Finite Group Databasebeta

← C2×#10606003 #12268709

Subgroups — C2×#10606003 #12268709

Order 1280.

2074 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#383C211yesmaximal, characteristic, complemented
2C2×#65229C211yesmaximal, characteristic
3C2×C4×#683C211yesmaximal, characteristic, complemented
4#10606003C2116yesmaximal, direct product factor
5C2×#64964C211yesmaximal, characteristic
6C2×#64965C211yesmaximal, characteristic
7C2×#64947C211yesmaximal, characteristic, complemented
8C2×#64946C211yesmaximal, characteristic, complemented
9C2×#64936C211yesmaximal, characteristic, complemented
10C2×#64959C211yesmaximal, characteristic
11C2×#64959C211yesmaximal, characteristic
12C2×#64958C211yesmaximal, characteristic
13C2×#64958C211yesmaximal, characteristic
14C2×#64943C211yesmaximal, characteristic, complemented
15C2×#64942C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C22×C42×C5C2211yescharacteristic
18C22×#685C2211yescharacteristic
19C22×#685C2211yescharacteristic
20C22×#685C2211yescharacteristic
21C22×#685C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×#683C2211yescharacteristic
29C22×#683C2211yescharacteristic
30C22×#683C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C5×#383C2218yescomplemented
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65229C2218yes—
54C4×#683C2218yescomplemented
55#64965C2218yes—
56#64964C2218yes—
57#64959C2218yes—
58#64959C2218yes—
59#64958C2218yes—
60#64958C2218yes—
61#64947C2218yescomplemented
62#64946C2218yescomplemented
63#64943C2218yescomplemented
64#64942C2218yescomplemented
65#64938C2218yescomplemented
66#64936C2218yescomplemented
67C2×#2525—51nomaximal, Sylow
68C24×D5C2311yescharacteristic
69C23×C4×C5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×Dic5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C2×C42×C5—24no—
84C2×C42×C5C2314yes—
85C2×#685—24no—
86C2×#685—24no—
87C2×#685—24no—
88C2×#685—24no—
89C2×#685—24no—
90C2×#685—42no—
91C2×#685—42no—
92C2×#685C2314yes—
93C2×#685C2314yes—
94C2×#685C2314yes—
95C2×#685C2314yes—
96C2×#685C2314yes—
97C2×#685C2314yes—
98C2×#685C2314yes—
99C2×C4⋊Dic5—24no—
100C2×C4⋊Dic5—24no—
101C2×C4⋊Dic5C2314yes—
102C2×C4⋊Dic5C2314yes—
103C2×#683—24no—
104C2×#683—24no—
105C2×#683—24no—
106C2×#683—24no—
107C2×#683—24no—
108C2×#683—42no—
109C2×#683—42no—
110C2×#683C2314yes—
111C2×#683C2314yes—
112C2×#683C2314yes—
113C2×#683C2314yes—
114C2×#683C2314yes—
115C2×#683C2314yes—
116C2×#683C2314yes—
117C2×C4×Dic5—24no—
118C2×C4×Dic5—24no—
119C2×C4×Dic5—42no—
120C2×C4×Dic5—42no—
121C2×C4×Dic5C2314yes—
122C2×C4×Dic5C2314yes—
123C2×C4×Dic5C2314yes—
124C2×C4×Dic5C2314yes—
125C5×#95C2314yes—
126C5×#95C2314yes—
127C5×#95C2314yes—
128C5×#95C2314yes—
129C5×#95C2314yes—
130C5×#95C2314yes—
131#3963C2314yes—
132#3963C2314yes—
133#3963C2314yes—
134#3963C2314yes—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#2525—516no—
140C2×#400—51no—
141C2×#398—51no—
142C2×#397—51no—
143C2×#396—51no—
144C2×#389—51no—
145C2×#388—51no—
146C2×#388—51no—
147C2×#388—51no—
148C2×#388—51no—
149C2×#388—51no—
150C2×#387—51no—
151C2×#387—51no—
152C2×#383D511yescharacteristic, complemented
