Finite Group Databasebeta

← C2×#10608586 #12305684

Subgroups — C2×#10608586 #12305684

Order 1280.

2174 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×#393C211yesmaximal, characteristic, complemented
2C2×#65520C211yesmaximal, characteristic, complemented
3C2×#65518C211yesmaximal, characteristic, complemented
4C2×#65248C211yesmaximal, characteristic
5C2×#65241C211yesmaximal, characteristic, complemented
6C2×#65241C211yesmaximal, characteristic, complemented
7C2×#65237C211yesmaximal, characteristic, complemented
8C2×#65250C211yesmaximal, characteristic
9C2×#65246C211yesmaximal, characteristic
10#10608586C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64965C211yesmaximal, characteristic, complemented
13C2×#64946C211yesmaximal, characteristic, complemented
14C2×#64963C211yesmaximal, characteristic, complemented
15C2×#64944C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C22×C5×C22⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C5×#393C2218yescomplemented
41C2×C5×#95C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44#65520C2218yescomplemented
45#65518C2218yescomplemented
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55#65250C2218yes—
56#65248C2218yes—
57#65246C2218yes—
58#65241C2218yescomplemented
59#65241C2218yescomplemented
60#65237C2218yescomplemented
61#64965C2218yescomplemented
62#64964C2218yescomplemented
63#64963C2218yescomplemented
64#64946C2218yescomplemented
65#64944C2218yescomplemented
66#64942C2218yescomplemented
67C2×#2830—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C22×C5×Q8—42no—
71C22×C5×Q8—42no—
72C22×C5×Q8—42no—
73C22×C5×Q8C2314yes—
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—24no—
81C22×C22⋊D5—42no—
82C22×C22⋊D5—42no—
83C22×C22⋊D5C2314yes—
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C2×C5×C22⋊C4—42no—
92C2×C5×C22⋊C4—42no—
93C2×C5×C22⋊C4—42no—
94C2×C5×C22⋊C4C2314yes—
95C2×C5×C22⋊C4C2314yes—
96C2×C5×C22⋊C4C2314yes—
97C2×C22⋊Dic5—42no—
98C2×C22⋊Dic5—42no—
99C2×C22⋊Dic5—42no—
100C2×C22⋊Dic5C2314yes—
101C2×C22⋊Dic5C2314yes—
102C2×C22⋊Dic5C2314yes—
103C2×#685—42no—
104C2×#685—42no—
105C2×#685—42no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685—42no—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×C4⋊Dic5—24no—
116C2×C4⋊Dic5—42no—
117C2×C4⋊Dic5C2314yes—
118C2×C4⋊Dic5C2314yes—
119C2×#683—24no—
120C2×#683—42no—
121C2×#683—42no—
122C2×#683—42no—
123C2×#683—42no—
124C2×#683—42no—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×C4×Dic5—42no—
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#2830—516no—
146C2×#398—51no—
147C2×#397—51no—
148C2×#397—51no—
149C2×#397—51no—
150C2×#397—51no—
151C2×#396—51no—
152C2×#396—51no—
153C2×#395—51no—
154C2×#394—51no—
155C2×#394—51no—
156C2×#393—51no—
157C2×#393D511yescharacteristic, complemented
158C2×#390—51no—
159C2×#387—51no—
160C2×#387—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—22no—
177C23×D5C2412yes—
178C2×C5×Q8—44no—
179C2×C5×Q8—44no—
180C2×C5×Q8—44no—
181C2×C5×Q8—416no—
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—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C2×C22⋊D5—28no—
207C2×C22⋊D5—44no—
208C2×C22⋊D5—44no—
209C2×C22⋊D5—416no—
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—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5#4114yes—
231C22×Dic5C2412yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C5×C22⋊C4—44no—
239C5×C22⋊C4—44no—
240C5×C22⋊C4—44no—
241C22⋊Dic5—44no—
242C22⋊Dic5—44no—
243C22⋊Dic5—44no—
244#685—44no—
245#685—44no—
246#685—44no—
247#685—44no—
248#685—44no—
249#685—44no—
