Finite Group Databasebeta

← C2×#10606196 #12268288

Subgroups — C2×#10606196 #12268288

Order 1280.

2658 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#385C211yesmaximal, characteristic, complemented
2C2×#65502C211yesmaximal, characteristic
3C22×#3963C211yesmaximal, characteristic, complemented
4C2×#65282C211yesmaximal, characteristic, complemented
5C2×#65271C211yesmaximal, characteristic, complemented
6C2×#65279C211yesmaximal, characteristic, complemented
7C2×#65267C211yesmaximal, characteristic, complemented
8C2×#65247C211yesmaximal, characteristic
9C2×#65247C211yesmaximal, characteristic
10C2×#65231C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12#10606196C2116yesmaximal, direct product factor
13C2×#64964C211yesmaximal, characteristic, complemented
14C2×C5⋊#401C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64940C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×C4×Dic5C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C5×#385C2218yescomplemented
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39#65502C2218yes—
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2218yescomplemented
55#65282C2218yescomplemented
56#65279C2218yescomplemented
57#65271C2218yescomplemented
58#65267C2218yescomplemented
59#65247C2218yes—
60#65247C2218yes—
61#65231C2218yescomplemented
62C22⋊C4×Dic5C2218yescomplemented
63#64964C2218yescomplemented
64#64958C2218yescomplemented
65C5⋊#401C2218yescomplemented
66#64940C2218yescomplemented
67C2×#2510—51nomaximal, Sylow
68C25×C5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5—24no—
71C23×C4×C5—42no—
72C23×C4×C5—42no—
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2314yes—
80C22×C22⋊D5—24no—
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5C2314yes—
84C23×Dic5—24no—
85C23×Dic5—24no—
86C23×Dic5—24no—
87C23×Dic5—24no—
88C23×Dic5—42no—
89C23×Dic5—42no—
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2314yes—
96C23×Dic5C2314yes—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C2×C5×C4⋊C4—42no—
100C2×C5×C4⋊C4—42no—
101C2×C5×C4⋊C4C2314yes—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—24no—
105C2×C5×C22⋊C4C2314yes—
106C2×C5×C22⋊C4C2314yes—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5C2314yes—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—42no—
112C2×#685—42no—
113C2×#685—42no—
114C2×#685—42no—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#683—24no—
122C2×#683—42no—
123C2×#683C2314yes—
124C2×#683C2314yes—
125C2×C4×Dic5—24no—
126C2×C4×Dic5—42no—
127C2×C4×Dic5C2314yes—
128C2×C4×Dic5C2314yes—
129C5×#95C2314yes—
130C5×#95C2314yes—
131#3963C2314yes—
132#3963C2314yes—
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#2510—516no—
146C2×#401—51no—
147C2×#400—51no—
148C2×#397—51no—
149C2×#397—51no—
150C2×#388—51no—
151C2×#388—51no—
152C2×#387—51no—
153C2×#386—51no—
154C2×#386—51no—
155C2×#386—51no—
156C2×#385D511yescharacteristic, complemented
157C2×#383—51no—
158C2×#380—51no—
159C2×C4×C22⋊C4—51no—
160C22×#95—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5#4114yes—
166C24×C5#4114yes—
167C24×C5#4114yes—
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—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—28no—
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—44no—
198C22×C4×C5—44no—
199C22×C4×C5—416no—
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—28no—
208C2×C22⋊D5—28no—
209C2×C22⋊D5—416no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—28no—
217C22×Dic5—28no—
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—22no—
231C22×Dic5—28no—
232C22×Dic5—28no—
233C22×Dic5—44no—
234C22×Dic5—44no—
235C22×Dic5—416no—
236C22×Dic5—416no—
237C22×Dic5#4114yes—
238C22×Dic5#4114yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C5×C4⋊C4—44no—
247C5×C4⋊C4—44no—
248C5×C22⋊C4—28no—
249C5×C22⋊C4—28no—
250C22⋊Dic5—28no—
251#685—28no—
252#685—28no—
253#685—44no—
254#685—44no—
255#685—44no—
256#685—44no—
257#683—28no—
258#683—44no—
259C4×Dic5—28no—
260C4×Dic5—44no—
261C23×D4—51no—
262C24×C4—51no—