153C2×C4×C4⋊C4—51no—
154C2×C4×C4⋊C4—51no—
155C24×C5C2411yescharacteristic
156C23×D5—22no—
157C23×D5—22no—
158C23×D5—22no—
159C23×D5—22no—
160C23×D5—22no—
161C23×D5—22no—
162C23×D5—22no—
163C23×D5C2412yes—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—22no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
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#4114yes—
185C22×C4×C5C2412yes—
186C22×C4×C5C2412yes—
187C22×C4×C5C2412yes—
188C22×C4×C5C2412yes—
189C22×C4×C5C2412yes—
190C22×C4×C5C2412yes—
191C22×C4×C5C2412yes—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5#4114yes—
210C22×Dic5#4114yes—
211C22×Dic5#4114yes—
212C22×Dic5#4114yes—
213C22×Dic5C2412yes—
214C22×Dic5C2412yes—
215C22×Dic5C2412yes—
216C22×Dic5C2412yes—
217C22×Dic5C2412yes—
218C22×Dic5C2412yes—
219C22×Dic5C2412yes—
220C42×C5—28no—
221#685—28no—
222#685—28no—
223#685—28no—
224#685—28no—
225#685—28no—
226#685—44no—
227#685—44no—
228C4⋊Dic5—28no—
229C4⋊Dic5—28no—
230#683—28no—
231#683—28no—
232#683—28no—
233#683—28no—
234#683—28no—
235#683—44no—
236#683—44no—
237C4×Dic5—28no—
238C4×Dic5—28no—
239C4×Dic5—44no—
240C4×Dic5—44no—
241C22×C4⋊C4—51no—
242C22×C4⋊C4—51no—
243C22×C4⋊C4—51no—
244C22×C4⋊C4—51no—
245C22×C4⋊C4—51no—
246C22×C4⋊C4—51no—
247C22×C4⋊C4—51no—
248C22×C4⋊C4—51no—
249C22×C4⋊C4—51no—
250C22×C22⋊C4—51no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—51no—
253C22×C22⋊C4—51no—
254C22×C22⋊C4—51no—
255C22×C22⋊C4—51no—
256C22×C22⋊C4—51no—
257C22×C42—51no—
258C22×C42—51no—
259C22×C42—51no—
260C22×C42—51no—
261C22×C42C2×D511yescharacteristic
262#400—58no—
263#398—58no—
264#397—58no—
265#396—58no—
266#389—58no—
267#388—58no—
268#388—58no—
269#388—58no—
270#388—58no—
271#388—58no—
272#387—58no—
273#387—58no—
274#383C2×D518yescomplemented
275C4×C4⋊C4—58no—
276C4×C4⋊C4—58no—
277C2×#95—51no—
278C2×#95—51no—
279C2×#95—51no—
280C2×#95—51no—
281C2×#95—51no—
282C2×#95—51no—
283C2×#95—51no—
284C2×#95—51no—
285C2×#95C2×D511yescharacteristic
286C2×#95C2×D511yescharacteristic
287C2×#95C2×D511yescharacteristic
288C2×#95C2×D511yescharacteristic
289C2×#95C2×D511yescharacteristic
290C2×#95C2×D511yescharacteristic
291C23×C5C2×#4112yes—
292C23×C5C2×#4112yes—
293C23×C5C2×#4112yes—
294C23×C5C2×#4112yes—
295C23×C5C2×#4112yes—
296C23×C5H(5,𝔽2)12yes—
297C23×C52−1+412yes—
298C23×C5C2511yescharacteristic
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—22no—
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—44no—
307C22×D5—44no—
308C22×D5—44no—
309C22×D5—44no—
310C22×D5—44no—
311C22×D5—44no—
312C22×D5—44no—
313C2×C4×C5—28no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—44no—
335C2×C4×C5—44no—
336C2×C4×C5—44no—
337C2×C4×C5—44no—
338C2×C4×C5—44no—
339C2×C4×C5—44no—
340C2×C4×C5C2×#4114yes—
341C2×Dic5—28no—
342C2×Dic5—28no—
343C2×Dic5—28no—
344C2×Dic5—28no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—44no—
363C2×Dic5—44no—
364C2×Dic5—44no—
365C2×Dic5C2×#4114yes—
366C2×Dic5C2×#4114yes—
367C2×Dic5C2×#4114yes—
368C2×Dic5C2×#4114yes—
369C25—51no—
370C23×C4—51no—
371C23×C4—51no—
372C23×C4—51no—
373C23×C4—51no—
374C23×C4—51no—
375C23×C4—51no—
376C23×C4—51no—
