Finite Group Databasebeta

← C2×#10606764 #12268724

Subgroups — C2×#10606764 #12268724

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×#387C211yesmaximal, characteristic, complemented
2C2×#65281C211yesmaximal, characteristic, complemented
3C2×#65279C211yesmaximal, characteristic, complemented
4C2×#65279C211yesmaximal, characteristic, complemented
5C2×#65279C211yesmaximal, characteristic, complemented
6C2×#65228C211yesmaximal, characteristic
7C2×C4×#683C211yesmaximal, characteristic, complemented
8#10606764C2116yesmaximal, direct product factor
9C2×#64964C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic
11C2×#64953C211yesmaximal, characteristic, complemented
12C2×#64948C211yesmaximal, characteristic, complemented
13C2×#64961C211yesmaximal, characteristic
14C2×#64958C211yesmaximal, characteristic, complemented
15C2×#64942C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×#685C2211yescharacteristic
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×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C5×#387C2218yescomplemented
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#65281C2218yescomplemented
54#65279C2218yescomplemented
55#65279C2218yescomplemented
56#65279C2218yescomplemented
57#65228C2218yes—
58C4×#683C2218yescomplemented
59#64964C2218yescomplemented
60#64961C2218yes—
61#64958C2218yescomplemented
62#64955C2218yescomplemented
63#64954C2218yes—
64#64953C2218yescomplemented
65#64948C2218yescomplemented
66#64942C2218yescomplemented
67C2×#2516—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—24no—
92C2×C5×C4⋊C4—42no—
93C2×C5×C4⋊C4C2314yes—
94C2×C5×C4⋊C4C2314yes—
95C2×C42×C5—42no—
96C2×C42×C5C2314yes—
97C2×#685—24no—
98C2×#685—24no—
99C2×#685—24no—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—42no—
104C2×#685—42no—
105C2×#685—42no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685C2314yes—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5C2314yes—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—42no—
124C2×#683C2314yes—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×C4×Dic5—24no—
128C2×C4×Dic5—42no—
129C2×C4×Dic5—42no—
130C2×C4×Dic5C2314yes—
131C2×C4×Dic5C2314yes—
132C2×C4×Dic5C2314yes—
133C5×#95C2314yes—
134C5×#95C2314yes—
135C5×#95C2314yes—
136C5×#95C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2516—516no—
146C2×#400—51no—
147C2×#399—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×#387D511yescharacteristic, complemented
157C2×#386—51no—
158C2×#381—51no—
159C2×C4×C4⋊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—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—28no—
239C5×C4⋊C4—44no—
240C42×C5—44no—
241#685—28no—
242#685—28no—
243#685—28no—
244#685—28no—
245#685—28no—
246#685—28no—
247#685—44no—
248#685—44no—
249#685—44no—
250#685—44no—
251#685—44no—
252C4⋊Dic5—28no—
253#683—28no—
254#683—28no—
255#683—44no—
256C4×Dic5—28no—
257C4×Dic5—44no—
258C4×Dic5—44no—
259C23×D4—51no—
260C24×C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
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×C42C2×D511yescharacteristic
282#400—58no—
283#399—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#387C2×D518yescomplemented
293#386—58no—
294#381—58no—
295C4×C4⋊C4—58no—
296C4×C22⋊C4—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×#95C2×D511yescharacteristic
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—24no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4—202no—
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—42no—
457C2×C42—54no—
458C2×C42—54no—
459C2×C42—54no—
460C2×C42—104no—
461C2×C42—202no—
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#95C22×D514yes—
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#55914yes—
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—108no—
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—102no—
585C22×C4—204no—
586C22×C4—2016no—
587C22×C4#70914yes—
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—28no—
597C4⋊C4—44no—
598C4⋊C4—108no—
599C4⋊C4—108no—
600C4⋊C4—108no—
601C4⋊C4—204no—
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—44no—
614C42—108no—
615C42—204no—
616C42—204no—
617C2×C5#251618yescomplemented
618C2×C5C2×#52911yescharacteristic
619C2×C5C2×#52911yescharacteristic
620C2×C5C2×#54011yescharacteristic
621C2×C5C2×#55111yescharacteristic
622C2×C5C2×#55111yescharacteristic
623C2×C5C2×#55311yescharacteristic
624C2×C5C2×#55911yescharacteristic
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—
655C23C2×#70912yes—
656C23#414412yes—
657C23C2×#71312yes—
658C23D5×#4112yes—
659C23D5×#4112yes—
660C23D5×#4112yes—
661C23#414912yes—
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—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—108no—
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×#70914yes—
716C2×C4C2×#71314yes—
717C5C2×#251611yescharacteristic, complemented, Sylow
718C22—104no—
719C22—104no—
720C22—104no—
721C22—202no—
722C22—202no—
723C22—202no—
724C22—202no—
725C22—2016no—
726C22—202no—
727C22—202no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—408no—
734C22#6586214yes—
735C22#6587414yes—
736C22#6591914yes—
737C22#6597114yes—
738C22#6599714yes—
739C22#6602514yes—
740C22#6603914yes—
741C22C22×#70911yescharacteristic
742C22C2×#414411yescharacteristic
743C22C22×#71311yescharacteristic
744C22C2×D5×#4111yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×D5×#4111yescharacteristic
747C22C2×#414911yescharacteristic
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#1060676418yesdirect product factor
764C2C2×#6586211yescharacteristic
765C2C2×#6587411yescharacteristic
766C2C2×#6591911yescharacteristic
767C2C2×#6597111yescharacteristic
768C2C2×#6599711yescharacteristic
769C2C2×#6602511yescharacteristic
770C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2516
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×#65281C2semidirect
3. C2×#65279C2semidirect
4. C2×#65279C2semidirect
5. C2×#65279C2semidirect
7. C2×C4×#683C2semidirect
8. #10606764C2direct (N × H)
9. C2×#64964C2semidirect
11. C2×#64953C2semidirect
12. C2×#64948C2semidirect
14. C2×#64958C2semidirect
15. C2×#64942C2semidirect
16. C2×#64955C2semidirect
40. C5×#387C22semidirect
53. #65281C22semidirect
54. #65279C22semidirect
55. #65279C22semidirect
56. #65279C22semidirect
58. C4×#683C22semidirect
59. #64964C22semidirect
61. #64958C22semidirect
62. #64955C22semidirect
64. #64953C22semidirect
65. #64948C22semidirect
66. #64942C22semidirect
156. C2×#387D5semidirect
292. #387C2×D5semidirect
617. C2×C5#2516semidirect
717. C5C2×#2516semidirect
763. C2#10606764direct (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×#652812
C2×#652792
C2×#652282
C2×C4×#6832
#106067642
C2×#649642
C2×#649542
C2×#649532
C2×#649482
C2×#649612
C2×#649582
C2×#649422
C2×#649552
C2×#25165