263C24×C4—51no—
264C24×C4C2×D511yescharacteristic
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4C2×D511yescharacteristic
268C22×C4⋊C4C2×D511yescharacteristic
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×C42—51no—
279C22×C42—51no—
280#401—58no—
281#400—58no—
282#397—58no—
283#397—58no—
284#388—58no—
285#388—58no—
286#387—58no—
287#386—58no—
288#386—58no—
289#386—58no—
290#385C2×D518yescomplemented
291#383—58no—
292#380—58no—
293C4×C22⋊C4—58no—
294C2×#95—51no—
295C2×#95—51no—
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—58no—
306C2×#95—51no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95C2×D511yescharacteristic
310C2×#95C2×D511yescharacteristic
311C23×C5—28no—
312C23×C5—28no—
313C23×C5—28no—
314C23×C5—28no—
315C23×C5—28no—
316C23×C5—28no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5#126116yes—
322C23×C5C2×#4114yes—
323C23×C5C2×#4112yes—
324C23×C5C2×#4114yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4114yes—
327C23×C5C2×#4112yes—
328C23×C5C2×#4112yes—
329C23×C5C2×#4112yes—
330C23×C5H(5,𝔽2)12yes—
331C23×C5H(5,𝔽2)12yes—
332C23×C5C2511yescharacteristic
333C22×D5—22no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C22×D5—44no—
345C22×D5—44no—
346C22×D5—44no—
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—416no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5—44no—
369C2×C4×C5—44no—
370C2×C4×C5—44no—
371C2×C4×C5—44no—
372C22⋊D5—416no—
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—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—416no—
395C2×Dic5—416no—
396C2×Dic5—44no—
397C2×Dic5—44no—
398C2×Dic5—44no—
399C2×Dic5—44no—
400C2×Dic5—44no—
401C2×Dic5C2×#4114yes—
402C2×Dic5C2×#4114yes—
403C25—51no—
404C25C22×D511yescharacteristic
405C22×D4—54no—
406C22×D4—104no—
407C22×D4—104no—
408C22×D4—104no—
409C23×C4—24no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—54no—
420C23×C4—54no—
421C23×C4—104no—
422C23×C4—104no—
423C23×C4—104no—
424C23×C4—104no—
425C23×C4—202no—
426C23×C4—202no—
427C23×C4C22×D511yescharacteristic
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D514yes—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—104no—
439C2×C4⋊C4—202no—
440C2×C4⋊C4C22×D514yes—
441C2×C4⋊C4C22×D514yes—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
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—54no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—104no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C22⋊C4—202no—
457C2×C22⋊C4—202no—
458C2×C22⋊C4C22×D514yes—
459C2×C22⋊C4C22×D514yes—
460C2×C42—54no—
461C2×C42—54no—
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#95—54no—
474#95—54no—
475#95—54no—
476#95—54no—
477#95—54no—
478#95C22×D514yes—
479#95C22×D514yes—
480C22×C5—24no—
481C22×C5—24no—
482C22×C5—24no—
483C22×C5—24no—
484C22×C5—24no—
485C22×C5—24no—
486C22×C5—232no—
487C22×C5C2×#12618yes—
488C22×C5C2×#12614yes—
489C22×C5#52914yes—
490C22×C5#53814yes—
491C22×C5#55114yes—
492C22×C5#55114yes—
493C22×C5#55314yes—
494C22×C5#55314yes—
495C22×C5C22×#4111yescharacteristic
496C22×C5C22×#4111yescharacteristic
497C22×C5C22×#4111yescharacteristic
498C22×C5C22×#4111yescharacteristic
499C22×C5C22×#4111yescharacteristic
500C22×C5C2×H(5,𝔽2)11yescharacteristic
501C22×C5C2×H(5,𝔽2)11yescharacteristic
502C2×D5—42no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C2×D5—42no—
509C2×D5—88no—
510C4×C5—42no—
511C4×C5—42no—
512C4×C5—42no—
513C4×C5—42no—
514C4×C5—42no—
515C4×C5—42no—
516Dic5—24no—
517Dic5—24no—
518Dic5—42no—
519Dic5—42no—
520Dic5—42no—
521Dic5—42no—
522Dic5—42no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—52no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24#70914yes—
536C24#71114yes—
537C24#71314yes—
538C24C23×D512yes—
539C24C23×D511yescharacteristic
540C2×D4—108no—
541C2×D4—108no—
542C2×D4—108no—
543C2×D4—2016no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—28no—
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—44no—
564C22×C4—44no—
565C22×C4—416no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—108no—