250C4⋊Dic5—28no—
251C4⋊Dic5—44no—
252#683—28no—
253#683—44no—
254#683—44no—
255#683—44no—
256#683—44no—
257#683—44no—
258C4×Dic5—44no—
259C23×Q8C2×D511yescharacteristic
260C23×D4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4—51no—
268C22×C4⋊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×C22⋊C4C2×D511yescharacteristic
279C22×C22⋊C4C2×D511yescharacteristic
280C22×C22⋊C4C2×D511yescharacteristic
281C22×C42—51no—
282#398—58no—
283#397—58no—
284#397—58no—
285#397—58no—
286#397—58no—
287#396—58no—
288#396—58no—
289#395—58no—
290#394—58no—
291#394—58no—
292#393—58no—
293#393C2×D518yescomplemented
294#390—58no—
295#387—58no—
296#387—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×C5—22no—
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—22no—
316C23×C5—44no—
317C23×C5—44no—
318C23×C5—44no—
319C23×C5—44no—
320C23×C5—44no—
321C23×C5—44no—
322C23×C5—44no—
323C23×C5C2×#4112yes—
324C23×C5H(5,𝔽2)12yes—
325C23×C5H(5,𝔽2)12yes—
326C23×C5H(5,𝔽2)12yes—
327C23×C5H(5,𝔽2)12yes—
328C23×C52−1+412yes—
329C23×C52−1+412yes—
330C23×C5C2511yescharacteristic
331C22×D5—22no—
332C22×D5—22no—
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5—44no—
345C5×Q8—416no—
346C2×C4×C5—22no—
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×C5—44no—
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—
399C25—51no—
400C25C22×D511yescharacteristic
401C22×Q8—42no—
402C22×Q8—42no—
403C22×Q8—42no—
404C22×Q8C22×D514yes—
405C22×D4—54no—
406C22×D4—104no—
407C22×D4—202no—
408C22×D4—202no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C2×C4⋊C4—54no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—54no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—54no—
428C2×C4⋊C4—54no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4—104no—
432C2×C4⋊C4—202no—
433C2×C4⋊C4—202no—
434C2×C4⋊C4—202no—
435C2×C4⋊C4—202no—
436C2×C4⋊C4—202no—
437C2×C4⋊C4—202no—
438C2×C22⋊C4—42no—
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—54no—
450C2×C22⋊C4—202no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C22⋊C4—202no—
459C2×C22⋊C4C22×D514yes—
460C2×C22⋊C4C22×D514yes—
461C2×C22⋊C4C22×D514yes—
462C2×C42—54no—
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—42no—
477C22×C5—42no—
478C22×C5—42no—
479C22×C5—42no—
480C22×C5—42no—
481C22×C5—42no—
482C22×C5—42no—
483C22×C5—88no—
484C22×C5#53814yes—
485C22×C5#54214yes—
486C22×C5#54214yes—
487C22×C5#56014yes—
488C22×C5#56214yes—
489C22×C5#56214yes—
490C22×C5#56314yes—
491C22×C5C22×#4111yescharacteristic
492C22×C5C2×H(5,𝔽2)11yescharacteristic
493C22×C5C2×H(5,𝔽2)11yescharacteristic
494C22×C5C2×H(5,𝔽2)11yescharacteristic
495C22×C5C2×H(5,𝔽2)11yescharacteristic
496C22×C5C2×2−1+411yescharacteristic
497C22×C5C2×2−1+411yescharacteristic
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—42no—
507C4×C5—42no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—42no—
511C4×C5—42no—
512Dic5—24no—
513Dic5—42no—
514Dic5—42no—
515Dic5—42no—
516Dic5—42no—
517Dic5—42no—
518Dic5—42no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—52no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24C23×D512yes—
535C24C23×D511yescharacteristic
536C2×Q8—44no—
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—416no—
540C2×D4—108no—
541C2×D4—204no—
542C2×D4—204no—
543C2×D4—2016no—
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—22no—
562C22×C4—54no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—52no—
569C22×C4—52no—
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—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4C23×D512yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C4⋊C4—108no—
