
253#685—44no—
254#685—44no—
255C4⋊Dic5—44no—
256#683—28no—
257#683—44no—
258C4×Dic5—28no—
259C4×Dic5—44no—
260C23×D4—51no—
261C24×C4—51no—
262C24×C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4C2×D511yescharacteristic
267C22×C4⋊C4C2×D511yescharacteristic
268C22×C22⋊C4—51no—
269C22×C22⋊C4—51no—
270C22×C22⋊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⋊C4—51no—
278C22×C42—51no—
279C22×C42—51no—
280C22×C42C2×D511yescharacteristic
281#401—58no—
282#397—58no—
283#396—58no—
284#394—58no—
285#388—58no—
286#388—58no—
287#387—58no—
288#387C2×D518yescomplemented
289#386—58no—
290#386—58no—
291#385—58no—
292#382—58no—
293#381—58no—
294C4×C22⋊C4—58no—
295C4×C22⋊C4—58no—
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×#95C2×D511yescharacteristic
307C2×#95C2×D511yescharacteristic
308C2×#95C2×D511yescharacteristic
309C2×#95C2×D511yescharacteristic
310C23×C5C2×#4112yes—
311C23×C5C2×#4112yes—
312C23×C5C2×#4112yes—
313C23×C5C2×#4112yes—
314C23×C5C2×#4112yes—
315C23×C5H(5,𝔽2)12yes—
316C23×C5H(5,𝔽2)12yes—
317C23×C5C2511yescharacteristic
318C22×D5—28no—
319C22×D5—28no—
320C22×D5—28no—
321C22×D5—28no—
322C22×D5—28no—
323C22×D5—28no—
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—44no—
337C22×D5—44no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5C2×#4114yes—
345C22×D5C2×#4114yes—
346C2×C4×C5—28no—
347C2×C4×C5—28no—
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—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5—44no—
372C2×C4×C5C2×#4114yes—
373C2×C4×C5C2×#4114yes—
374C2×Dic5—28no—
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—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5C2×#4114yes—
398D20—416no—
399C4×D5—416no—
400C4×D5—416no—
401C25—51no—
402C25—51no—
403C22×D4—54no—
404C22×D4—104no—
405C22×D4—104no—
406C22×D4—202no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—54no—
414C23×C4—54no—
415C23×C4—104no—
416C23×C4—104no—
417C23×C4—104no—
418C23×C4—202no—
419C23×C4—202no—
420C23×C4—202no—
421C23×C4C22×D511yescharacteristic
422C23×C4C22×D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C2×C4⋊C4—24no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—54no—
432C2×C4⋊C4—54no—
433C2×C4⋊C4—104no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4—202no—
436C2×C4⋊C4C22×D514yes—
437C2×C4⋊C4C22×D514yes—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—54no—
440C2×C22⋊C4—54no—
441C2×C22⋊C4—54no—
442C2×C22⋊C4—54no—
443C2×C22⋊C4—54no—
444C2×C22⋊C4—54no—
445C2×C22⋊C4—54no—
446C2×C22⋊C4—54no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—104no—
454C2×C22⋊C4—104no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C42—42no—
459C2×C42—54no—
460C2×C42—54no—
461C2×C42—104no—
462C2×C42—202no—
463C2×C42C22×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#95C22×D514yes—
475#95C22×D514yes—
476#95C22×D514yes—
477#95C22×D514yes—
478C22×C5#52914yes—
479C22×C5#52914yes—
480C22×C5#53814yes—
481C22×C5#55114yes—
482C22×C5#55114yes—
483C22×C5#55314yes—
484C22×C5#55314yes—
485C22×C5C22×#4111yescharacteristic
486C22×C5C22×#4111yescharacteristic
487C22×C5C22×#4111yescharacteristic
488C22×C5C22×#4111yescharacteristic
489C22×C5C22×#4111yescharacteristic
490C22×C5C2×H(5,𝔽2)11yescharacteristic
491C22×C5C2×H(5,𝔽2)11yescharacteristic
492C2×D5—24no—
493C2×D5—24no—
494C2×D5—24no—
495C2×D5—24no—
496C2×D5—24no—
497C2×D5—24no—
498C2×D5—416no—
499C2×D5—416no—
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C4×C5—24no—
509C4×C5—24no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514C4×C5—42no—
515Dic5—24no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521C24—54no—
522C24—54no—
523C24—52no—
524C24—52no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24—102no—
537C24C23×D511yescharacteristic
538C2×D4—108no—
539C2×D4—108no—
540C2×D4—204no—
541C2×D4—2016no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
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—22no—
561C22×C4—54no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—108no—
569C22×C4—108no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
