Finite Group Databasebeta

← C2×#10607390 #12265789

Subgroups — C2×#10607390 #12265789

Order 1280.

2394 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×#388C211yesmaximal, characteristic, complemented
2C2×#65282C211yesmaximal, characteristic, complemented
3C2×#65273C211yesmaximal, characteristic, complemented
4C2×#65248C211yesmaximal, characteristic
5C2×#65248C211yesmaximal, characteristic
6C2×#65245C211yesmaximal, characteristic
7C2×#65242C211yesmaximal, characteristic, complemented
8C2×#65236C211yesmaximal, characteristic, complemented
9C2×#65234C211yesmaximal, characteristic, complemented
10C2×#65222C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10607390C2116yesmaximal, direct product factor
13C2×#64962C211yesmaximal, characteristic, complemented
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×C5⋊#401C211yesmaximal, characteristic, complemented
16C2×#64935C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C5×#388C2218yescomplemented
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65282C2218yescomplemented
54#65273C2218yescomplemented
55#65248C2218yes—
56#65248C2218yes—
57#65245C2218yes—
58#65242C2218yescomplemented
59#65236C2218yescomplemented
60#65234C2218yescomplemented
61C4×#685C2218yescomplemented
62#65222C2218yescomplemented
63#64962C2218yescomplemented
64#64957C2218yescomplemented
65C5⋊#401C2218yescomplemented
66#64935C2218yescomplemented
67C2×#2653—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C22×C22⋊D5—24no—
77C22×C22⋊D5—42no—
78C22×C22⋊D5—42no—
79C22×C22⋊D5C2314yes—
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C22×C4×D5—24no—
88C22×C4×D5—42no—
89C22×C4×D5—42no—
90C22×C4×D5C2314yes—
91C22×Dic10—24no—
92C22×Dic10—42no—
93C22×Dic10—42no—
94C22×Dic10C2314yes—
95C2×C5×C4⋊C4—42no—
96C2×C5×C4⋊C4C2314yes—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—42no—
99C2×C5×C22⋊C4—42no—
100C2×C5×C22⋊C4C2314yes—
101C2×C5×C22⋊C4C2314yes—
102C2×C5×C22⋊C4C2314yes—
103C2×C42×C5—42no—
104C2×C42×C5C2314yes—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—42no—
107C2×C22⋊Dic5—42no—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—42no—
115C2×#685—42no—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—42no—
122C2×C4⋊Dic5C2314yes—
123C2×#683—24no—
124C2×#683—42no—
125C2×#683—42no—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×C4×Dic5—42no—
130C2×C4×Dic5C2314yes—
131C5×#95C2314yes—
132C5×#95C2314yes—
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#2653—516no—
146C2×#401—51no—
147C2×#398—51no—
148C2×#397—51no—
149C2×#397—51no—
150C2×#394—51no—
151C2×#394—51no—
152C2×#393—51no—
153C2×#393—51no—
154C2×#391—51no—
155C2×#388—51no—
156C2×#388D511yescharacteristic, complemented
157C2×#387—51no—
158C2×#386—51no—
159C2×#385—51no—
160C2×C4×C22⋊C4—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5—22no—
168C24×C5C2412yes—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5#4114yes—
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#4114yes—
196C22×C4×C5C2412yes—
197C22×C4×C5C2412yes—
198C22×C4×C5C2412yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C2×C22⋊D5—28no—
203C2×C22⋊D5—44no—
204C2×C22⋊D5—44no—
205C2×C22⋊D5—416no—
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—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5#4114yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C2×C4×D5—28no—
235C2×C4×D5—44no—
236C2×C4×D5—44no—
237C2×C4×D5—416no—
238C2×Dic10—28no—
239C2×Dic10—44no—
240C2×Dic10—44no—
241C2×Dic10—416no—
242C5×C4⋊C4—44no—
243C5×C22⋊C4—28no—
244C5×C22⋊C4—44no—
245C5×C22⋊C4—44no—
246C42×C5—44no—
247C22⋊Dic5—28no—
248C22⋊Dic5—44no—
249C22⋊Dic5—44no—
250#685—28no—
251#685—28no—