377C23×C4C22×D511yescharacteristic
378C23×C4C22×D511yescharacteristic
379C23×C4C22×D511yescharacteristic
380C23×C4C22×D511yescharacteristic
381C23×C4C22×D511yescharacteristic
382C23×C4C22×D511yescharacteristic
383C23×C4C22×D511yescharacteristic
384C2×C4⋊C4—54no—
385C2×C4⋊C4—54no—
386C2×C4⋊C4—54no—
387C2×C4⋊C4—54no—
388C2×C4⋊C4—54no—
389C2×C4⋊C4—54no—
390C2×C4⋊C4—54no—
391C2×C4⋊C4—54no—
392C2×C4⋊C4—54no—
393C2×C4⋊C4—104no—
394C2×C4⋊C4—104no—
395C2×C4⋊C4—104no—
396C2×C4⋊C4—104no—
397C2×C4⋊C4—104no—
398C2×C4⋊C4—104no—
399C2×C4⋊C4—104no—
400C2×C4⋊C4—202no—
401C2×C4⋊C4—202no—
402C2×C22⋊C4—54no—
403C2×C22⋊C4—54no—
404C2×C22⋊C4—54no—
405C2×C22⋊C4—54no—
406C2×C22⋊C4—54no—
407C2×C22⋊C4—54no—
408C2×C22⋊C4—54no—
409C2×C22⋊C4—104no—
410C2×C22⋊C4—104no—
411C2×C22⋊C4—104no—
412C2×C22⋊C4—104no—
413C2×C22⋊C4—104no—
414C2×C22⋊C4—202no—
415C2×C22⋊C4—202no—
416C2×C42—24no—
417C2×C42—54no—
418C2×C42—54no—
419C2×C42—54no—
420C2×C42—54no—
421C2×C42—104no—
422C2×C42—104no—
423C2×C42—202no—
424C2×C42—202no—
425C2×C42C22×D514yes—
426#95—54no—
427#95—54no—
428#95—54no—
429#95—54no—
430#95—54no—
431#95—54no—
432#95—54no—
433#95—54no—
434#95C22×D514yes—
435#95C22×D514yes—
436#95C22×D514yes—
437#95C22×D514yes—
438#95C22×D514yes—
439#95C22×D514yes—
440C22×C5#52914yes—
441C22×C5#52914yes—
442C22×C5#54214yes—
443C22×C5#55214yes—
444C22×C5#55314yes—
445C22×C5#55314yes—
446C22×C5#55614yes—
447C22×C5C22×#4111yescharacteristic
448C22×C5C22×#4111yescharacteristic
449C22×C5C22×#4111yescharacteristic
450C22×C5C22×#4111yescharacteristic
451C22×C5C22×#4111yescharacteristic
452C22×C5C2×H(5,𝔽2)11yescharacteristic
453C22×C5C2×2−1+411yescharacteristic
454C2×D5—42no—
455C2×D5—42no—
456C2×D5—42no—
457C2×D5—42no—
458C2×D5—42no—
459C2×D5—42no—
460C2×D5—42no—
461C2×D5—88no—
462C4×C5—24no—
463C4×C5—42no—
464C4×C5—42no—
465C4×C5—42no—
466C4×C5—42no—
467C4×C5—42no—
468C4×C5—42no—
469Dic5—24no—
470Dic5—24no—
471Dic5—24no—
472Dic5—24no—
473Dic5—42no—
474Dic5—42no—
475Dic5—42no—
476C24—52no—
477C24—102no—
478C24—102no—
479C24—102no—
480C24—102no—
481C24—102no—
482C24—102no—
483C24—102no—
484C24C23×D511yescharacteristic
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—54no—
506C22×C4—54no—
507C22×C4—54no—
508C22×C4—54no—
509C22×C4—52no—
510C22×C4—52no—
511C22×C4—52no—
512C22×C4—52no—
513C22×C4—52no—
514C22×C4—52no—
515C22×C4—52no—
516C22×C4—102no—
517C22×C4—102no—
518C22×C4—102no—
519C22×C4—102no—
520C22×C4—102no—
521C22×C4—102no—
522C22×C4—102no—
523C22×C4—102no—
524C22×C4—102no—
525C22×C4—102no—
526C22×C4—102no—
527C22×C4—102no—
528C22×C4—102no—
529C22×C4—102no—
530C22×C4—102no—
531C22×C4—102no—
532C22×C4—102no—
533C22×C4#70914yes—
534C22×C4C23×D512yes—
535C22×C4C23×D512yes—
536C22×C4C23×D512yes—
537C22×C4C23×D512yes—
538C22×C4C23×D512yes—
539C22×C4C23×D512yes—
540C22×C4C23×D512yes—
541C4⋊C4—108no—
542C4⋊C4—108no—
543C4⋊C4—108no—
544C4⋊C4—108no—
545C4⋊C4—108no—
546C4⋊C4—108no—
547C4⋊C4—108no—
548C4⋊C4—204no—
549C4⋊C4—204no—
550C22⋊C4—108no—
551C22⋊C4—108no—
552C22⋊C4—108no—
553C22⋊C4—108no—
554C22⋊C4—108no—
555C22⋊C4—204no—
556C22⋊C4—204no—
557C42—28no—
558C42—108no—
559C42—108no—
560C42—204no—
