Finite Group Databasebeta

← C2×#10609513 #12268901

Subgroups — C2×#10609513 #12268901

Order 1280.

2442 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×C5×#398C211yesmaximal, characteristic, complemented
2C2×#65282C211yesmaximal, characteristic, complemented
3C2×#65276C211yesmaximal, characteristic, complemented
4C2×#65277C211yesmaximal, characteristic
5C2×#65279C211yesmaximal, characteristic, complemented
6C2×#65279C211yesmaximal, characteristic, complemented
7C2×#65279C211yesmaximal, characteristic, complemented
8C2×#65279C211yesmaximal, characteristic, complemented
9C2×#65267C211yesmaximal, characteristic, complemented
10#10609513C2116yesmaximal, direct product factor
11C2×#64954C211yesmaximal, characteristic
12C2×#64963C211yesmaximal, characteristic, complemented
13C2×#64961C211yesmaximal, characteristic
14C2×#64942C211yesmaximal, characteristic, complemented
15C2×#64955C211yesmaximal, characteristic, complemented
16C2×#64937C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C5×#398C2218yescomplemented
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65282C2218yescomplemented
54#65279C2218yescomplemented
55#65279C2218yescomplemented
56#65279C2218yescomplemented
57#65279C2218yescomplemented
58#65277C2218yes—
59#65276C2218yescomplemented
60#65267C2218yescomplemented
61#64963C2218yescomplemented
62#64961C2218yes—
63#64955C2218yescomplemented
64#64954C2218yes—
65#64942C2218yescomplemented
66#64937C2218yescomplemented
67C2×#2531—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—42no—
90C22×C4×D5C2314yes—
91C2×C5×C4⋊C4—42no—
92C2×C5×C4⋊C4—42no—
93C2×C5×C4⋊C4—42no—
94C2×C5×C4⋊C4—42no—
95C2×C5×C4⋊C4C2314yes—
96C2×C5×C4⋊C4C2314yes—
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C4⋊C4C2314yes—
99C2×#685—24no—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—42no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685—42no—
109C2×#685—42no—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—24no—
122C2×C4⋊Dic5C2314yes—
123C2×#683—24no—
124C2×#683C2314yes—
125C2×C4×Dic5—24no—
126C2×C4×Dic5—24no—
127C2×C4×Dic5—24no—
128C2×C4×Dic5—42no—
129C2×C4×Dic5C2314yes—
130C2×C4×Dic5C2314yes—
131C2×C4×Dic5C2314yes—
132C2×C4×Dic5C2314yes—
133C5×#95C2314yes—
134C5×#95C2314yes—
135C5×#95C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2531—516no—
146C2×#398D511yescharacteristic, complemented
147C2×#397—51no—
148C2×#397—51no—
149C2×#394—51no—
150C2×#390—51no—
151C2×#388—51no—
152C2×#388—51no—
153C2×#388—51no—
154C2×#388—51no—
155C2×#387—51no—
156C2×#387—51no—
157C2×#386—51no—
158C2×#380—51no—
159C2×C4×C22⋊C4—51no—
160C2×#376—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—22no—
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#4114yes—
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—44no—
237C2×C4×D5—416no—
238C5×C4⋊C4—44no—
239C5×C4⋊C4—44no—
240C5×C4⋊C4—44no—
241C5×C4⋊C4—44no—
242#685—28no—
243#685—28no—
244#685—28no—
245#685—28no—
246#685—28no—
247#685—28no—
248#685—44no—
249#685—44no—
250#685—44no—
251#685—44no—
252#685—44no—
253C4⋊Dic5—28no—
254#683—28no—
255C4×Dic5—28no—
256C4×Dic5—28no—
257C4×Dic5—28no—
258C4×Dic5—44no—
259C23×D4—51no—
260C24×C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4C2×D511yescharacteristic
264C22×C4⋊C4C2×D511yescharacteristic
265C22×C4⋊C4C2×D511yescharacteristic
266C22×C4⋊C4C2×D511yescharacteristic
267C22×C22⋊C4—51no—
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×C42—51no—
281C22×C42—51no—
282#398C2×D518yescomplemented