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—108no—
588C22×C4—204no—
589C22×C4—204no—
590C22×C4—204no—
591C22×C4—2016no—
592C22×C4—2016no—
593C22×C4#70914yes—
594C22×C4#71314yes—
595C22×C4C23×D512yes—
596C22×C4C23×D512yes—
597C22×C4C23×D512yes—
598C22×C4C23×D512yes—
599C22×C4C23×D512yes—
600C22×C4C23×D512yes—
601C22×C4C23×D512yes—
602C4⋊C4—28no—
603C4⋊C4—44no—
604C4⋊C4—108no—
605C4⋊C4—204no—
606C4⋊C4—204no—
607C22⋊C4—108no—
608C22⋊C4—108no—
609C22⋊C4—108no—
610C22⋊C4—108no—
611C22⋊C4—108no—
612C22⋊C4—108no—
613C22⋊C4—108no—
614C22⋊C4—204no—
615C22⋊C4—204no—
616C22⋊C4—204no—
617C42—44no—
618C42—108no—
619C42—204no—
620C2×C5#257618yescomplemented
621C2×C5C2×#52911yescharacteristic
622C2×C5C2×#52911yescharacteristic
623C2×C5C2×#53811yescharacteristic
624C2×C5C2×#55111yescharacteristic
625C2×C5C2×#55111yescharacteristic
626C2×C5C2×#55311yescharacteristic
627C2×C5C2×#55311yescharacteristic
628D5—44no—
629D5—44no—
630C23—54no—
631C23—54no—
632C23—108no—
633C23—108no—
634C23—108no—
635C23—108no—
636C23—102no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—102no—
645C23—102no—
646C23—108no—
647C23—102no—
648C23—102no—
649C23—108no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23—204no—
658C23C2×#70912yes—
659C23#414412yes—
660C23C2×#71312yes—
661C23D5×#4112yes—
662C23D5×#4112yes—
663C23D5×#4112yes—
664C23#414912yes—
665C23C24×D511yescharacteristic
666D4—2016no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—22no—
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—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—54no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—108no—
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—2016no—
713C2×C4—2016no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4—204no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4C2×#70914yes—
720C2×C4C2×#71314yes—
721C5C2×#257611yescharacteristic, complemented, Sylow
722C22—104no—
723C22—104no—
724C22—104no—
725C22—104no—
726C22—104no—
727C22—104no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—202no—
734C22—202no—
735C22—202no—
736C22—2016no—
737C22—2016no—
738C22#6586414yes—
739C22#6587414yes—
740C22#6591414yes—
741C22#6597814yes—
742C22#6599314yes—
743C22#6602514yes—
744C22#6603914yes—
745C22C22×#70911yescharacteristic
746C22C2×#414411yescharacteristic
747C22C22×#71311yescharacteristic
748C22C2×D5×#4111yescharacteristic
749C22C2×D5×#4111yescharacteristic
750C22C2×D5×#4111yescharacteristic
751C22C2×#414911yescharacteristic
752C4—24no—
753C4—24no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—104no—
760C4—202no—
761C4—202no—
762C4—202no—
763C4—202no—
764C4—202no—
765C2—204no—
766C2—204no—
767C2#1060681718yesdirect product factor
768C2C2×#6586411yescharacteristic
769C2C2×#6587411yescharacteristic
770C2C2×#6591411yescharacteristic
771C2C2×#6597811yescharacteristic
772C2C2×#6599311yescharacteristic
773C2C2×#6602511yescharacteristic
774C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2576
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C2×C5×#387C2semidirect
2. C2×#65283C2semidirect
4. C2×#65279C2semidirect
5. C2×#65266C2semidirect
6. C2×#65229C2semidirect
7. C2×C4×#685C2semidirect
8. #10606817C2direct (N × H)
9. C2×#64964C2semidirect
12. C2×#64957C2semidirect
13. C2×#64953C2semidirect
14. C2×C5⋊#401C2semidirect
15. C2×#64941C2semidirect
16. C2×#64955C2semidirect
38. C5×#387C22semidirect
53. #65283C22semidirect
55. #65279C22semidirect
56. #65266C22semidirect
57. #65229C22semidirect
58. C4×#685C22semidirect
59. #64964C22semidirect
60. #64957C22semidirect
61. #64955C22semidirect
64. #64953C22semidirect
65. C5⋊#401C22semidirect
66. #64941C22semidirect
153. C2×#387D5semidirect
288. #387C2×D5semidirect
620. C2×C5#2576semidirect
721. C5C2×#2576semidirect
767. C2#10606817direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3872
C2×#652832
C2×#652802
C2×#652792
C2×#652662
C2×#652292
C2×C4×#6852
#106068172
C2×#649642
C2×#649542
C2×#649572
C2×#649532
C2×C5⋊#4012
C2×#649412
C2×#649552
C2×#25765