252#685—28no—
253#685—44no—
254#685—44no—
255C4⋊Dic5—44no—
256#683—28no—
257#683—44no—
258#683—44no—
259C4×Dic5—44no—
260C23×Q8—51no—
261C23×D4—51no—
262C24×C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
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⋊C4C2×D511yescharacteristic
277C22×C22⋊C4C2×D511yescharacteristic
278C22×C22⋊C4C2×D511yescharacteristic
279C22×C42—51no—
280C22×C42C2×D511yescharacteristic
281#401—58no—
282#398—58no—
283#397—58no—
284#397—58no—
285#394—58no—
286#394—58no—
287#393—58no—
288#393—58no—
289#391—58no—
290#388—58no—
291#388C2×D518yescomplemented
292#387—58no—
293#386—58no—
294#385—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×#95—51no—
307C2×#95—51no—
308C2×#95C2×D511yescharacteristic
309C2×#95C2×D511yescharacteristic
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—22no—
317C23×C5—44no—
318C23×C5—44no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5—44no—
323C23×C5—44no—
324C23×C5C2×#4112yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5H(5,𝔽2)12yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C52−1+412yes—
331C23×C5C2511yescharacteristic
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—28no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5—44no—
345C22×D5C2×#4114yes—
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—44no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5C2×#4114yes—
370C22⋊D5—416no—
371C2×Dic5—28no—
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—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5C2×#4114yes—
399C4×D5—416no—
400Dic10—416no—
401C25—51no—
402C25C22×D511yescharacteristic
403C22×Q8—54no—
404C22×Q8—104no—
405C22×Q8—202no—
406C22×Q8—202no—
407C22×D4—54no—
408C22×D4—104no—
409C22×D4—202no—
410C22×D4—202no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—54no—
419C23×C4—104no—
420C23×C4—202no—
421C23×C4—202no—
422C23×C4C22×D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C2×C4⋊C4—42no—
429C2×C4⋊C4—54no—
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⋊C4—202no—
437C2×C4⋊C4C22×D514yes—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
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—54no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4C22×D514yes—
458C2×C22⋊C4C22×D514yes—
459C2×C22⋊C4C22×D514yes—
460C2×C42—42no—
461C2×C42—54no—
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#95—54no—
475#95—54no—
476#95C22×D514yes—
477#95C22×D514yes—
478C22×C5—42no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—88no—
486C22×C5#52914yes—
487C22×C5#53814yes—
488C22×C5#53814yes—
489C22×C5#53814yes—
490C22×C5#53914yes—
491C22×C5#54214yes—
492C22×C5#54214yes—
493C22×C5C22×#4111yescharacteristic
494C22×C5C22×#4111yescharacteristic
495C22×C5C22×#4111yescharacteristic
496C22×C5C2×H(5,𝔽2)11yescharacteristic
497C22×C5C2×H(5,𝔽2)11yescharacteristic
498C22×C5C2×H(5,𝔽2)11yescharacteristic
499C22×C5C2×2−1+411yescharacteristic
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—24no—
503C2×D5—416no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C4×C5—24no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514Dic5—24no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—54no—
529C24—52no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24C23×D512yes—
537C24C23×D511yescharacteristic
538C2×Q8—108no—
539C2×Q8—204no—
540C2×Q8—204no—
541C2×Q8—2016no—
542C2×D4—108no—
543C2×D4—204no—
544C2×D4—204no—
545C2×D4—2016no—
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—22no—
562C22×C4—22no—
563C22×C4—54no—
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—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—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—108no—