283#397—58no—
284#397—58no—
285#394—58no—
286#390—58no—
287#388—58no—
288#388—58no—
289#388—58no—
290#388—58no—
291#387—58no—
292#387—58no—
293#386—58no—
294#380—58no—
295C4×C22⋊C4—58no—
296#376—58no—
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
309C23×C5C2×#4112yes—
310C23×C5C2×#4112yes—
311C23×C5C2×#4112yes—
312C23×C5C2×#4112yes—
313C23×C5C2×#4112yes—
314C23×C5H(5,𝔽2)12yes—
315C23×C5H(5,𝔽2)12yes—
316C23×C5C2511yescharacteristic
317C22×D5—28no—
318C22×D5—28no—
319C22×D5—28no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—22no—
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—44no—
334C22×D5—44no—
335C22×D5—44no—
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—
345C2×C4×C5—28no—
346C2×C4×C5—28no—
347C2×C4×C5—22no—
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—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5C2×#4114yes—
372C2×C4×C5C2×#4114yes—
373C2×Dic5—28no—
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—44no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5C2×#4114yes—
396C2×Dic5C2×#4114yes—
397D20—416no—
398C4×D5—416no—
399C25—51no—
400C25—51no—
401C22×D4—54no—
402C22×D4—104no—
403C22×D4—104no—
404C22×D4—202no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—54no—
412C23×C4—104no—
413C23×C4—104no—
414C23×C4—202no—
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4C22×D514yes—
431C2×C4⋊C4C22×D514yes—
432C2×C4⋊C4C22×D514yes—
433C2×C4⋊C4C22×D514yes—
434C2×C22⋊C4—54no—
435C2×C22⋊C4—54no—
436C2×C22⋊C4—54no—
437C2×C22⋊C4—54no—
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—104no—
446C2×C22⋊C4—104no—
447C2×C22⋊C4—104no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C42—54no—
457C2×C42—54no—
458C2×C42—54no—
459C2×C42—54no—
460C2×C42—104no—
461C2×C42—104no—
462C2×C42—104no—
463C2×C42—202no—
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#95C22×D514yes—
474#95C22×D514yes—
475#95C22×D514yes—
476C22×C5#52914yes—
477C22×C5#52914yes—
478C22×C5#54014yes—
479C22×C5#55114yes—
480C22×C5#55114yes—
481C22×C5#55314yes—
482C22×C5#55514yes—
483C22×C5C22×#4111yescharacteristic
484C22×C5C22×#4111yescharacteristic
485C22×C5C22×#4111yescharacteristic
486C22×C5C22×#4111yescharacteristic
487C22×C5C22×#4111yescharacteristic
488C22×C5C2×H(5,𝔽2)11yescharacteristic
489C22×C5C2×H(5,𝔽2)11yescharacteristic
490C2×D5—24no—
491C2×D5—24no—
492C2×D5—24no—
493C2×D5—42no—
494C2×D5—42no—
495C2×D5—42no—
496C2×D5—42no—
497C2×D5—416no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—88no—
506C4×C5—24no—
507C4×C5—24no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513Dic5—24no—
514Dic5—24no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519C24—54no—
520C24—52no—
521C24—52no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24C23×D511yescharacteristic
536C2×D4—108no—
537C2×D4—108no—
538C2×D4—204no—
539C2×D4—2016no—
540C22×C4—22no—
541C22×C4—22no—
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—54no—
560C22×C4—54no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—108no—
568C22×C4—102no—
569C22×C4—102no—
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—108no—
585C22×C4—204no—
586C22×C4—2016no—
587C22×C4#71314yes—
588C22×C4#71314yes—
589C22×C4C23×D512yes—
590C22×C4C23×D512yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—108no—
601C4⋊C4—108no—
602C22⋊C4—108no—
603C22⋊C4—108no—
604C22⋊C4—108no—
605C22⋊C4—108no—
606C22⋊C4—108no—
607C22⋊C4—108no—
608C22⋊C4—204no—
609C22⋊C4—204no—
610C22⋊C4—204no—
611C22⋊C4—204no—
612C22⋊C4—204no—