576C22×C4—108no—
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—108no—
590C22×C4—108no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—204no—
599C22×C4—204no—
600C22×C4—2016no—
601C22×C4—2016no—
602C22×C4C23×D512yes—
603C22×C4C23×D512yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—108no—
611C4⋊C4—204no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—108no—
615C22⋊C4—108no—
616C22⋊C4—108no—
617C22⋊C4—204no—
618C22⋊C4—204no—
619C22⋊C4—204no—
620C22⋊C4—204no—
621C42—108no—
622C42—204no—
623C2×C5—28no—
624C2×C5#251018yescomplemented
625C2×C5C22×#12611yescharacteristic
626C2×C5C2×#52911yescharacteristic
627C2×C5C2×#53811yescharacteristic
628C2×C5C2×#55111yescharacteristic
629C2×C5C2×#55111yescharacteristic
630C2×C5C2×#55311yescharacteristic
631C2×C5C2×#55311yescharacteristic
632D5—82no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—102no—
644C23—102no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—102no—
650C23—204no—
651C23—204no—
652C23—204no—
653C23—204no—
654C23—204no—
655C23—204no—
656C23—204no—
657C23#4044116yes—
658C23C2×#70914yes—
659C23C2×#70912yes—
660C23C2×#71114yes—
661C23C2×#71112yes—
662C23#414412yes—
663C23#414412yes—
664C23C2×#71314yes—
665C23C2×#71312yes—
666C23D5×#4112yes—
667C23D5×#4112yes—
668C23C24×D511yescharacteristic
669D4—2016no—
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—22no—
687C2×C4—22no—
688C2×C4—416no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—54no—
696C2×C4—54no—
697C2×C4—108no—
698C2×C4—108no—
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—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—2016no—
719C2×C4—2016no—
720C2×C4—204no—
721C2×C4—204no—
722C2×C4—204no—
723C2×C4—204no—
724C2×C4—204no—
725C5C2×#251011yescharacteristic, complemented, Sylow
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—232no—
732C22—24no—
733C22—202no—
734C22—202no—
735C22—202no—
736C22—202no—
737C22—202no—
738C22—202no—
739C22—202no—
740C22—408no—
741C22C2×#404418yes—
742C22C2×#404414yes—
743C22#6587414yes—
744C22#6587414yes—
745C22#6592714yes—
746C22#6597114yes—
747C22#6597114yes—
748C22#6598314yes—
749C22C22×#70911yescharacteristic
750C22C22×#71111yescharacteristic
751C22C2×#414411yescharacteristic
752C22C2×#414411yescharacteristic
753C22C22×#71311yescharacteristic
754C22C2×D5×#4111yescharacteristic
755C22C2×D5×#4111yescharacteristic
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—104no—
763C4—104no—
764C4—202no—
765C4—202no—
766C4—202no—
767C4—202no—
768C4—202no—
769C2—28no—
770C2—402no—
771C2#1060619618yesdirect product factor
772C2C22×#404411yescharacteristic
773C2C2×#6587411yescharacteristic
774C2C2×#6587411yescharacteristic
775C2C2×#6592711yescharacteristic
776C2C2×#6597111yescharacteristic
777C2C2×#6597111yescharacteristic
778C2C2×#6598311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#385C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#385D5
hypocenterC5C2×#2510
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×C5×#385C2semidirect
3. C22×#3963C2semidirect
4. C2×#65282C2semidirect
5. C2×#65271C2semidirect
6. C2×#65279C2semidirect
7. C2×#65267C2semidirect
10. C2×#65231C2semidirect
11. C2×C22⋊C4×Dic5C2semidirect
12. #10606196C2direct (N × H)
13. C2×#64964C2semidirect
14. C2×C5⋊#401C2semidirect
15. C2×#64958C2semidirect
16. C2×#64940C2semidirect
36. C5×#385C22semidirect
54. C2×#3963C22semidirect
55. #65282C22semidirect
56. #65279C22semidirect
57. #65271C22semidirect
58. #65267C22semidirect
61. #65231C22semidirect
62. C22⋊C4×Dic5C22semidirect
63. #64964C22semidirect
64. #64958C22semidirect
65. C5⋊#401C22semidirect
66. #64940C22semidirect
156. C2×#385D5semidirect
290. #385C2×D5semidirect
624. C2×C5#2510semidirect
725. C5C2×#2510semidirect
771. C2#10606196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3852
C2×#655022
C22×#39632
C2×#652822
C2×#652712
C2×#652792
C2×#652672
C2×#652472
C2×#652312
C2×C22⋊C4×Dic52
#106061962
C2×#649642
C2×C5⋊#4012
C2×#649582
C2×#649402
C2×#25105