592C22×C4—204no—
593C22×C4—204no—
594C22×C4—2016no—
595C22×C4#70914yes—
596C22×C4C23×D512yes—
597C22×C4C23×D512yes—
598C22×C4C23×D512yes—
599C22×C4C23×D512yes—
600C22×C4C23×D512yes—
601C22×C4C23×D512yes—
602C4⋊C4—44no—
603C4⋊C4—108no—
604C4⋊C4—204no—
605C4⋊C4—204no—
606C4⋊C4—204no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—108no—
611C22⋊C4—108no—
612C22⋊C4—108no—
613C22⋊C4—108no—
614C22⋊C4—204no—
615C22⋊C4—204no—
616C22⋊C4—204no—
617C22⋊C4—204no—
618C42—44no—
619C42—204no—
620C2×C5—82no—
621C2×C5#265318yescomplemented
622C2×C5C2×#52911yescharacteristic
623C2×C5C2×#53811yescharacteristic
624C2×C5C2×#53811yescharacteristic
625C2×C5C2×#53811yescharacteristic
626C2×C5C2×#53911yescharacteristic
627C2×C5C2×#54211yescharacteristic
628C2×C5C2×#54211yescharacteristic
629D5—44no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—54no—
645C23—108no—
646C23—108no—
647C23—102no—
648C23—102no—
649C23—102no—
650C23—102no—
651C23—102no—
652C23—102no—
653C23—108no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23—204no—
658C23C2×#70912yes—
659C23#414412yes—
660C23#414412yes—
661C23D5×#4112yes—
662C23D5×#4112yes—
663C23#414912yes—
664C23#415012yes—
665C23C24×D511yescharacteristic
666Q8—2016no—
667D4—2016no—
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—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—54no—
692C2×C4—108no—
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—2016no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4—204no—
717C2×C4—204no—
718C2×C4—204no—
719C2×C4—204no—
720C2×C4C2×#70914yes—
721C5C2×#265311yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—88no—
730C22—104no—
731C22—104no—
732C22—104no—
733C22—2016no—
734C22—202no—
735C22—202no—
736C22—202no—
737C22—202no—
738C22#6586214yes—
739C22#6589414yes—
740C22#6589514yes—
741C22#6594714yes—
742C22#6599614yes—
743C22#6601214yes—
744C22#6604114yes—
745C22C22×#70911yescharacteristic
746C22C2×#414411yescharacteristic
747C22C2×#414411yescharacteristic
748C22C2×D5×#4111yescharacteristic
749C22C2×D5×#4111yescharacteristic
750C22C2×#414911yescharacteristic
751C22C2×#415011yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—104no—
759C4—202no—
760C4—202no—
761C4—202no—
762C4—202no—
763C4—202no—
764C4—202no—
765C2—82no—
766C2—204no—
767C2#1060739018yesdirect product factor
768C2C2×#6586211yescharacteristic
769C2C2×#6589411yescharacteristic
770C2C2×#6589511yescharacteristic
771C2C2×#6594711yescharacteristic
772C2C2×#6599611yescharacteristic
773C2C2×#6601211yescharacteristic
774C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2653
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C5×#388C2semidirect
2. C2×#65282C2semidirect
3. C2×#65273C2semidirect
7. C2×#65242C2semidirect
8. C2×#65236C2semidirect
9. C2×#65234C2semidirect
10. C2×#65222C2semidirect
11. C2×C4×#685C2semidirect
12. #10607390C2direct (N × H)
13. C2×#64962C2semidirect
14. C2×#64957C2semidirect
15. C2×C5⋊#401C2semidirect
16. C2×#64935C2semidirect
38. C5×#388C22semidirect
53. #65282C22semidirect
54. #65273C22semidirect
58. #65242C22semidirect
59. #65236C22semidirect
60. #65234C22semidirect
61. C4×#685C22semidirect
62. #65222C22semidirect
63. #64962C22semidirect
64. #64957C22semidirect
65. C5⋊#401C22semidirect
66. #64935C22semidirect
156. C2×#388D5semidirect
291. #388C2×D5semidirect
621. C2×C5#2653semidirect
721. C5C2×#2653semidirect
767. C2#10607390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3882
C2×#652822
C2×#652732
C2×#652482
C2×#652452
C2×#652422
C2×#652362
C2×#652342
C2×#652222
C2×C4×#6852
#106073902
C2×#649622
C2×#649572
C2×C5⋊#4012
C2×#649352
C2×#26535