561C42—204no—
562C2×C5#252518yescomplemented
563C2×C5C2×#52911yescharacteristic
564C2×C5C2×#52911yescharacteristic
565C2×C5C2×#54211yescharacteristic
566C2×C5C2×#55211yescharacteristic
567C2×C5C2×#55311yescharacteristic
568C2×C5C2×#55311yescharacteristic
569C2×C5C2×#55611yescharacteristic
570D5—82no—
571C23—102no—
572C23—102no—
573C23—102no—
574C23—102no—
575C23—102no—
576C23—102no—
577C23—102no—
578C23—204no—
579C23—204no—
580C23—204no—
581C23—204no—
582C23—204no—
583C23—204no—
584C23—204no—
585C23C2×#70912yes—
586C23D5×#4112yes—
587C23D5×#4112yes—
588C23D5×#4112yes—
589C23D5×#4112yes—
590C23#414912yes—
591C23#415012yes—
592C23C24×D511yescharacteristic
593C2×C4—28no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—54no—
621C2×C4—54no—
622C2×C4—54no—
623C2×C4—54no—
624C2×C4—108no—
625C2×C4—108no—
626C2×C4—102no—
627C2×C4—102no—
628C2×C4—102no—
629C2×C4—102no—
630C2×C4—102no—
631C2×C4—102no—
632C2×C4—102no—
633C2×C4—102no—
634C2×C4—108no—
635C2×C4—108no—
636C2×C4—102no—
637C2×C4—102no—
638C2×C4—102no—
639C2×C4—102no—
640C2×C4—102no—
641C2×C4—102no—
642C2×C4—102no—
643C2×C4—102no—
644C2×C4—102no—
645C2×C4—204no—
646C2×C4—204no—
647C2×C4—204no—
648C2×C4C2×#70914yes—
649C5C2×#252511yescharacteristic, complemented, Sylow
650C22—202no—
651C22—202no—
652C22—202no—
653C22—202no—
654C22—202no—
655C22—202no—
656C22—202no—
657C22—408no—
658C22#6586214yes—
659C22#6586414yes—
660C22#6586514yes—
661C22#6603614yes—
662C22#6604014yes—
663C22#6604314yes—
664C22#6604414yes—
665C22C22×#70911yescharacteristic
666C22C2×D5×#4111yescharacteristic
667C22C2×D5×#4111yescharacteristic
668C22C2×D5×#4111yescharacteristic
669C22C2×D5×#4111yescharacteristic
670C22C2×#414911yescharacteristic
671C22C2×#415011yescharacteristic
672C4—24no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—104no—
680C4—104no—
681C4—104no—
682C4—104no—
683C4—202no—
684C4—202no—
685C4—202no—
686C2—402no—
687C2#1060600318yesdirect product factor
688C2C2×#6586511yescharacteristic
689C2C2×#6586211yescharacteristic
690C2C2×#6586411yescharacteristic
691C2C2×#6604011yescharacteristic
692C2C2×#6604411yescharacteristic
693C2C2×#6604311yescharacteristic
694C2C2×#6603611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#383C2
socleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#383D5
hypocenterC5C2×#2525
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. C2×C5×#383C2semidirect
3. C2×C4×#683C2semidirect
4. #10606003C2direct (N × H)
7. C2×#64947C2semidirect
8. C2×#64946C2semidirect
9. C2×#64936C2semidirect
14. C2×#64943C2semidirect
15. C2×#64942C2semidirect
16. C2×#64938C2semidirect
38. C5×#383C22semidirect
54. C4×#683C22semidirect
61. #64947C22semidirect
62. #64946C22semidirect
63. #64943C22semidirect
64. #64942C22semidirect
65. #64938C22semidirect
66. #64936C22semidirect
152. C2×#383D5semidirect
274. #383C2×D5semidirect
562. C2×C5#2525semidirect
649. C5C2×#2525semidirect
687. C2#10606003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3832
C2×#652292
C2×C4×#6832
#106060032
C2×#649642
C2×#649652
C2×#649472
C2×#649462
C2×#649362
C2×#649592
C2×#649582
C2×#649432
C2×#649422
C2×#649382
C2×#25255