597C4⋊C4—108no—
598C4⋊C4—204no—
599C4⋊C4—204no—
600C4⋊C4—204no—
601C4⋊C4—204no—
602C4⋊C4—204no—
603C4⋊C4—204no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—204no—
608C22⋊C4—204no—
609C22⋊C4—204no—
610C22⋊C4—204no—
611C22⋊C4—204no—
612C22⋊C4—204no—
613C22⋊C4—204no—
614C22⋊C4—204no—
615C22⋊C4—204no—
616C42—204no—
617C2×C5—82no—
618C2×C5#283018yescomplemented
619C2×C5C2×#53811yescharacteristic
620C2×C5C2×#54211yescharacteristic
621C2×C5C2×#54211yescharacteristic
622C2×C5C2×#56011yescharacteristic
623C2×C5C2×#56211yescharacteristic
624C2×C5C2×#56211yescharacteristic
625C2×C5C2×#56311yescharacteristic
626D5—82no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—102no—
642C23—102no—
643C23—102no—
644C23—102no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—204no—
649C23—204no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23#414412yes—
656C23#414412yes—
657C23#414412yes—
658C23#414712yes—
659C23D5×#4112yes—
660C23#414912yes—
661C23#415012yes—
662C23C24×D511yescharacteristic
663Q8—416no—
664D4—2016no—
665C2×C4—22no—
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—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—54no—
690C2×C4—108no—
691C2×C4—102no—
692C2×C4—102no—
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—204no—
712C2×C4—204no—
713C2×C4—204no—
714C2×C4—204no—
715C2×C4—204no—
716C2×C4—204no—
717C5C2×#283011yescharacteristic, complemented, Sylow
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—88no—
726C22—202no—
727C22—202no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—408no—
734C22#6592914yes—
735C22#6597414yes—
736C22#6598014yes—
737C22#6598114yes—
738C22#6600314yes—
739C22#6601214yes—
740C22#6601814yes—
741C22C2×#414411yescharacteristic
742C22C2×#414411yescharacteristic
743C22C2×#414411yescharacteristic
744C22C2×#414711yescharacteristic
745C22C2×D5×#4111yescharacteristic
746C22C2×#414911yescharacteristic
747C22C2×#415011yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—104no—
755C4—202no—
756C4—202no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4—202no—
761C2—82no—
762C2—402no—
763C2#1060858618yesdirect product factor
764C2C2×#6592911yescharacteristic
765C2C2×#6597411yescharacteristic
766C2C2×#6598011yescharacteristic
767C2C2×#6598111yescharacteristic
768C2C2×#6600311yescharacteristic
769C2C2×#6601811yescharacteristic
770C2C2×#6601211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#393C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#393D5
hypocenterC5C2×#2830
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C2×C5×#393C2semidirect
2. C2×#65520C2semidirect
3. C2×#65518C2semidirect
5. C2×#65241C2semidirect
6. C2×#65241C2semidirect
7. C2×#65237C2semidirect
10. #10608586C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64965C2semidirect
13. C2×#64946C2semidirect
14. C2×#64963C2semidirect
15. C2×#64944C2semidirect
16. C2×#64942C2semidirect
40. C5×#393C22semidirect
44. #65520C22semidirect
45. #65518C22semidirect
58. #65241C22semidirect
59. #65241C22semidirect
60. #65237C22semidirect
61. #64965C22semidirect
62. #64964C22semidirect
63. #64963C22semidirect
64. #64946C22semidirect
65. #64944C22semidirect
66. #64942C22semidirect
157. C2×#393D5semidirect
293. #393C2×D5semidirect
618. C2×C5#2830semidirect
717. C5C2×#2830semidirect
763. C2#10608586direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3932
C2×#655202
C2×#655182
C2×#652482
C2×#652412
C2×#652372
C2×#652502
C2×#652462
#106085862
C2×#649642
C2×#649652
C2×#649462
C2×#649632
C2×#649442
C2×#649422
C2×#28305