613C42—108no—
614C42—108no—
615C42—108no—
616C42—204no—
617C2×C5#253118yescomplemented
618C2×C5C2×#52911yescharacteristic
619C2×C5C2×#52911yescharacteristic
620C2×C5C2×#54011yescharacteristic
621C2×C5C2×#55111yescharacteristic
622C2×C5C2×#55111yescharacteristic
623C2×C5C2×#55311yescharacteristic
624C2×C5C2×#55511yescharacteristic
625D5—44no—
626D5—82no—
627C23—54no—
628C23—108no—
629C23—108no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—108no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—204no—
645C23—204no—
646C23—204no—
647C23—204no—
648C23—204no—
649C23—204no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23#414412yes—
656C23#414412yes—
657C23C2×#71312yes—
658C23C2×#71312yes—
659C23D5×#4112yes—
660C23D5×#4112yes—
661C23D5×#4112yes—
662C23C24×D511yescharacteristic
663D4—2016no—
664C2×C4—28no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
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—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—54no—
691C2×C4—54no—
692C2×C4—108no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—108no—
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—2016no—
711C2×C4—204no—
712C2×C4—204no—
713C2×C4—204no—
714C2×C4—204no—
715C2×C4C2×#71314yes—
716C2×C4C2×#71314yes—
717C5C2×#253111yescharacteristic, complemented, Sylow
718C22—104no—
719C22—104no—
720C22—104no—
721C22—202no—
722C22—2016no—
723C22—202no—
724C22—202no—
725C22—202no—
726C22—202no—
727C22—202no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—408no—
734C22#6594914yes—
735C22#6597114yes—
736C22#6597114yes—
737C22#6599514yes—
738C22#6602514yes—
739C22#6602514yes—
740C22#6606814yes—
741C22C2×#414411yescharacteristic
742C22C2×#414411yescharacteristic
743C22C22×#71311yescharacteristic
744C22C22×#71311yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×D5×#4111yescharacteristic
747C22C2×D5×#4111yescharacteristic
748C4—24no—
749C4—24no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—104no—
756C4—104no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4—202no—
761C2—204no—
762C2—402no—
763C2#1060951318yesdirect product factor
764C2C2×#6594911yescharacteristic
765C2C2×#6597111yescharacteristic
766C2C2×#6597111yescharacteristic
767C2C2×#6599511yescharacteristic
768C2C2×#6602511yescharacteristic
769C2C2×#6602511yescharacteristic
770C2C2×#6606811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#398C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#398D5
hypocenterC5C2×#2531
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C2×C5×#398C2semidirect
2. C2×#65282C2semidirect
3. C2×#65276C2semidirect
5. C2×#65279C2semidirect
6. C2×#65279C2semidirect
7. C2×#65279C2semidirect
8. C2×#65279C2semidirect
9. C2×#65267C2semidirect
10. #10609513C2direct (N × H)
12. C2×#64963C2semidirect
14. C2×#64942C2semidirect
15. C2×#64955C2semidirect
16. C2×#64937C2semidirect
40. C5×#398C22semidirect
53. #65282C22semidirect
54. #65279C22semidirect
55. #65279C22semidirect
56. #65279C22semidirect
57. #65279C22semidirect
59. #65276C22semidirect
60. #65267C22semidirect
61. #64963C22semidirect
63. #64955C22semidirect
65. #64942C22semidirect
66. #64937C22semidirect
146. C2×#398D5semidirect
282. #398C2×D5semidirect
617. C2×C5#2531semidirect
717. C5C2×#2531semidirect
763. C2#10609513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3982
C2×#652822
C2×#652762
C2×#652772
C2×#652792
C2×#652672
#106095132
C2×#649542
C2×#649632
C2×#649612
C2×#649422
C2×#649552
C2×#649372
C2×#25315